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We introduce a solvable model of a measurement-induced phase transition (MIPT) in a deterministic but chaotic dynamical system with a positive Lyapunov exponent. In this setup, an observer only has a probabilistic description of the system but mitigates chaos-induced uncertainty through repeated measurements. Using a minimal representation via a branching tree, we map this problem to the directed polymer (DP) model on the Cayley tree, although in a regime dominated by rare events. By studying the Shannon entropy of the probability distribution estimated by the observer, we demonstrate a phase transition distinguishing a chaotic phase with reduced Lyapunov exponent from a strong-measurement phase where uncertainty remains bounded. Remarkably, the location of the MIPT transition coincides with the freezing transition of the DP, although the critical properties differ. We provide an exact universal scaling function describing entropy growth in the critical regime. Numerical simulations confirm our theoretical predictions, highlighting a simple yet powerful framework to explore measurement-induced transitions in classical chaotic systems., Comment: 14 pages, 5 figures

We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-N entanglement, with a proportionality factor dependent on the strength of the unitary coupling., Comment: 40 pages, 5 figures

The discovery of pulsations in (at least) six ultraluminous X-ray sources (ULXs) has shown that neutron stars can accrete at (highly) super-Eddington rates, challenging the standard accretion theories. M51 ULX-7, with a spin signal of $P\simeq2.8$ s, is the pulsating ULX (PULX) with the shortest known orbital period ($P_\mathrm{orb}\simeq2$ d) and has been observed multiple times by XMM-Newton, Chandra, and NuSTAR. We report on the timing and spectral analyses of three XMM-Newton observations of M51 ULX-7 performed between the end of 2021 and the beginning of 2022, together with a timing re-analysis of XMM-Newton, Chandra, and NuSTAR archival observations. We investigated the spin signal by applying accelerated search techniques and studied the power spectrum through the fast Fourier transform, looking for (a)periodic variability in the source flux. We analysed the energy spectra of the 2021-2022 observations and compared them to the older ones. We report the discovery of a recurrent, significant ($>$3$\sigma$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$\sigma$ upper limit on the pulsed fraction of $\lesssim10\%$ for the single observation. The complex is significantly detected also in five Chandra observations performed in 2012. M51 ULX-7 represents the second PULX for which we have a significant detection of mHz-QPOs at super-Eddington luminosities. These findings suggest that one should avoid using the observed QPO frequency to infer the mass of the accretor in a ULX. The absence of spin pulsations when the broad complex is detected suggests that the mechanism responsible for the aperiodic modulation also dampens the spin signal's pulsed fraction. If true, this represents an additional obstacle in the detection of new PULXs, suggesting an even larger occurrence of PULXs among ULXs., Comment: 14 pages (12 main text + Appendix), 5 figures. Accepted for publication on A&A

The essence of the Mpemba effect is that non-equilibrium systems may relax faster the further they are from their equilibrium configuration. In the quantum realm, this phenomenon arises in the dynamics of closed systems, where it is witnessed by fundamental features such as symmetry and entanglement. Here, we study the quantum Mpemba effect in charge-preserving random circuits on qudits combining extensive numerical simulations and analytical arguments. We show that the more asymmetric certain classes of initial states (tilted ferromagnets) are, the faster they restore symmetry and reach the grand-canonical ensemble. Conversely, other classes of states (tilted antiferromagnets) do not show the Mpemba effect. We provide a simple and general mechanism underlying the effect, based on the spreading of nonconserved operators in terms of conserved densities. Our analysis is based on minimal principles -- locality, unitarity, and symmetry. Consequently, our results represent a significant advancement in clarifying the emergence of Mpemba physics in chaotic systems., Comment: 5+4+7 pages, comments are welcome!

We report on the orbit of the binary system powering the most extreme ultraluminous X-ray pulsar known to date: NGC 5907 ULX-1 (hereafter ULX1). ULX1 has been the target of a substantial multi-instrument campaign, mainly in the X-ray band, but no clear counterparts are known in other bands. Although ULX1 is highly variable and pulsations can be transient (regardless of the source flux), the timing data collected so far allow us to investigate the orbit of this system. We find an orbital period $P_{orb}=5.7^{+0.1}_{-0.6}\text{ d}$ and a projected semi-axis $A_1 =3.1^{+0.8}_{-0.9}\text{ lts}$. The most likely ephemeris is: $P_{orb}=5.6585(6)\text{ d}$, $A_1 = 3.1(4)\text{ lts}$, and the epoch of ascending nodes passage is: $T_{asc} = 57751.37(5)\text{ MJD}$. However, there are 6 similar solutions, acceptable within $3\,\sigma$. We find further indications that ULX1 is a high-mass X-ray binary. This implies that we are observing its orbit face-on, with an inclination $<5\text{ deg}$., Comment: 11 pages, 2 tables, 6 figures

We study the preparation of a quantum state using a circuit of depth $t$ from a factorized state of $N$ sites. We argue that in the appropriate scaling limit of large $t$ and $N$, the overlap between states evolved under generic many-body chaotic dynamics belongs to a family of universal distribution that generalizes the celebrated Porter-Thomas distribution. This is a consequence of a mapping in the space of replicas to a model of dilute domain walls. Our result provides a rare example in which analysis at an arbitrary number of replicas is possible, giving rise to the complete overlap distribution. Our general picture is derived and corroborated by the exact solution of the random phase model and of an emergent random matrix model given by the Ginibre ensemble. Finally, numerical simulations of two distinct random circuits show excellent agreement, thereby demonstrating universality., Comment: 15 pages, 6 figures

The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the $k$-th moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension $q$, we find that all moments converge simultaneously with a time scaling linearly in the size of region $A$, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite $q$ on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times $t_k = O(\log k)$. Our results are supported with numerical simulations performed at $q=2$., Comment: 25 pages, 7 figures. Accepted version for the special issue of Journal of Physics A: Mathematical and Theoretical on Quantum-Circuit Models for Many-Body Physics Out of Equilibrium

We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at every time from the gaussian unitary ensemble (GUE). Due to invariance by unitary transformations, the dynamics of the eigenvalues $\{\lambda_\alpha\}_{\alpha=1}^n$ of the density matrix can be decoupled from that of the eigenvectors. Thus, stochastic equations are derived that exactly describe the dynamics of $\lambda$'s. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large sizes the distribution of $\lambda$'s is described by an inverse Marchenko Pastur distribution. In the case of perfect measurements instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of $\lambda$'s at each time $t$ and for each size $n$. Two relevant regimes emerge: at small times $t\Gamma= O(1)$, the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the limit of $n\to\infty$. In that case, all moments of the density matrix become self-averaging and it is possible to characterize the entanglement spectrum exactly. In the limit of large times $t \Gamma = O(n)$ one enters instead a regime in which the eigenvalues are exponentially separated $\log(\lambda_\alpha/\lambda_\beta) = O(\Gamma t/n)$, but fluctuations $\sim O(\sqrt{\Gamma t/n})$ play an essential role. We are still able to characterize the asymptotic behaviors of entanglement entropy in this regime., Comment: 29 pages, 3 figures

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random matrices. Each kind of process is associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification, and that (i) and (ii) represent distinct ``universality classes'' with distinct scaling functions. Using the replica trick, these universality classes correspond to one-dimensional effective statistical mechanics models for a gas of ``kinks'', representing domain walls between elements of the permutation group. (This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks.) These results apply to long-time purification in spatially local monitored circuit models on the entangled side of the measurement phase transition., Comment: 22 pages, 13 figures, many improvements for clarity in v2, inc extended introductory text, new figures and one more technical appendix

We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, we prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows us to obtain analytical predictions for simple local observables. We demonstrate the validity of our theory by comparison with Monte Carlo simulations, displaying excellent agreement with the latter for different choices of observables., Comment: 25 pages, 6 figures; typos corrected, references 19,28 added, Fig. 5 added,equation 15 added, appendices A and C added

We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random direction. We make use of the replica trick to account for the Born's rule weighting of the measurement outcomes in the study of purification and other observables, with an exact description in the large-$N$ limit. We find that the nature of the phase transition strongly depends on the number $n$ of replicas used in the calculation, with the appearance of non-perturbative logarithmic corrections that destroy the disentangled/purifying phase in the relevant $n \rightarrow 1$ replica limit. Specifically, we observe that the purification time of a mixed state in the weak measurement phase is always exponentially long in the system size for arbitrary strong measurement rates., Comment: 7+16 pages, 3+4 figures

We consider the Brownian SYK, i.e. a system of $N$ Majorana (Dirac) fermions with a white-noise $q$-body interaction term. We focus on the dynamics of the Frame potentials, a measure of the scrambling and chaos, given by the moments of the overlap between two independent realisations of the model. By means of a Keldysh path-integral formalism, we compute its early and late-time value. We show that, for $q>2$, the late time path integral saddle point correctly reproduces the saturation to the value of the Haar frame potential. On the contrary, for $q=2$, the model is quadratic and consistently we observe saturation to the Haar value in the restricted space of Gaussian states (Gaussian Haar). The latter is characterised by larger system size corrections that we correctly capture by counting the Goldstone modes of the Keldysh saddle point. Finally, in the case of Dirac fermions, we highlight and resolve the role of the global $U(1)$ symmetry., Comment: major revision, U(1) symmetry discussed and implemented in the complex SYK

We investigate the crucial role played by a global symmetry in the purification timescales and the phase transitions of monitored free fermionic systems separating a mixed and a pure phase. Concretely, we study Majorana and Dirac circuits with $\mathbb{Z}_2$ and U(1) symmetries, respectively. In the first case, we demonstrate the mixed phase of $L$ sites has a purification timescale that scales as $\tau_P\sim L \ln L $. At $1\ll t\ll \tau_P$ the system attains a finite residual entropy, that we use to unveil the critical properties of the purification transition. In contrast, free fermions with U(1) manifest a sublinear purification timescale at any measurement rate and an apparent Berezinskii-Kosterlitz-Thouless criticality. We find the mixed phase is characterized by $\tau_P\sim L^{\alpha(p)}$, with a continuously varying exponent $\alpha(p)<1$., Comment: 7 pgase, 3 figures, 3 pages of supplementary material

Time-domain analysis of an archival XMM-Newton observation unveiled a very unusual variability pattern in the soft X-ray emission of PSR J1311-3430, a black widow millisecond pulsar in a tight binary (P_B=93.8 min) with a very low-mass (M~0.01 Msun) He companion star, known to show flaring emission in the optical and in the X-rays. A series of six pulses with a regular recurrence time of ~124 min is apparent in the 0.2-10 keV light curve of the system, also featuring an initial, bright flare and a quiescent phase lasting several hours. The X-ray spectrum does not change when the pulses are seen and is consistent with a power law with photon index Gamma~1.6, also describing the quiescent emission. The peak luminosity of the pulses is of several 10^32 erg/s. Simultaneous observations in the U band with the Optical Monitor onboard XMM and in the g' band from the Las Cumbres Observatory do not show any apparent counterpart of the pulses and only display the well-known orbital modulation of the system. We consider different hypotheses to explain the recurrent pulses: we investigate their possible analogy with other phenomena already observed in this pulsar and in similar systems and we also study possible explanations related to the interaction of the energetic pulsar wind with intrabinary material, but we found none of these pictures to be convincing. We identify simultaneous X-ray observations and optical spectroscopy as a possible way to constrain the nature of the phenomenon., Comment: Accepted for publication in Astronomy & Astrophysics as a Letter

We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by $M$ random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, $m=M/(2N_F)$, we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for $m=1/2$ and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below $m=1/2$, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling., Comment: 41 pages, 9 figures. v2: minor corrections, as published

Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we consider a tree-like porous structure for which the problem of the flow can be resolved exactly thanks to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the non-linear behavior of the flow and expresses its full pressure-dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations., Comment: 5 pages,3 figures + 1 Supplementary material

In non-interacting isolated quantum systems out of equilibrium, local subsystems typically relax to non-thermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a Generalized Gibbs Ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study in particular the $k$-moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures., Comment: 13 pages, 4 figures; v2: minor revision

We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially-extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction. Starting with translational invariant models, which can be associated with dual transfer matrices with complex-valued spectra, we show that the linear ramp of the spectral form factor necessitates that the dual spectra have non-trivial correlations, which in fact fall under the universality class of the Ginibre ensemble, demonstrated by computing the level spacing distribution and the dissipative spectral form factor. As a result of this connection, the exact spectral form factor for the Ginibre ensemble can be used to universally describe the spectral form factor for translational invariant many-body quantum chaotic systems in the scaling limit where $t$ and $L$ are large, while the ratio between $L$ and $L_{\mathrm{Th}}$, the many-body Thouless length is fixed. With appropriate variations of Ginibre models, we analytically demonstrate that our claim generalizes to models without translational invariance as well. The emergence of the Ginibre ensemble is a genuine consequence of the strongly interacting and spatially extended nature of the quantum chaotic systems we consider, unlike the traditional emergence of Hermitian random matrix ensembles., Comment: 7+16 pages, 2+12 figures

XMM-Newton provides unprecedented insight into the X-ray Universe, recording variability information for hundreds of thousands of sources. Manually searching for interesting patterns in light curves is impractical, requiring an automated data-mining approach for the characterization of sources. Straightforward fitting of temporal models to light curves is not a sure way to identify them, especially with noisy data. We used unsupervised machine learning to distill a large data set of light-curve parameters, revealing its clustering structure in preparation for anomaly detection and subsequent searches for specific source behaviors (e.g., flares, eclipses). Self-organizing maps (SOMs) achieve dimensionality reduction and clustering within a single framework. They are a type of artificial neural network trained to approximate the data with a two-dimensional grid of discrete interconnected units, which can later be visualized on the plane. We trained our SOM on temporal-only parameters computed from more than 100,000 detections from the EXTraS catalog. The resulting map reveals that about 2500 most variable sources are clustered based on temporal characteristics. We find distinctive regions of the SOM map associated with flares, eclipses, dips, linear light curves, and others. Each group contains sources that appear similar by eye. We single out a handful of interesting sources for further study. The condensed view of our dataset provided by SOMs allowed us to identify groups of similar sources, speeding up manual characterization by orders of magnitude. Our method also highlights problems with fitting simple temporal models to light curves and can be used to mitigate them to an extent. This will be crucial for fully exploiting the high data volume expected from upcoming X-ray surveys, and may also help with interpreting supervised classification models., Comment: Accepted in Astronomy & Astrophysics (A&A). Main part: 12 pages, 12 figures, 1 video (appendix: 5 pages and 4 figures)

We analyzed the unexposed to the sky outFOV region of the MOS2 detector on board XMM-Newton covering 15 years of data amounting to 255 Ms. We show convincing evidence that the origin of the unfocused background in XMM-Newton is due to energetic protons, electrons and hard X-ray photons. Galactic Cosmic Rays are the main contributors as shown by the tight correlation (2.6% of total scatter) with 1 GeV protons data of the SOHO EPHIN detector. Tight correlations are found with a proxy of the Chandra background rate, revealing the common source of background for detectors in similar orbits, and with the data of the EPIC Radiation Monitor (ERM), only when excluding Solar Energetic Particles events (SEPs). The entrance to the outer electron belts is associated to a sudden increase in the outFOV MOS2 rate and a spectral change. These facts support the fact that MeV electrons can generate an unfocused background signal. The correlation between MOS2 outFOV data and the SOHO EPHIN data reveals a term constant in time and isotropic similar to the one found in the study of the pn data. The most plausible origin of this component is hard unfocused X-ray photons of the Cosmic X-ray Background (CXB) Compton-scattering in the detector as supported by the strength of the signal in the two detectors with different thicknesses. Based on this physical understanding a particle radiation monitor on board ATHENA has been proposed and it is currently under study. It will be able to track different species with the necessary accuracy and precision to guarantee the challenging requirement of 2% reproducibility of the background., Comment: 14 pages, 15 figures, accepted for publication in ApJ

We consider critical one dimensional quantum systems initially prepared in their groundstate and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any $2$--pt chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast with the general expectation of heating, we demonstrate that the system reaches a non-trivial and universal stationary state characterized by broad distributions. As an example, we analyse the local energy density: while its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with $3/2$ decay exponent. We obtain a similar result for the entanglement entropy production associated to a given interval of size $\ell$. The corresponding stationary distribution has a $3/2$ right tail for all $\ell$, and converges to a one-sided Levy stable for large $\ell$. Our results are benchmarked via analytical and numerical calculations for a chain of non-interacting spinless fermions with excellent agreement., Comment: 9 pages, 5 figures, Supplemental material (16 pages)

Discrete time crystals represent a paradigmatic nonequilibrium phase of periodically driven matter. Protecting its emergent spatiotemporal order necessitates a mechanism that hinders the spreading of defects, such as localization of domain walls in disordered quantum spin chains. In this work, we establish the effectiveness of a different mechanism arising in clean spin chains: the confinement of domain walls into ``mesonic'' bound states. We consider translationally invariant quantum Ising chains periodically kicked at arbitrary frequency, and discuss two possible routes to domain-wall confinement: longitudinal fields and interactions beyond nearest neighbors. We study the impact of confinement on the order parameter evolution by constructing domain-wall-conserving effective Hamiltonians and analyzing the resulting dynamics of domain walls. On the one hand, we show that for arbitrary driving frequency the symmetry-breaking-induced confining potential gets effectively averaged out by the drive, leading to deconfined dynamics. On the other hand, we rigorously prove that increasing the range $R$ of spin-spin interactions $J_{i,j}$ beyond nearest neighbors enhances the order-parameter lifetime \textit{exponentially} in $R$. Our theory predictions are corroborated by a combination of exact and matrix-product-state simulations for finite and infinite chains, respectively. The long-lived stability of spatiotemporal order identified in this work does not rely on Floquet prethermalization nor on eigenstate order, but rather on the nonperturbative origin of vacuum-decay processes. We point out the experimental relevance of this new mechanism for stabilizing a long-lived time-crystalline response in Rydberg-dressed spin chains., Comment: 24+9 pages, 16 figures. v3: Final version accepted in Phys. Rev. X

We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings, as a minimal model of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor (SFF) as a sum over many-body Feynman diagrams, which simplifies in the limit of large local Hilbert space dimension $q$. At sufficiently large $t$, diagrams corresponding to rigid translations dominate, reproducing the chaotic behavior of random matrix theory (RMT). At finite $t$, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams, known as the crossed and deranged diagrams, which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both $t$ and $L$ are large while the ratio between $L$ and $L_\mathrm{Th}(t)$, the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that in such a scaling limit, most microscopic details become unimportant, and the resulting scaling functions are largely universal, remarkably being only dependent on a few global properties of the system like the spatial dimensionality, and the space-time symmetries., Comment: 8+13 pages, 5+24 figures

We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts entropy increase and thermal states as the only stationary states. The equation applies to any hydrodynamic system with any number of local, PT-symmetric conserved quantities, in arbitrary dimension. It is fully expressed in terms of elements of an extended Onsager matrix. In integrable systems, this matrix admits an expansion in the density of excitations. We evaluate exactly its 2-particle-hole contribution, which dominates at low density, in terms of the scattering phase and dispersion of the quasiparticles, giving a lower bound for the extended Onsager matrix and entropy production. We conclude with a molecular dynamics simulation, demonstrating thermalisation over diffusive time scales in the Toda interacting particle model with an inhomogeneous energy field.

We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an out-of-equilibrium protocol engineered activating the defect in an initially homogeneous and far from the equilibrium state. We find that large enough defects induce full thermalisation at their center, but nonetheless the outgoing flow of carriers emerging from the defect is non-thermal due to a generalization of the celebrated Boundary Thermal Resistance effect, occurring at the edges of the chaotic region. Our results are obtained combining ab-initio numerical simulations for relatively small-sized defects, with the solution of the Boltzmann equation, which becomes exact in the scaling limit of large, but weak defects., Comment: 21 pages, 7 figures

We review recent progress in understanding nearly integrable models within the framework of generalized hydrodynamics (GHD). Integrable systems have infinitely many conserved quantities and stable quasiparticle excitations: when integrability is broken, only a few residual conserved quantities survive, eventually leading to thermalization, chaotic dynamics and conventional hydrodynamics. In this review, we summarize recent efforts to take into account small integrability breaking terms, and describe the transition from GHD to standard hydrodynamics. We discuss the current state of the art, with emphasis on weakly inhomogeneous potentials, generalized Boltzmann equations and collision integrals, as well as bound-state recombination effects. We also identify important open questions for future works., Comment: Review paper, 57 pages, 7 figures. Published in JSTAT special issue 2021 "Emergent Hydrodynamics in Integrable Many-body Systems"

We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized phases (MBL). The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that, for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call \textit{spectral Lyapunov exponents}. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block-diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of non-interacting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher point spectral form factors (hpSFF) in the large-$q$ limit, and show that the generalized Thouless time scales logarithmically in system size for all hpSFF in the large-$q$ chaotic phase., Comment: 14+6 pages. 19 figures

Our understanding of the background of the EPIC/pn camera onboard XMM-Newton is incomplete. This affects the study of extended sources and can influence the predictions of the background of future X-ray missions. We provide new results based on the analysis of the largest data set ever used. We focus on the unconcentrated component of the EPIC/pn background - supposedly related to cosmic rays interacting with the telescope. We find that the out-field of view region of the pn detector is actually exposed to the sky. After cleaning from the sky contamination, the unconcentrated background does not show significant spatial variations and its time behaviour is anti-correlated with the solar cycle. We find a very tight, linear correlation between unconcentrated backgrounds detected in the EPIC/pn and MOS2 cameras: this permits the correct evaluation of the pn unconcentrated background of each exposure on the basis of MOS2 data, avoiding the use (as usual) of the contaminated pn regions. We find a tight, linear correlation between the pn unconcentrated background and the proton flux in the 630-970 MeV energy band measured by SOHO/EPHIN. Through this relationship we quantify the contribution of cosmic ray interactions to the pn unconcentrated background and we find a second source which contributes to the pn unconcentrated background for a significant fraction (30%-70%), that does not vary with time and is roughly isotropic. Hard X-ray photons of the CXB satisfy all the known properties of this new component. Our findings provide an important observational confirmation of simulation results on ATHENA., Comment: 21 pages, 14 figures, 2 tables; accepted by the Astrophysical Journal

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalise at late times. We show that the full thermalising dynamics can be described by the generalised hydrodynamics with diffusion and force terms, and we compare these predictions with numerical simulations. Finally, we provide an explanation for the slow thermalisation rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterised by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalisation can display pre-thermal plateau and relaxation dynamics with long polynomial finite-time corrections., Comment: 5 pages + SM, 3 figures, typos corrected, references added

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the non-linear Schrodinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures., Comment: 7+7 pages, 2 figures

We study the out-of-equilibrium properties of a classical integrable non-relativistic theory, with a time evolution initially prepared with a finite energy density in the thermodynamic limit. The theory considered here is the Non-Linear Schrodinger equation which describes the dynamics of the one-dimensional interacting Bose gas in the regime of high occupation numbers. The main emphasis is on the determination of the late-time Generalised Gibbs Ensemble (GGE), which can be efficiently semi-numerically computed on arbitrary initial states, completely solving the famous quench problem in the classical regime. We take advantage of known results in the quantum model and the semiclassical limit to achieve new exact results for the momenta of the density operator on arbitrary GGEs, which we successfully compare with ab-initio numerical simulations. Furthermore, we determine the whole probability distribution of the density operator (full counting statistics), whose exact expression is still out of reach in the quantum model., Comment: 42 pages, 9 figures, resubmission to SciPost Physics

In spin chains with local unitary evolution preserving the magnetization $S^{\rm z}$, the domain-wall state $\left| \dots \uparrow \uparrow \uparrow \uparrow \uparrow \downarrow \downarrow \downarrow \downarrow \downarrow \dots \right>$ typically "melts". At large times, a non-trivial magnetization profile develops in an expanding region around the initial position of the domain-wall. For non-integrable dynamics the melting is diffusive, with entropy production within a melted region of size $\sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: the spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasi-particle charge (or Luttinger parameter $K$) which acquires a fractal dependence on the XXZ chain anisotropy parameter $\Delta$., Comment: 10 pages (including Supplementary Material), 3 figures

Modern soft X-ray observatories can yield unique insights into time domain astrophysics, and a huge amount of information is stored - and largely unexploited - in data archives. Like a treasure-hunt, the EXTraS project harvested the hitherto unexplored temporal domain information buried in the serendipitous data collected by the European Photon Imaging Camera instrument onboard the ESA XMM-Newton, in 16 years of observations. All results have been released to the scientific community, together with new software analysis tools. This paper presents the architecture of the EXTraS science gateway, that has the goal to provide the software to the scientific community through a Web based portal using the EGI Federated Cloud infrastructure. The main focus is on the light software architecture of the portal and on the technological insights for an effective use of the EGI ecosystem.

Modern soft X-ray observatories can yield unique insights into time domain astrophysics, and a huge amount of information is stored - and largely unexploited - in data archives. Like a treasure-hunt, the EXTraS project harvested the hitherto unexplored temporal domain information buried in the serendipitous data collected by the European Photon Imaging Camera instrument onboard the XMM- Newton satellite in 20 years of observations. The result is a vast catalogue, describing the temporal behaviour of hundreds of thousands of X-ray sources. But the catalogue is just a starting point because it has to be, in its turn, further analysed. During the project an education activity has been defined and run in several workshops for high school students in Italy, Germany and UK. The final goal is to engage the students, and in perspective citizen scientists, to go through the whole validation process: they look into the data and try to discover new sources, or to characterize already known sources. This paper describes how the EXTraS science gateway is used to accomplish these tasks and highlights the first discovery, a flaring X-ray source in the globular cluster NGC 6540., Comment: Accepted for publication in Future Generation Computing Systems, Special issue on Science gateways 2018

Ultraluminous X-ray sources (ULXs) are extragalactic X-ray emitters located off-center of their host galaxy and with a luminosity in excess of a few ${10^{39}\text{ erg s}^{-1}}$, if emitted isotropically. The discovery of periodic modulation revealed that in some ULXs the accreting compact object is a neutron star, indicating luminosities substantially above their Eddington limit. The most extreme object in this respect is ${NGC 5907~ULX-1}$ (ULX1), with a peak luminosity that is 500 times its Eddington limit. During a Chandra observation to probe a low state of ULX1, we detected diffuse X-ray emission at the position of ULX1. Its diameter is $2.7 \pm 1.0$ arcsec and contains 25 photons, none below 0.8 keV. We interpret this extended structure as an expanding nebula powered by the wind of ULX1. Its diameter of about ${200\text{ pc}}$, characteristic energy of ${\sim 1.9\text{ keV}}$, and luminosity of ${\sim 2\times10^{38}\text{ erg s}^{-1}}$ imply a mechanical power of ${1.3\times10^{41}\text{ erg s}^{-1}}$ and an age ${\sim 7 \times 10^{4}\text{ yr}}$. This interpretation suggests that a genuinely super-Eddington regime can be sustained for time scales much longer than the spin-up time of the neutron star powering the system. As the mechanical power from a single ULX nebula can rival the injection rate of cosmic rays of an entire galaxy, ULX nebulae could be important cosmic ray accelerators., Comment: 28 pages, 6 figures, 1 table - accepted for publication

We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front which never fades. We argue that these effects are valid for generic systems whose correlations propagate inside a light-cone. To assess the fully chaotic regime, we formulate a random circuit model which supports a moving impurity and a sharp lightcone. Although the qualitative behavior is similar to the integrable case, the endogenous regime is only visible at short times due to the onset of diffusive energy transport. Our predictions are supported by numerical simulations in the different regimes., Comment: 13 pages, 9 figures

We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor $K(t)$ analytically for a minimal Floquet circuit model that has a $U(1)$ symmetry encoded via auxiliary spin-$1/2$ degrees of freedom. Averaging over an ensemble of realizations, we relate $K(t)$ to a partition function for the spins, given by a Trotterization of the spin-$1/2$ Heisenberg ferromagnet. Using Bethe Ansatz techniques, we extract the 'Thouless time' $t^{\vphantom{*}}_{\rm Th}$ demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for $K(t)$ at $t\lesssim t^{\vphantom{*}}_{\rm Th}$. We also report numerical results for $K(t)$ in a generic Floquet spin model, which are consistent with these analytic predictions., Comment: 5 pages main text + 11 pages supplementary material, v2: minor changes, numerics to L=18, improved scaling analysis

The relation between magnetic activity and rotation in late-type stars provides fundamental information on stellar dynamos and angular momentum evolution. Rotation/activity studies found in the literature suffer from inhomogeneity in the measure of activity indexes and rotation periods. We overcome this limitation with a study of the X-ray emitting late-type main-sequence stars observed by XMM-Newton and Kepler. We measure rotation periods from photometric variability in Kepler light curves. As activity indicators, we adopt the X-ray luminosity, the number frequency of white-light flares, the amplitude of the rotational photometric modulation, and the standard deviation in the Kepler light curves. The search for X-ray flares in the light curves provided by the EXTraS (Exploring the X-ray Transient and variable Sky) FP-7 project allows us to identify simultaneous X-ray and white-light flares. A careful selection of the X-ray sources in the Kepler field yields 102 main-sequence stars with spectral types from A to M. We find rotation periods for 74 X-ray emitting main-sequence stars, 22 of which without period reported in the previous literature. In the X-ray activity/rotation relation, we see evidence for the traditional distinction of a saturated and a correlated part, the latter presenting a continuous decrease in activity towards slower rotators. For the optical activity indicators the transition is abrupt and located at a period of ~ 10 d but it can be probed only marginally with this sample which is biased towards fast rotators due to the X-ray selection. We observe 7 bona-fide X-ray flares with evidence for a white-light counterpart in simultaneous Kepler data. We derive an X-ray flare frequency of ~ 0.15 d^{-1} , consistent with the optical flare frequency obtained from the much longer Kepler time-series., Comment: Accepted for publication in A&A. 31 pages, 19 figures

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects., Comment: 15 pages, 8 figures

Predicting the flow of non-Newtonian fluids in porous structure is still a challenging issue due to the interplay betwen the microscopic disorder and the non-linear rheology. In this letter, we study the case of an yield stress fluid in a two-dimensional structure. Thanks to a performant optimization algorithm, we show that the system undergoes a continuous phase transition in the behavior of the flow controlled by the applied pressure drop. In analogy with the studies of the plastic depinning of vortex lattices in high-$T_c$ superconductors we characterize the nonlinearity of the flow curve and relate it to the change in the geometry of the open channels. In particular, close to the transition, an universal scale free distribution of the channel length is observed and explained theoretically via a mapping to the KPZ equation., Comment: 5 pages, 4 figures + 1 Supplementary material

We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the butterfly effect implies structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additional correlations., Comment: 5 pages, 4 figures. To appear in PRL

Background: Clinical decision support systems (CDSS) are a category of health information technologies that can assist clinicians to choose optimal treatments. These support systems are based on clinical trials and expert knowledge; however, the amount of data available to these systems is limited. For this reason, CDSSs could be significantly improved by using the knowledge obtained by treating patients. This knowledge is mainly contained in patient records, whose usage is restricted due to privacy and confidentiality constraints. Methods: A treatment effectiveness measure, containing valuable information for treatment prescription, was defined and a method to extract this measure from patient records was developed. This method uses an advanced cryptographic technology, known as secure Multiparty Computation (henceforth referred to as MPC), to preserve the privacy of the patient records and the confidentiality of the clinicians' decisions. Results: Our solution enables to compute the effectiveness measure of a treatment based on patient records, while preserving privacy. Moreover, clinicians are not burdened with the computational and communication costs introduced by the privacy-preserving techniques that are used. Our system is able to compute the effectiveness of 100 treatments for a specific patient in less than 24 minutes, querying a database containing 20,000 patient records. Conclusion: This paper presents a novel and efficient clinical decision support system, that harnesses the potential and insights acquired from treatment data, while preserving the privacy of patient records and the confidentiality of clinician decisions., Comment: 15 pages, 4 figures

We present the first X-ray and UV/optical observations of a very bright and fast nova in the disc of M31, M31N 2013-01b. The nova reached a peak magnitude $R\sim$15 mag and decayed by 2 magnitudes in only 3 days, making it one of the brightest and fastest novae ever detected in Andromeda. From archival multi-band data we have been able to trace its fast evolution down to $U>21$ mag in less than two weeks and to uncover for the first time the Super-Soft X-ray phase, whose onset occurred 10-30 days from the optical maximum. The X-ray spectrum is consistent with a blackbody with a temperature of $\sim$50 eV and emitting radius of $\sim$4$\times 10^{9}$ cm, larger than a white dwarf radius, indicating an expanded region. Its peak X-ray luminosity, 3.5$\times 10^{37}$ erg s$^{-1}$, locates M31N 2013-01b among the most luminous novae in M31. We also unambiguously detect a short 1.28$\pm$0.02 h X-ray periodicity that we ascribe to the binary orbital period, possibly due to partial eclipses. This makes M31N 2013-01b the first nova in M31 with an orbital period determined. The short period also makes this nova one of the few known below the 2-3 h orbital period gap. All the observed characteristics strongly indicate that M31N 2013-01b harbours a massive white dwarf and a very low-mass companion, consistent with being a nova belonging to the disc population of the Andromeda Galaxy., Comment: 9 pages, 3 figures, 2 tables; accepted by the Astrophysical Journal

We analyzed two Chandra observations of PSR J2055+2539 (for a total integration time of $\sim$130 ks) in order to measure its proper motion and study its two elongated nebular features. We did not detect the proper motion, setting an upper limit of 240 mas yr$^{-1}$ (3$\sigma$ level), that translates into an upper limit on the transverse velocity of $\sim$700 km s$^{-1}$, for an assumed distance of 600 pc. A deep H$\alpha$ observation did not reveal the bow-shock associated with a classical pulsar wind nebula, thus precluding an indirect measurement of the proper motion direction. We determined the main axes of the two nebulae, which are separated by an angle of 160.8$^{\circ} \pm 0.7^{\circ}$, using a new approach based on the Rolling Hough Transformation (RHT). We analyzed the shape of the first 8' (out of the 12' seen by XMM-Newton) of the brighter, extremely collimated one. Based on a combination of our results from a standard analysis and a nebular modeling obtained from the RHT, we find that the brightest nebula is curved on an arcmin-scale, with a thickness ranging from $\sim9$" to $\sim31$" and a possible (single or multiple) helicoidal pattern. We could not constrain the shape of the fainter nebula. We discuss our results in the context of other known similar features, with particular emphasis on the Lighthouse nebula (associated with PSR J1101$-$6101). We speculate that a peculiar geometry of the powering pulsar may play an important role in the formation of such features., Comment: 12 pages, 9 figures, 1 table; accepted by Astronomy & Astrophysics

We report the discovery of a flaring X-ray source in the globular cluster NGC 6540, obtained during the EXTraS project devoted to a systematic search for variability in archival data of the XMM-Newton satellite. The source had a quiescent X-ray luminosity of the order of ~10^32 erg/s in the 0.5-10 keV range (for a distance of NGC 6540 of 4 kpc) and showed a flare lasting about 300 s. During the flare, the X-ray luminosity increased by more than a factor 40, with a total emitted energy of ~10^36 erg. These properties, as well as Hubble Space Telescope photometry of the possible optical counterparts, suggest the identification with a chromospherically active binary. However, the flare luminosity is significantly higher than what commonly observed in stellar flares of such a short duration, leaving open the possibility of other interpretations., Comment: To appear in Astronomy and Astrophysics

Quantum excitations in lattice systems always propagate at a finite maximum velocity. We probe this mechanism by considering a defect travelling at a constant velocity in the quantum Ising spin chain in transverse field. Independently of the microscopic details of the defect, we characterize the expectation value of local observables at large times and large distances from the impurity, where a Local Quasi Stationary State (LQSS) emerges. The LQSS is strongly affected by the defect velocity: for superluminal defects, it exhibits a growing region where translational invariance is spontaneously restored. We also analyze the behavior of the friction force exerted by the many-body system on the moving defect, which reflects the energy required by the LQSS formation. Exact results are provided in the two limits of extremely narrow and very smooth impurity. Possible extensions to more general free-fermion models and interacting systems are discussed, Comment: 15 pages, 7 figures

We report the discovery with XMM-Newton of 3-s X-ray pulsations from 3XMM J004232.1+411314, a dipping source that dominates the hard X-ray emission of M31. This finding unambiguously assesses the neutron star (NS) nature of the compact object. We also measured an orbital modulation of 4.15 h and a projected semi-axis at $a_{\mathrm{X}} \sin i= 0.6$ lt-s, which implies a low-mass companion of about 0.2$-$0.3$M_{\odot}$ assuming a NS of 1.5 $M_{\odot}$ and an orbital inclination $i=70^{\circ}-80^{\circ}$. The barycentric orbit-corrected pulse period decreased by $\sim$28 ms in about 16 yr, corresponding to an average spin-up rate of $\dot{P} \sim -6 \times 10^{-11}$ s s$^{-1}$ ; pulse period variations, probably caused to by X-ray luminosity changes, were observed on shorter time scales. We identify two possible scenarios for the source: a mildly magnetic NS with $B_{\mathrm{p}}\simeq$ few $\times10^{10}$ G if the pulsar is far from its equilibrium period $P_{\mathrm{eq}}$, and a relatively young highly magnetic NS with $B_{\mathrm{eq}}\simeq 10^{13}$ G if spinning close to $P_{\mathrm{eq}}$., Comment: 5 pages, 3 figures, 2 tables, Submitted to the Astrophysical Journal Letters

We study energy transport in the integrable $\mathbb Z_3$ parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the non-equilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge $c=4/5$, which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with $c=1$. By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a novel framework, where it can be profitably used for exploring new physical phenomena., Comment: 13 pages, 12 figures