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We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations diverge linearly in particular time differences. This behaviour can be understood by means of a simple semiclassical analysis based on the kinematics and scattering of wave packets of quasiparticles. We verify that our wave packet analysis correctly predicts the long-time limit of the four-point function in the transverse field Ising model through a form factor expansion. We present evidence in favour of the same behaviour in integrable quantum field theories. In addition, we extend our discussion to experimental protocols where two times of the four-point function coincide, e.g. 2D coherent spectroscopy and pump-probe experiments. Finally, focusing on the Ising model, we discuss subleading corrections that grow as the square root of time differences. We show that the subleading corrections can be correctly accounted for by the same semiclassical analysis, but also taking into account wave packet spreading., Comment: 59 pages, 8 figures

The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange couplings and transverse fields, whose bulk exhibits an infinite randomness critical point. This approach enables an asymptotically numerically exact extraction of universal scaling data from very large systems with many thousands of spins that cannot be efficiently simulated directly. We identify three distinct classes of boundary criticality, and extract key scaling exponents governing boundary-boundary and boundary-bulk correlations and dynamics. We anticipate that this approach can be generalized to studying a broad class of (disordered) boundary criticality, including symmetry-enriched criticality and edge modes of gapless symmetry-protected topological states, in contexts were other numerical methods are restricted to one-dimensional chains.

We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a general setting, the energy dissipation rate is proportional to $\bar U \bar V ^2$, where $\bar U$ is the strength of the suction and $\bar V$ is the tangential component of the difference between Euler and Navier-Stokes on the outflow boundary. Moreover, we show that the enstrophy within a layer of order $\nu / \bar U$ is comparable with the total enstrophy. The rate of enstrophy production near the boundary is inversely proportional to $\nu$., Comment: 25 pages, 3 figures

We identify a pseudolocal conserved charge in the Fredkin and Motzkin quantum spin chains and explore its consequences for the hydrodynamics of systems with Fredkin- or Motzkin-type kinetic constraints. We use this quantity to formulate an exact upper bound ${\cal O}(L^{-5/2})$ on the gap of the Fredkin and Motzkin spin chains. Our results establish that transport in kinetically constrained dynamical systems with Fredkin or Motzkin constraints is subdiffusive, with dynamical exponent $z \geq 5/2$.

In this paper, we show that a geometrical condition on $2\times2$ systems of conservation laws leads to non-uniqueness in the class of 1D continuous functions. This demonstrates that the Liu Entropy Condition alone is insufficient to guarantee uniqueness, even within the mono-dimensional setting. We provide examples of systems where this pathology holds, even if they verify stability and uniqueness for small BV solutions. Our proof is based on the convex integration process. Notably, this result represents the first application of convex integration to construct non-unique continuous solutions in one dimension.

Steady-state currents generically occur both in systems with continuous translation invariance and in nonequilibrium settings with particle drift. In either case, thermal fluctuations advected by the current act as a source of noise for slower hydrodynamic modes. This noise is unconventional, since it is highly correlated along spacetime rays. We argue that, in quasi-one-dimensional geometries, the correlated noise from ballistic modes generically gives rise to anomalous full counting statistics (FCS) for diffusively spreading charges. We present numerical evidence for anomalous FCS in two settings: (1) a two-component continuum fluid, and (2) the totally asymmetric exclusion process (TASEP) initialized in a nonequilibrium state., Comment: 5 pages, 4 figures

Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here, by combining extensive numerical simulations of classical and quantum integrable isotropic spin chains with a framework developed by exact studies of the KPZ class, we characterize various two-point quantities that remain hitherto unexplored in spin chains, and find full agreement with KPZ scaling laws without adjustable parameters. This establishes the partial emergence of the KPZ class in integrable isotropic spin chains. Moreover, we reveal that the KPZ scaling laws are intact in the presence of an energy current, under the appropriate Galilean boost required by the propagation of spacetime correlation., Comment: 8+6 pages, 5+2 figures, 1 table; quantum spin simulations added

For a finite set $A\subset\mathbb{N}$ and $k\in \mathbb{N}$, let $\omega_k(A) = \sum_{i\in A, i\neq k}1$. For each $n\in \mathbb{N}$, define $$a_{k, n}\ =\ |\{E\subset \mathbb{N}\,:\, E = \emptyset\mbox{ or } \omega_k(E) < \min E\leqslant \max E\leqslant n\}|.$$ First, we prove that $$a_{k,k+\ell} \ =\ 2F_{k+\ell},\mbox{ for all }\ell\geqslant 0\mbox{ and }k\geqslant \ell+2,$$ where $F_n$ is the $n$th Fibonacci number. Second, we show that $$|\{E\subset \mathbb{N}\,:\, \max E = n+1, \min E > \omega_{2,3}(E), \mbox{ and }|E|\neq 2\}|\ =\ F_{n},$$ where $\omega_{2,3}(E) = \sum_{i\in E, i\neq 2, 3}1$., Comment: 14 pages

We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the incompressible Navier-Stokes equations. By analyzing circuit-to-circuit fluctuations in the ensemble we argue that these are negligible, so the circuit-averaged value of transport coefficients like the viscosity is also (in the long-time limit) the value in a typical circuit. The circuit-averaged transport coefficients can be mapped onto a classical irreversible Markov process. Therefore, remarkably, our construction allows us to efficiently compute the viscosity of a family of strongly interacting chaotic two-dimensional quantum systems., Comment: 4+epsilon pages, 3 figures; 8 pages supplemental material

The Super-Kamiokande and T2K collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7(16.3) \times 10^{20}$ protons on target in (anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-conservation (defined as $J_{CP}=0$) and a preference for the normal mass ordering., Comment: 12 pages, 4 figures

Randomized algorithms have proven to perform well on a large class of numerical linear algebra problems. Their theoretical analysis is critical to provide guarantees on their behaviour, and in this sense, the stochastic analysis of the randomized low-rank approximation error plays a central role. Indeed, several randomized methods for the approximation of dominant eigen- or singular modes can be rewritten as low-rank approximation methods. However, despite the large variety of algorithms, the existing theoretical frameworks for their analysis rely on a specific structure for the covariance matrix that is not adapted to all the algorithms. We propose a general framework for the stochastic analysis of the low-rank approximation error in Frobenius norm for centered and non-standard Gaussian matrices. Under minimal assumptions on the covariance matrix, we derive accurate bounds both in expectation and probability. Our bounds have clear interpretations that enable us to derive properties and motivate practical choices for the covariance matrix resulting in efficient low-rank approximation algorithms. The most commonly used bounds in the literature have been demonstrated as a specific instance of the bounds proposed here, with the additional contribution of being tighter. Numerical experiments related to data assimilation further illustrate that exploiting the problem structure to select the covariance matrix improves the performance as suggested by our bounds.

The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak quasiperiodic modulations; however, as the quasiperiodic modulation gets increasingly strong, it is increasingly renormalized and eventually fails, as the system becomes localized. We explore how quasiperiodic modulation renormalizes the Luttinger parameter characterizing this emergent Luttinger liquid, using the renormalization of transmission coefficients across a barrier as a proxy that remains valid for general quasiperiodic modulation. We find, unexpectedly, that quasiperiodic modulation weakens the effects of short-range interactions, but enhances those of long-range interactions. We support the former finding with matrix-product numerics. We also discuss how interactions affect the localization phase boundary.

Reliable multimodal sensor fusion algorithms require accurate spatiotemporal calibration. Recently, targetless calibration techniques based on implicit neural representations have proven to provide precise and robust results. Nevertheless, such methods are inherently slow to train given the high computational overhead caused by the large number of sampled points required for volume rendering. With the recent introduction of 3D Gaussian Splatting as a faster alternative to implicit representation methods, we propose to leverage this new rendering approach to achieve faster multi-sensor calibration. We introduce 3DGS-Calib, a new calibration method that relies on the speed and rendering accuracy of 3D Gaussian Splatting to achieve multimodal spatiotemporal calibration that is accurate, robust, and with a substantial speed-up compared to methods relying on implicit neural representations. We demonstrate the superiority of our proposal with experimental results on sequences from KITTI-360, a widely used driving dataset., Comment: Accepted at IROS 2024 (Oral presentation). Project page: https://qherau.github.io/3DGS-Calib/

Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous nonabelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet isotropic perturbations of strength $\lambda$. We identify an anomalously-long crossover time scale $t_\star \sim \lambda^{-\alpha}$ with $\alpha \approx 6$ in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.

The present paper is concerned with the well-posedness theory for non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. Differently from previous works, we consider here the full odd viscosity tensor. Similarly to the work of Bresch and Desjardins in compressible fluid mechanics, we identify the presence of an effective velocity in the system, linking the velocity field of the fluid and the gradient of a suitable function of the density. By use of this effective velocity, we propose a new formulation of the original system of equations, thus highlighting a strong similarity with the equations of the ideal magnetohydrodynamics. By taking advantage of the new formulation of the equations, we establish a local in time well-posedness theory in Besov spaces based on $L^\infty$ and prove a lower bound for the lifespan of the solutions implying ``asymptotically global'' existence: in the regime of small initial density variations, $\rho_0-1= O(\varepsilon)$ for small $\varepsilon>0$, the corresponding solution is defined up to some time $T_\varepsilon>0$ satisfying the property $T_\varepsilon\,\longrightarrow\,+\infty$ when $\varepsilon\to0^+$., Comment: Submitted

In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of solving this intricate problem, particularly concerning singular solutions, persists in both compressible and incompressible scenarios. This article focuses on small $BV$ solutions to the barotropic Euler equation in one spatial dimension. Our investigation demonstrates that these solutions are inviscid limits for solutions to the associated compressible Navier-Stokes equation. Moreover, we extend our findings by establishing the well-posedness of such solutions within the broader class of inviscid limits of Navier-Stokes equations with locally bounded energy initial values., Comment: We fixed typos and retouched parts of the manuscript for better readability

Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals., Comment: 5 pages, 2 figures

Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials., Comment: 14+2 pages, 10+1 figures; v2: published version, added DMRG simulation for the XXZ model

In rapidly-evolving domains such as autonomous driving, the use of multiple sensors with different modalities is crucial to ensure high operational precision and stability. To correctly exploit the provided information by each sensor in a single common frame, it is essential for these sensors to be accurately calibrated. In this paper, we leverage the ability of Neural Radiance Fields (NeRF) to represent different sensors modalities in a common volumetric representation to achieve robust and accurate spatio-temporal sensor calibration. By designing a partitioning approach based on the visible part of the scene for each sensor, we formulate the calibration problem using only the overlapping areas. This strategy results in a more robust and accurate calibration that is less prone to failure. We demonstrate that our approach works on outdoor urban scenes by validating it on multiple established driving datasets. Results show that our method is able to get better accuracy and robustness compared to existing methods., Comment: Accepted at CVPR 2024. Project page: https://qherau.github.io/SOAC/

In recent years, interest in autonomous shipping in urban waterways has increased significantly due to the trend of keeping cars and trucks out of city centers. Classical approaches such as Frenet frame based planning and potential field navigation often require tuning of many configuration parameters and sometimes even require a different configuration depending on the situation. In this paper, we propose a novel path planning approach based on reinforcement learning called Model Predictive Reinforcement Learning (MPRL). MPRL calculates a series of waypoints for the vessel to follow. The environment is represented as an occupancy grid map, allowing us to deal with any shape of waterway and any number and shape of obstacles. We demonstrate our approach on two scenarios and compare the resulting path with path planning using a Frenet frame and path planning based on a proximal policy optimization (PPO) agent. Our results show that MPRL outperforms both baselines in both test scenarios. The PPO based approach was not able to reach the goal in either scenario while the Frenet frame approach failed in the scenario consisting of a corner with obstacles. MPRL was able to safely (collision free) navigate to the goal in both of the test scenarios., Comment: \c{opyright} 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Conventional hydrodynamics describes systems with few long-lived excitations. In one dimension, however, many experimentally relevant systems feature a large number of long-lived excitations even at high temperature, because they are proximate to integrable limits. Such models cannot be treated using conventional hydrodynamics. The framework of generalized hydrodynamics (GHD) was recently developed to treat the dynamics of one-dimensional models: it combines ideas from integrability, hydrodynamics, and kinetic theory to come up with a quantitative theory of transport. GHD has successfully settled several longstanding questions about one-dimensional transport; it has also been leveraged to study dynamical questions beyond the transport of conserved quantities, and to systems that are not integrable. In this article we introduce the main ideas and predictions of GHD, survey some of the most recent theoretical extensions and experimental tests of the GHD framework, and discuss some open questions in transport that the GHD perspective might elucidate., Comment: 16 pages, 5 figures, perspective article, feedback is welcome

The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware.

We consider the effects of quasiperiodic spatial modulation on the quantum Hall plateau transition, by analyzing the Chalker-Coddington network model for the integer quantum Hall transition with quasiperiodically modulated link phases. In the conventional case (uncorrelated random phases), there is a critical point separating topologically distinct integer quantum Hall insulators. Surprisingly, the quasiperiodic version of the model supports an extended critical phase for some angles of modulation. We characterize this critical phase and the transitions between critical and insulating phases. For quasiperiodic potentials with two incommensurate wavelengths, the transitions we find are in a different universality class from the random transition. Upon adding more wavelengths they undergo a crossover to the uncorrelated random case. We expect our results to be relevant to the quantum Hall phases of twisted bilayer graphene or other Moir\'e systems with large unit cells., Comment: 11 pages, 9 figures

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs., Comment: 17 pages, 12 figures, 1 table

We report an updated measurement of the $\nu_{\mu}$-induced, and the first measurement of the $\bar{\nu}_{\mu}$-induced coherent charged pion production cross section on $^{12}C$ nuclei in the T2K experiment. This is measured in a restricted region of the final-state phase space for which $p_{\mu,\pi} > 0.2$ GeV, $\cos(\theta_{\mu}) > 0.8$ and $\cos(\theta_{\pi}) > 0.6$, and at a mean (anti)neutrino energy of 0.85 GeV using the T2K near detector. The measured $\nu_{\mu}$ CC coherent pion production flux-averaged cross section on $^{12}C$ is $(2.98 \pm 0.37 (stat.) \pm 0.31 (syst.) \substack{ +0.49 \\ -0.00 } \mathrm{ (Q^2\,model)}) \times 10^{-40}~\mathrm{cm}^{2}$. The new measurement of the $\bar{\nu}_{\mu}$-induced cross section on $^{12}{C}$ is $(3.05 \pm 0.71 (stat.) \pm 0.39 (syst.) \substack{ +0.74 \\ -0.00 } \mathrm{(Q^2\,model)}) \times 10^{-40}~\mathrm{cm}^{2}$. The results are compatible with both the NEUT 5.4.0 Berger-Sehgal (2009) and GENIE 2.8.0 Rein-Sehgal (2007) model predictions.

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\beta$ to exceed the Luck bound $\nu \ge 1/(1-\beta)$ for the stability of the MIPT, where $\nu=1.28(2)$. Via robust numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $\beta$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\psi \cong \beta$, finding excellent agreement with the conclusions of real space renormalization group calculations., Comment: 14 pages, 13 figures

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states

A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in hard-core boson ladders, contrasting systems with ballistic and chaotic dynamics. We find excellent agreement between our results and MFT predictions, which allows us to accurately extract diffusion constants from fluctuation growth. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, expanding the applicability of MFT to the quantum regime.

We establish the time-asymptotic stability of solutions to the one-dimensional compressible Navier-Stokes-Fourier equations, with initial data perturbed from Riemann data that forms a generic Riemann solution. The Riemann solution under consideration is composed of a viscous shock, a viscous contact wave, and a rarefaction wave. We prove that the perturbed solution of Navier-Stokes-Fourier converges, uniformly in space as time goes to infinity, to a viscous ansatz composed of viscous shock with time-dependent shift, a viscous contact wave and an inviscid rarefaction wave. This is a first resolution of the challenging open problem associated with the generic Riemann solution. Our approach relies on the method of a-contraction with shifts, specifically applied to both the shock wave and the contact discontinuity wave. It enables the application of a global energy method for the generic combination of three waves., Comment: arXiv admin note: text overlap with arXiv:2104.06590

Although integrable spin chains only host ballistically propagating particles they can still feature diffusive spin transport. This diffusive spin transport originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long range correlations lead to superdiffusive spin transport with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and explain how deviations arise from finite time and finite size effects., Comment: 4+epsilon pages, 3 figures; Comments welcome

We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures FCS starting from number-indefinite initial states or in the presence of noisy dynamics. In addition, by mapping the FCS onto a single-body observable, it allows for stable numerical calculations of FCS using approximate tensor-network methods. We demonstrate the wide-ranging utility of this approach by computing the FCS of the transferred magnetization in a Floquet Heisenberg spin chain, as studied in a recent experiment with superconducting qubits, as well as the FCS of charge transfer in random circuits., Comment: 8+3 pages, 4+4 figures

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads in time $t$ to a width $t^{2/3}$. This exponent, as well as the functional form of the dynamical spin correlation function, suggest that spin transport is in the Kardar-Parisi-Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry, and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry., Comment: review article, 17 pages + refs. Comments welcome

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot., Comment: 8 pages (6 figures) + appendices (11.5 pages)

Muon neutrino and antineutrino disappearance probabilities are identical in the standard three-flavor neutrino oscillation framework, but CPT violation and non-standard interactions can violate this symmetry. In this work we report the measurements of $\sin^{2} \theta_{23}$ and $\Delta m_{32}^2$ independently for neutrinos and antineutrinos. The aforementioned symmetry violation would manifest as an inconsistency in the neutrino and antineutrino oscillation parameters. The analysis discussed here uses a total of 1.97$\times$10$^{21}$ and 1.63$\times$10$^{21}$ protons on target taken with a neutrino and antineutrino beam respectively, and benefits from improved flux and cross-section models, new near detector samples and more than double the data reducing the overall uncertainty of the result. No significant deviation is observed, consistent with the standard neutrino oscillation picture.