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The Hatano-Nelson model is a cornerstone of non-Hermitian physics, describing asymmetric hopping dynamics on a one-dimensional lattice, which gives rise to fascinating phenomena such as directional transport, non-Hermitian topology, and the non-Hermitian skin effect. It has been widely studied in both classical and quantum systems, with applications in condensed matter physics, photonics, and cold atomic gases. Recently, nonlinear extensions of the Hatano-Nelson model have opened a new avenue for exploring the interplay between nonlinearity and non-Hermitian effects. Particularly, in lattices with open boundary conditions, nonlinear skin modes and solitons, localized at the edge or within the bulk of the lattice, have been predicted. In this work, we examine the nonlinear extension of the Hatano-Nelson model with periodic boundary conditions and reveal a novel dynamical phenomenon arising from the modulational instability of nonlinear plane waves: growth blockade. This phenomenon is characterized by the abrupt halt of norm growth, as observed in the linear Hatano-Nelson model, and can be interpreted as a stopping of convective motion arising from self-induced disorder in the lattice., Comment: 14 pages, 5 figures

We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations which must annihilate the count, and which dequantize to a mirror of the geometry. We show algebraically that the resulting equations determine the count uniquely, and that the result agrees with the topological vertex from topological string theory., Comment: 28 pages, 10 figures

We propose a mirror derivation of the quiver description of open topological strings known as the knots-quivers correspondence, based on enumerative invariants of augmentation curves encoded by exponential networks. Quivers are obtained by studying M2 branes wrapping holomorphic disks with Lagrangian boundary conditions on an M5 brane, through their identification with a distinguished sector of BPS kinky vortices in the 3d-3d dual QFT. Our proposal suggests that holomorphic disks with Lagrangian boundary conditions are mirror to calibrated 1-chains on the associated augmentation curve, whose intersections encode the linking of boundaries., Comment: 34 pages + appendices

In lattices with uncorrelated on-site potential disorder, Anderson localization near the band edges can exhibit anomalously weak localization in the form of Lifshitz tail states. These states correspond to clusters of contiguous sites with nearly identical on-site energies, allowing excitations to extend significantly beyond the characteristic localization length determined by the inverse of Lyapunov exponent. Since Lifshitz tail states are rare events, with an exponentially small density of states, they are typically considered of limited practical importance. In this work, we demonstrate that when Anderson localization is induced by disorder in an imaginary on-site potential, Lifshitz tail states can dominate the system's dynamics and become experimentally observable. This phenomenon is illustrated through the Anderson-Bernoulli model in a non-Hermitian photonic lattice, shedding light on the unique interplay between disorder and non-Hermiticity in such systems, Comment: 5 pages, 3 figures, to appear in Optics Letters

The behavior of systems far from equilibrium is often complex and unpredictable, challenging and sometimes overturning the physical intuition derived from equilibrium scenarios. One striking example of this is the Mpemba effect, which implies that non-equilibrium states can sometimes relax more rapidly when they are further from equilibrium. Despite a rich historical background, the precise conditions and mechanisms behind this phenomenon remain unclear. Recently, there has been growing interest in investigating Mpemba-like effects within quantum systems. In this work, we explore a quantum manifestation of the Mpemba effect in a simple and paradigmatic model of open quantum systems: the damped quantum harmonic oscillator, which describes the thermalization process of a bosonic mode in contact with a thermal bath at finite temperature $T$. By means of an exact analytical analysis of the relaxation dynamics, we demonstrate that any initial distribution of populations with a mean excitation number exactly equal to the mean number of quanta in the thermal equilibrium state displays an accelerated relaxation to equilibrium, leading to a pronounced Mpemba effect. In particular, one can find a broad class of far-from-equilibrium distributions that relax to equilibrium faster than any other initial thermal state with a temperature $T'$ arbitrarily close to $T$. Thermalization becomes even faster when the initial out-of-equilibrium population distribution matches the first $r$ moments of the equilibrium distribution. In this scenario, the relaxation rate increases linearly with $r$, resulting in a super-accelerated thermalization process., Comment: 18 pages, 4 figures

Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally-spaced sites within the lattice, with a spacing $M \geq 2$. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang {\it et al.}, Phys. Rev. Lett. {\bf 125}, 196604 (2020)]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice., Comment: 13 pages, 6 figures, accepted for publication in the Phys. Rev. B

The Mpemba effect refers to the surprising observation where, under certain conditions, a far-from-equilibrium state can relax toward equilibrium faster than a state closer to equilibrium. A paradigmatic example is provided by the curious fact that hot water can sometimes freeze faster than cold water. The Mpemba effect has intrigued scientists since long time and has been predicted and observed in a variety of classical and quantum systems. Recently, the search for Mpemba-like effects of purely quantum nature has raised a major interest. Here we predict the emergence of Mpemba effect in the quantum optics context exploiting non-classical states of light. By analyzing the decay dynamics of photon fields in a leaky optical resonator or waveguide, it is demonstrated that bosonic Mpemba effect emerges in the context of the quantum nature of light. Specifically, the relaxation dynamics is strongly influenced by the photon statistics of the initially trapped light field. The Mpemba effect is observed when comparing the decay dynamics of classical light fields (coherent states) with certain non-classical states, such as Fock states, squeezed states and Schr\"odinger cat states., Comment: 7 pages, 4 figures, accepted for publication in APL Quantum

In arXiv:2306.07329 we established a connection between symplectic cuts of Calabi-Yau threefolds and open topological strings, and used this to introduce an equivariant deformation of the disk potential of toric branes. In this paper we establish a connection to higher-dimensional Calabi-Yau geometries by showing that the equivariant disk potential arises as an equivariant period of certain Calabi-Yau fourfolds and fivefolds, which encode moduli spaces of one and two symplectic cuts (the maximal case) by a construction of Braverman arXiv:alg-geom/9712024. Extended Picard-Fuchs equations for toric branes, capturing dependence on both open and closed string moduli, are derived from a suitable limit of the equivariant quantum cohomology rings of the higher Calabi-Yau geometries., Comment: 45 pages + appendix, 8 figures

The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the random walk of intense classical light under dephasing dynamics can disentangle quantum and ensemble averaging, making it possible to observe a subdiffusive walker dynamics, i.e. a behavior very distinct from both a classical and a quantum walker. These findings are demonstrated through proposing photonic random walks in synthetic temporal lattices, based on pulse dynamics in coupled fiber loops., Comment: 8 pages, 6 figures, included supplemental document, to appear in Optics Letters

Non-Hermitian skin effect (NHSE), i.e., the localization of eigenstates near lattice boundaries, has recently spurred tremendous interest in topological physics. Beyond the well-explored linear NHSE, the interplay of nonlinearity and skin localization represents a cutting-edge area of research, offering novel insights into wave propagation and localization control in various physical systems. Unlike the linear NHSE successfully observed in weak-power optical systems, the observation of nonlinear NHSE and resulting skin solitons remains so far elusive, mainly due to the high energy levels required in most of nonlinear effects. Here we report the experimental demonstration of nonlinear NHSE in a Kerr nonlinear temporal photonic lattice, where the high-power limitation and lack of tunability intrinsic to optical materials are overcome by an artificial nonlinearity arising from opto-electronic feedback. Thanks to Kerr self-trapping, the nonlinear NHSE is demonstrated to possess much better localization strength and robustness at the preferred boundary compared to the linear case. Away from the preferred boundary, Kerr self-trapping can even inhibit NHSE-induced transport and form stable skin solitons. Harnessing the nonlinearity-controlled NHSE, we judiciously design an optical router with a flexibly-tuned output port. Our findings promise great applications in robust signal transmission, routing, and processing.

Socially Unacceptable Discourse (SUD) analysis is crucial for maintaining online positive environments. We investigate the effectiveness of Entailment-based zero-shot text classification (unsupervised method) for SUD detection and characterization by leveraging pre-trained transformer models and prompting techniques. The results demonstrate good generalization capabilities of these models to unseen data and highlight the promising nature of this approach for generating labeled datasets for the analysis and characterization of extremist narratives. The findings of this research contribute to the development of robust tools for studying SUD and promoting responsible communication online.

The Mpemba effect is the counterintuitive phenomenon in statistical physics for which a far-from-equilibrium state can relax toward equilibrium faster than a state closer to equilibrium. This effect has raised a great curiosity since long time and has been studied extensively in many classical and quantum systems. Here it is shown that the Mpemba effect can be observed in optics as well. Specifically, the process of light diffusion in finite-sized photonic lattices under incoherent (dephasing) dynamics is considered. Rather surprisingly, it is shown that certain highly-localized initial light distributions can diffuse faster than initial broadly delocalized distributions. The effect is illustrated by considering random walk of optical pulses in fiber-based temporal mesh lattices, which should provide an experimentally-accessible setup for the demonstration of the Mpemba effect in optics., Comment: A cool paper, 6 pages, 3 figures

HOMFLYPT polynomials of knots in the 3-sphere in symmetric representations satisfy recursion relations. Their geometric origin is holomorphic curves at infinity on knot conormals that determine a $D$-module with characteristic variety the Legendrian knot conormal augmention variety and with the recursion relations as operator polynomial generators [arXiv:1304.5778, arXiv:1803.04011]. We consider skein lifts of recursions and $D$-modules corresponding to skein valued open curve counts [arXiv:1901.08027] that encode HOMFLYPT polynomials colored by arbitrary partitions. We define a worldsheet skein module which is the universal target for skein curve counts and a corresponding $D$-module. We then consider the concrete example of the Legendrian conormal of the Hopf link. We show that the worldsheet skein $D$-module for the Hopf link conormal is generated by three operator polynomials that annihilate the skein valued partition function for any choice of Lagrangian filling and recursively determine it uniquely. We find Lagrangian fillings for any point in the augmentation variety and show that their skein valued partition functions admit quiver-like expansions where all holomorphic curves are generated by a small number of basic holomorphic disks and annuli and their multiple covers., Comment: 73 pages; v2 missing figures added

We study 3d $\mathcal{N}=2$ $U(1)$ Chern-Simons-matter QFT on a cylinder $C\times\mathbb{R}$. The topology of $C$ gives rise to BPS sectors of low-energy solitons known as kinky vortices, which interpolate between (possibly) different vacua at the ends of the cylinder and at the same time carry magnetic flux. We compute the spectrum of BPS vortices on the cylinder in an isolated Higgs vacuum, through the framework of \emph{warped} exponential networks, which we introduce. We then conjecture a relation between these and standard vortices on $\mathbb{R}^2$, which are related to genus-zero open Gromov-Witten invariants of toric branes. More specifically, we show that in the limit of large Fayet-Iliopoulos coupling, the spectrum of kinky vortices on $C$ undergoes an infinite sequence of wall-crossing transitions, and eventually stabilizes. We then propose an exact relation between a generating series of stabilized CFIV indices and the Gromov-Witten disk potential, and discuss its consequences for the structure of moduli spaces of vortices., Comment: 49 pages

Topological winding in non-Hermitian systems are generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models topological winding naturally arise from the dynamical evolution of the system and related to a new form of geometric phase. Here we investigate dynamical topological winding in non-Hermitian photonic mesh lattices, where the mean survival time of an optical pulse circulating in coupled fiber loops is quantized and robust against Hamiltonian deformations. The suggested photonic model could provide an experimentally accessible platform for the observation of non-Hermitian dynamical topological windings., Comment: selected as Editor's Pick by Optics Letters 5 pages, 3 figures

In the field of dissipative systems, the non-Hermitian skin effect has generated significant interest due to its unexpected implications. A system is said to exhibit a skin effect if its properties are largely affected by the boundary conditions. Despite the burgeoning interest, the potential impact of this phenomenon on emerging quantum technologies remains unexplored. In this work, we address this gap by demonstrating that quantum neural networks can exhibit this behavior and that skin effects, beyond their fundamental interest, can also be exploited in computational tasks. Specifically, we show that the performance of a given complex network used as a quantum reservoir computer is dictated solely by the boundary conditions of a dissipative line within its architecture. The closure of one (edge) link is found to drastically change the performance in time series processing proving the possibility to exploit skin effects for machine learning., Comment: Comments are welcome

This paper studies the space of monodromy data of second order $q$-difference equations through the framework of WKB analysis. We compute the connection matrices associated to the Stokes phenomenon of WKB wavefunctions and develop a general framework to parameterize monodromies of $q$-difference equations. Computations of monodromies are illustrated with explicit examples, including a $q$-Mathieu equation and its degenerations. In all examples we show that the monodromy around the origin of $\mathbb{C}^*$ admits an expansion in terms of Voros symbols, or exponentiated quantum periods, with integer coefficients. Physically these monodromies correspond to expectation values of Wilson line operators in five dimensional quantum field theories with minimal supersymmetry. In the case of the $q$-Mathieu equation, we show that the trace of the monodromy can be identified with the Hamiltonian of a corresponding $q$-Painlev\'e equation., Comment: 58 pages

Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the photon can be destroyed and the walk terminates. While for a classical random walk the photon is unavoidably destroyed by the traps, for a quantum walk the photon can remain alive and the walk continues forever. Such an intriguing behavior is illustrated by considering photonic random walks in synthetic mesh lattices with controllable decoherence, which enables to switch from quantum to classical random walks., Comment: 6 pages, 3 figures, accepted for publication in Optics Letters

Mobility edges (ME), separating Anderson-localized states from extended states, are known to arise in the single-particle energy spectrum of certain one-dimensional lattices with aperiodic order. Dephasing and decoherence effects are widely acknowledged to spoil Anderson localization and to enhance transport, suggesting that ME and localization are unlikely to be observable in the presence of dephasing. Here it is shown that, contrary to such a wisdom, ME can be created by pure dephasing effects in quasicrystals in which all states are delocalized under coherent dynamics. Since the lifetimes of localized states induced by dephasing effects can be extremely long, rather counter-intuitively decoherence can enhance localization of excitation in the lattice. The results are illustrated by considering photonic quantum walks in synthetic mesh lattices., Comment: 17 pages, 9 figures (main text + supplementary material), accepted for publication in the Physical Review Letters

The non-Hermitian skin effect describes the concentration of an extensive number of eigenstates near the boundaries of certain dissipative systems. This phenomenon has raised a huge interest in different areas of physics, including photonics, deeply expanding our understanding of non-Hermitian systems and opening up new avenues in both fundamental and applied aspects of topological phenomena. The skin effect has been associated to a nontrivial point-gap spectral topology and has been experimentally demonstrated in a variety of synthetic matter systems, including photonic lattices. In most of physical models exhibiting the non-Hermitian skin effect full or partial wave coherence is generally assumed. Here we push the concept of skin effect into the fully incoherent regime and show that rather generally (but not universally) the non-Hermitian skin effect persists under dephasing dynamics. The results are illustrated by considering incoherent light dynamics in non-Hermitian photonic quantum walks., Comment: to appear in Light: Sci. & Appl. (4 figures, draft version)

Anderson localization, i.e. the suppression of diffusion in lattices with random or incommensurate disorder, is a fragile interference phenomenon which is spoiled out in the presence of dephasing effects or fluctuating disorder. As a consequence, Anderson localization-delocalization phase transitions observed in Hermitian systems, such as in one-dimensional quasicrystals when the amplitude of the incommensurate potential is increased above a threshold, are washed out when dephasing effects are included. Here we consider localization-delocalization spectral phase transitions occurring in non-Hermitian quasicrystals with local incommensurate gain and loss, and show that, contrary to the Hermitian case, the non-Hermitian phase transition is robust against dephasing effects. The results are illustrated by considering synthetic quasicrystals in photonic mesh lattices.

The localization and scattering properties of potential wells or barriers uniformly moving on a lattice are strongly dependent on the drift velocity owing to violation of the Galilean invariance of the discrete Schr\"odinger equation. Here a type of localization-delocalization phase transition of algebraic type is unravelled, which does not require any kind of disorder and arises when a power-law potential well drifts fast on a lattice. While for an algebraic exponent $\alpha$ lower than the critical value $\alpha_c=1$ dynamical delocalization is observed, for $\alpha> \alpha_c$ asymptotic localization, corresponding to an asymptotic frozen dynamics, is instead realized. At the critical phase transition point $\alpha_=\alpha_c=1$ an oscillatory dynamics is found, corresponding to Bloch oscillations. An experimentally-accessible photonic platform for the observation of the predicted algebraic phase transition, based on light dynamics in synthetic mesh lattices, is suggested., Comment: 9 pages, 7 figures, to appear in Annalen der Physik (Wiley)

This study explores the integration of Lamarckian system into evolutionary robotics (ER), comparing it with the traditional Darwinian model across various environments. By adopting Lamarckian principles, where robots inherit learned traits, alongside Darwinian learning without inheritance, we investigate adaptation in dynamic settings. Our research, conducted in six distinct environmental setups, demonstrates that Lamarckian systems outperform Darwinian ones in adaptability and efficiency, particularly in challenging conditions. Our analysis highlights the critical role of the interplay between controller \& morphological evolution and environment adaptation, with parent-offspring similarities and newborn \&survivors before and after learning providing insights into the effectiveness of trait inheritance. Our findings suggest Lamarckian principles could significantly advance autonomous system design, highlighting the potential for more adaptable and robust robotic solutions in complex, real-world applications. These theoretical insights were validated using real physical robots, bridging the gap between simulation and practical application., Comment: Nature. arXiv admin note: substantial text overlap with arXiv:2309.13099; text overlap with arXiv:2303.12594, arXiv:2309.14387

Let $\ell$ and $p$ be distinct primes, and let $\Gamma$ be an abelian pro-$p$-group. We study the structure of the algebra $\Lambda:=\mathbb{Z}_\ell[[\Gamma]]$ and of $\Lambda$-modules. In the case $\Gamma\simeq \mathbb{Z}_p^d$, we consider a $\mathbb{Z}_p^d$-extension $K/k$ of a global field $k$ and use the structure theorems to provide explicit formulas for the orders and $\ell$-ranks of certain Iwasawa modules (namely $\ell$-class groups and $\ell$-Selmer groups) associated with the finite subextensions of $K$. We apply this new approach to provide different proofs and generalizations of results of Washington and Sinnott on $\ell$-class groups., Comment: (Very) Preliminary version. Comments are welcome

In classical mechanics, a particle cannot escape from an unbounded potential well. Naively, one would expect a similar result to hold in wave mechanics, since high barriers make tunneling difficult. However, this is not always the case and it is known that wave delocalization can arise in certain models with incommensurate unbounded potentials sustaining critical states, i.e. states neither fully extended nor fully localized. Here we introduce a different and broader class of unbounded potentials, which are not quasi-periodic and do not require any specially-tailored shape, where wave delocalization is observed. The results are illustrated by considering light dynamics in synthetic photonic lattices, which should provide a feasible platform for the experimental observation of wave delocalization in unbounded potentials., Comment: 7 pages, 4 figures

Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical gain and loss, provide a prime and simple physical platform for tailoring non-Hermitian Hamiltonians and for unveiling the intriguing interplay between disorder and non-Hermiticity. Here it is shown that in mosaic photonic lattices with on-site uncorrelated disorder or quasi-periodic order, the addition of uniform loss at alternating sites of the lattice results in the suppression or enhancement of wave spreading, thus providing a simple method for non-Hermitian control of wave transport in disordered systems. The results are illustrated by considering discrete-time quantum walks in synthetic photonic lattices., Comment: 5 pages, 4 figures, to appear in Appl. Phys. Lett. (special issue on non-Hermitian photonics)

A certain class of $A$-branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of $A$-branes associated with `wild' BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of $m$-herds spectral networks into a number $|\Omega|$ of basic connected objects, where $\Omega$ is the the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of $m$-Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry., Comment: 33+11 pages