Papers

We derive two quantum fluctuation relations for systems undergoing repeated projective measurements. These fluctuation relations characterize the work that can be extracted from a quantum device when a first-detection event triggers a mechanical operation leading to positive work production. The correction to the standard quantum Jarzynski equality depends logarithmically on the mean first-detection time for the time-reversed dynamics. Application of Jensen's inequality leads to fundamental limits on both the total work involved in the repeated measurements and final mechanical operation, and the extracted work alone. The general case of a device connected to an external environment is also considered.

A thermodynamic theory for transport coefficients in hard-sphere fluids is developed from a general expression for the Onsager matrix. The theory predicts the ratio $\sigma/\sigma_{\rm id}$, where $\sigma$ is a transport coefficient and $\sigma_{\rm id}$ denotes its dilute-gas value. This ratio depends exclusively on equilibrium thermodynamic properties and can therefore be computed directly from the equation of state. Compact expressions are obtained for the thermal conductivity, viscosity, and self-diffusion coefficient. These expressions quantitatively reproduce simulation data over almost the entire fluid range and, in the case of self-diffusion, significantly improve upon the predictions of Enskog kinetic theory. The results demonstrate that transport coefficients can be accurately described within a purely thermodynamic framework.

We study a minimal lattice model of active search-and-capture in which persistent random walkers locate and irreversibly capture immobile targets through a finite-range, mutually exclusive assignment rule. We measure the collective completion time $T_c$ as a function of the walkers' reorientation rate $\alpha$ and the search radius $R$. The dependence $T_c(\alpha)$ is non-monotonic, with a minimum at intermediate persistence whose depth decreases as $R$ grows. Capture kinetics show that $T_c$ is not a typical capture time but is governed by the extreme, late-time tail of the capture process, while the bulk of targets are captured much earlier; this tail is controlled mainly by the free-exploration phase rather than by the final directed approach. We then compare the baseline single-round assignment rule with cascading reassignment and with maximum-cardinality matching on a candidate graph. The two greedy policies (single-round and cascading) agree at very small $R$, whereas maximum-cardinality matching already produces a strong speedup at moderate $R$: improved matching reduces $T_c$ by factors of several at large $R$, and by more than an order of magnitude at moderate $R$. Thus, in this collective, depletion-coupled search problem, the assignment policy can control the capture time more strongly than the walkers' persistence.

The Monte Carlo sampling of the stochastic differential equations (SDEs) based on the quasiprobability distribution function, such as the Glauber–Sudarshan P, Wigner, and Husimi Q functions provides a powerful framework for investigating bosonic open quantum many-body dynamics described by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, while considering the effects of quantum fluctuations beyond the mean-field approximation. However, the stochastic Monte Carlo simulation is possible only when the corresponding Fokker–Planck equation has a positive-semidefinite diffusion matrix, and the general conditions for the diffusion matrix to be positive semidefinite have remained unclear. In this work, starting from the path integral formulation, we first derive the sufficient conditions under which the diffusion matrix is positive semidefinite for an arbitrary Hamiltonian, jump operators, and choice of quasiprobability distribution functions. We also analytically derive the corresponding SDEs to be solved. We then investigate the dynamics of the GKSL equation in the thermodynamic limit and show that, depending on the form of the jump operators, the mean-field approximation may fail to describe the dynamics accurately, making stochastic Monte Carlo simulations indispensable. Furthermore, we derive the sufficient conditions under which the higher-order quantum fluctuation terms beyond the Fokker–Planck description vanish identically, even when the jump operators contain quadratic terms. Under these conditions, whenever the corresponding SDEs can be derived, the stochastic Monte Carlo simulation reproduces the exact dynamics. These results clarify the conditions under which the stochastic Monte Carlo simulations are both feasible and necessary for accurately describing the dynamics governed by the GKSL equation in phase space.

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

We study the entanglement Hamiltonian of an infinite hopping chain in its ground state, after partial projective measurements in the occupation basis. For a segment separated by two measurement regions from the rest of the chain, we show that the reduced density matrix can be related to a grand-canonical state via a conformal mapping and a gauge transformation in the underlying field-theory description. The entanglement Hamiltonian is then described by a local inverse temperature that vanishes as a square root around the endpoints and is independent of the particular measurement outcome. In sharp contrast, the local chemical potential is shown to be related to the induced charge density in the segment. Hence the entanglement Hamiltonian of a post-selected state contains much more information on the measurement outcome than the respective entropy.

Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and Rényi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.

We study the critical dynamics arising from a time-dependent periodic homogenous source coupled to the order-parameter field, which drives a classical ferromagnetic system across a continuous transition. For this purpose, we consider the paradigmatic two-dimensional (2D) Ising model in the presence of a periodic magnetic field $h(t)=-A\, \cos (2\pi t/P)$, evolving under a purely relaxational dynamics at the critical temperature. We show that the periodic driving gives rise to a peculiar dynamic scaling behavior in the thermodynamic limit, arising from a nontrivial interplay among the time $t$, the amplitude $A$ and period $P$ of $h(t)$. The relevant scaling variables are $\tau=t/P$ and $\sigma=A P^\kappa$, with $\kappa = y_h/z$, where $y_h=(d+2-\eta)/2$ is the critical dimension of the magnetic field, and $z$ is dynamic exponent for the critical relaxational dynamics ($\kappa\approx 0.865$ for the 2D Ising model). The dynamic scaling behaviors of the magnetization and bond-energy density show an oscillatory behavior around a smooth curve which approaches a large-$\tau$ stationary behavior. We also briefly discuss the dynamic behavior of an Ising system driven across the critical point by a periodic time-varying temperature at zero magnetic field.

Entanglement is a key resource for quantum technologies. We show that protocols employing quantum Mpemba effects allow one to exponentially accelerate the generation of entanglement, or to slow down the decay thereof. Two entanglement Mpemba effects with different operational meaning are introduced, focusing either on the task of rapidly generating a certain threshold value for entanglement or on achieving the asymptotic steady-state value. We show that entanglement Mpemba effects depend on the chosen entanglement measure. Using cluster elimination methods, many-body quantum systems also benefit from the exponential speedup of entanglement generation, as we demonstrate for a dissipative long-range Ising chain.

We calculated shear viscosities of 15 neat molecular liquids from equilibrium molecular dynamics (MD) simulations using the OrthoBoXY approach and compare them to viscosities calculated via the Green-Kubo method. Data from both methods agree very well. Here, we show how to avoid pitfalls while computing the OrthoBoXY-data to obtain optimal results. From simulations of multiple system sizes, we could verify that the viscosity of molecular liquids is not influenced by finite size effects down to systems as small as 250 molecules. Moreover, we demonstrate that also the standard error of the viscosity is nearly independent of the system size. This is shown to be a consequence of a compensation effect of an increasing accuracy of the self-diffusion coefficients with increasing systems-size and the system-size dependent weighting according to the OrthoBoXY-equation. As a consequence, we suggest that it is preferable to run simulations of smaller systems with longer simulation times rather than larger systems with shorter simulation runs. In addition, we discuss a refinement of the recently introduced "recipe" for OrthoBoXY simulations block-lengths $\tau_\mathrm{block}$. Based on data from simulations with varying run-lengths, we suggest the following modification: for highly viscous systems, the value of $\tau_\mathrm{block}$ might safely be scaled by a factor of $1/8$, significantly reducing the computational resources needed. For less viscous systems, the value of $\tau_\mathrm{block}$ might safely be scaled by a factor of $1/4$. For systems with high fluidity, the value of $\tau_\mathrm{block}$ should not be scaled down in order to achieve reliable results. When using a smaller system size of 250 molecules, these refinements are leading up to a 24-fold reduction in computational cost compared to the previous recommended set-up without sacrificing numerical accuracy.

Novel phases, beyond long-range order in two dimensions, have continued to be discovered within flocking models, establishing flocking as one of the pivotal paradigms in active matter. However, much of the discussion around “Malthusian” (constant density) flocks, an analytically more tractable alternative to the Vicsek model, has centred around the scaling exponents governing the intermediate regime prior to the proliferation of asters, leaving open the question of what other phases the model might display. Here, we study the two-dimensional dynamics of Malthusian flocks and identify a previously unnoticed phase, where the dynamics is that of the equilibrium XY Model. By identifying the symmetries of the model, we derive the effective equations of motion for the Goldstone modes and analyse the spin-wave fluctuations. We identify a novel critical point separating two distinct phases and, using a perturbative RG procedure, determine the RG flows in its vicinity. This allows us to calculate the universal scaling behaviour at the critical point, along with its logarithmic corrections. The novel phase transition here is due to the interaction of activity and spin-waves, unlike the equilibrium counterpart, which undergoes a phase transition in effective degrees of freedom, namely vortices. Nevertheless, the RG flows are similar to those of the Berezinskii-Kosterlitz-Thouless transition, and we show that for sufficiently strong noise, the activity becomes irrelevant and the system crosses over to the equilibrium XY universality class.

We investigate the entanglement entropy of a class of $N$-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $\Omega$. The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.

Majority threshold dynamics, in which each agent adopts the dominant state in a weighted neighborhood, relaxes a binary field toward consensus or stripes. We study what happens when this rule is made irreversible: each agent, interacting through a Gaussian kernel on a lattice, may flip out of its local weighted minority at most once. The reversible form is threshold dynamics of Merriman-Bence-Osher type, an exactly solvable calibration in which interfaces move by mean curvature with closed-form lattice pinning and mobility. Irreversibility changes the outcome. From random initial conditions, the one-flip rule freezes balanced non-consensus labyrinths that reversible relaxation drives away. The patterned regime is a window of initial spin compositions around equal balance, narrowing as the interaction range grows, controlled by a standardized bias whose onset is independent of scale over a fourfold range. The frozen morphology is arrested coarsening: bicontinuous at balance, with a feature width that grows sublinearly and falls below the interaction range at large scales. We determine the mechanism by intervention. Fixing the initial condition while varying the update order shows that the coarse domain layout is deterministic, while the update order enters only in a secondary first-passage race that fine-tunes the wall positions the deterministic dynamics has already set. Those walls are marked by frustration: agents frozen against their own local field. This signature is identically absent from any reversible relaxation, is overwhelmingly interfacial, and carries almost none of the pattern's large-scale shape.

Bottom-up coarse-graining expands the length and time scales accessible to molecular dynamics (MD) simulations, but information loss can hinder accurate representation of multistate phenomena in complex biomolecular dynamics. Ultra-Coarse-Graining (UCG) projects discrete "quantum-like" extended degrees of freedom, or "internal states," onto coarse-grained (CG) molecules, extending CG model expressiveness. The rapid-local-equilibrium (RLE) approximation in UCG depends on user-defined collective variables (CVs, e.g., local density) and neglects correlations between internal states within and between CG molecules. We present Self-Consistent UCG (SC-UCG), which uses the underlying UCG interactions directly to assign internal states without designing CVs in the CG ensemble. During simulation, internal state probabilities are determined self-consistently through graph message passing. We enhance the RLE Hamiltonian with the Bethe approximation and AI-based inference to represent explicit correlations between UCG beads. For force-field training, we develop Multilayer Internal State Consistency (MISC), a machine-learning method derived from relative entropy minimization that avoids iterative sampling of intermediate force fields. We apply SC-UCG to a tetramer exhibiting a second-order symmetry-breaking phase transition from a supercritical racemic fluid to subcritical D-rich and L-rich fluids. SC-UCG captures collective switching of internal states in the subcritical region and recapitulates the phase transition across temperatures, despite being trained on a single-temperature dataset.

We are interested in modelling superfluid helium-4, the common isotope of helium, of atomic number 4. We present a mathematically solvable toy model of the phase transition between the normal liquid and superfluid phases and use it to show how an order parameter can be obtained for the superfluid.

We adapt tools from the theory of quantum random walks to investigate slow relaxation dynamics through the many-body state graph. Specifically, we construct a probe of heterogeneity between basis states defined using hitting times derived from the unitary time-evolution operator. We find that the state-graph geometry, encoded by the pairwise hitting time of basis states, is a highly sensitive indicator of slow relaxation dynamics in a variety of systems. We study three paradigmatic models: the Rosenzweig-Porter model, the quantum East model, and the triangular lattice gas model, exhibiting a sudden onset of slow dynamics upon tuning of a control parameter. As a global characterization of the graph geometry, we analyze the spectral radius of the hitting matrix. We find that it increases sharply at the onset of slow dynamics, spanning many orders of magnitude, with a characteristic crossing point at the transition. Our work provides a geometric framework for describing and identifying phases with slow relaxation using a unified graph-theoretic formalism.

Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling.

Bistability, the existence of two alternative stable states with distinct basins of attraction, is common across ecology and many other biological, chemical, and physical systems. In spatially extended systems, the invasion of one state by the other proceeds through nucleation, the fluctuation-driven growth of a droplet beyond a critical size. Classical Nucleation Theory (CNT) quantifies this process using the energy landscape, but this description relies on detailed balance, the condition of microscopic reversibility that holds at equilibrium. Ecological dynamics generally violate detailed balance and are described not by a single scalar field but by several coupled, non-conserved abundances–a vector order parameter–for which no general nucleation theory exists. Here we derive such a theory for reaction-diffusion systems with a non-conserved vector order parameter, valid both close to the binodal, where invasion proceeds through propagating fronts, and close to the spinodal, where the metastable state loses stability. Extensive numerical computations of the quasipotential confirm the theory in both regimes. We show that the mathematical structure of CNT survives out of equilibrium, once energetic quantities are replaced by dynamical properties of fronts: the front speed plays the role of the bulk free-energy difference between phases, and the diffusivity that of the surface tension. Applied to the two-species Lotka-Volterra model, an archetypal system of bistable ecological antagonism, our theory shows that strong interspecific competition generates a pronounced depletion region within fronts, where the total abundance falls well below carrying capacity. This vectorial structure, invisible to a scalar description based on species frequency alone, makes invasion exponentially harder as competition strengthens at fixed competitive advantage–a prediction testable in microbial systems.

Exceptional points (EP's) are a hallmark of non-Hermitian quantum systems. We show that momentum-space deformation provides a general design principle for creating and controlling EP's in quadratic many-body Hamiltonians. We identify universal criteria for the momentum sectors to host EP's and the corresponding critical deformation strengths, while revealing that a single momentum-sector EP induces quite remarkably an exponential proliferation of many-body eigenvector coalescences. We further establish EP's as a universal mechanism for purifying arbitrary mixed quantum states, uncovering distinct purification regimes and a fundamental odd-even system-size dichotomy in the thermodynamic limit. Our framework also provides a systematic reverse-engineering protocol for generating short- and long-range, reciprocal and nonreciprocal non-Hermitian quantum matter, together with an explicit Lindblad embedding. These results thus establish momentum-space deformation as a unified route to exceptional-point engineering and controlled design of many-body non-Hermitian quantum systems.

In recent years, non-reciprocity has been explored as a ubiquitous manifestation of non-equilibrium activity at the microscopic scales for various active matter systems, from mixtures of chemically active enzymes, colloids, and droplets, to engineered light-controlled active colloids and robotic meta-materials. A commonly used minimal model to describe the dynamics of a binary mixture of conserved species with non-reciprocal interactions is the non-reciprocal Cahn-Hilliard (NRCH) model. The model is characterized by a temperature-like tuning parameter, which can trigger phase separation, and a non-reciprocal coupling, which can lead to the formation of spatio-temporal patterns, as it represents an intrinsic source of non-equilibrium activity and breaks parity and time-reversal symmetries. Here, we study the scaling behavior of the NRCH model near the critical point using perturbative dynamical renormalization group techniques. We find that structural and dynamical correlations are controlled by different correlation lengths, both of which diverge at the critical point, but governed by different scaling laws. In particular, while the structural correlations are always controlled by temperature and the classical Wilson-Fisher critical exponent, the dynamical correlation length exhibits multiple scaling regimes in which either temperature or non-reciprocal coupling can dominate as the key tuning parameter, with a new critical exponent characterizing the divergence. The critical point corresponds to a conserved equilibrium-like dynamics with odd mobility, which we denote as the odd Cahn-Hilliard (OCH) model. Our findings may have important implications on how living systems can control phase separation and spatio-temporal pattern formation using the rates of catalytic reactions, and in general metabolism, as control parameters.

Transport in fluids is generally reduced to continuum laws parametrized by bulk coefficients and effective interfacial parameters, such as viscosities, diffusivities, slip lengths, and interfacial resistances. This description becomes incomplete at the nanoscale, where spatial heterogeneity, molecular structure, and finite relaxation times are inseparable from the transport process. Here we formulate coupled transport in nanoconfined fluids as a space–time-resolved Onsager response matrix and extract it from equilibrium molecular dynamics simulations. Applied to a confined charged fluid, the framework resolves the nonlocal and transient pathways coupling particle, solute, heat, and charge transport. Momentum transport appears as a long-lived, nonlocal hydrodynamic mode, whereas charge transport relaxes rapidly through localized ionic friction. Off-diagonal responses reveal distinct projected dynamics, providing a microscopic basis for nonlocal, history-dependent transport laws.

Although Arnoldi reduction of a generally non-Hermitian Hamiltonian yields an upper Hessenberg matrix rather than the tridiagonal form of Hermitian Lanczos theory, we show that a closed Toda sector survives in its diagonal and subdiagonal coefficients. For a fixed finite-dimensional Hamiltonian and a cyclic state vector deformed holomorphically, the Krylov Gram determinants are $\tau$ functions of the finite two-dimensional Toda lattice, whose Flaschka variables coincide exactly with these Arnoldi coefficients. The Toda dynamics therefore closes on this sector without determining the remaining upper Hessenberg entries. The subdiagonal part of the same sector also has a direct geometric meaning: the squared subdiagonal coefficients determine both the Fubini–Study metric and the Berry curvature of holomorphic Krylov subspaces, whereas the geometric quantities associated with subspaces lost at Arnoldi breakdown cease to be defined. Along a smooth real path in the cyclic region, the Arnoldi-frame connection further provides a Hermitian tridiagonal generator of exact isospectral transport. When added to the Arnoldi matrix, this generator cancels transitions between instantaneous eigenspaces and realizes counterdiabatic driving whenever the matrix is diagonalizable with a nondegenerate spectrum.

Established routes to structural chirality in inorganic crystals depend on symmetry-lowering atomic displacements of an achiral parent structure. We show that chirality can instead be forced by the ordering of two anion species over the sites of an achiral parent, independent of atomic displacements. ReO$_3$-type oxyfluorides with a 2:1 anion stoichiometry, such as NbO$_2$F, exhibit two ordering patterns: cis octahedral coordination and period-three anion-chain ordering, both rooted in the off-centring of $d^0$ cations. By direct enumeration, we prove that every configuration combining both orderings on the smallest commensurate cell is chiral, belonging to a Sohncke space group. For the specific case of NbO$_2$F, density-functional theory calculations predict that the ground state is the maximally symmetric chiral configuration. Wang-Landau Monte Carlo simulations of a DFT-trained cluster-expansion model predict an equilibrium chiral phase up to a first-order transition at 494 K. These results establish configurational ordering as a chemically realisable route to structural chirality, and mark heteroanionic materials with analogous ordering chemistry as candidates for a new class of chiral functional materials.

Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbulent and laminar states coexist. In the lower range, $Re\in (1750,2300)$, turbulence appears in the form of localized traveling structures called "puffs", which form long-lived chaotic dynamical states, whose stochastic decays and splits control the steady state intermittency. At the other end, $Re\in (2300,3000)$, puffs are replaced by an extended turbulent state, with laminar pockets intermittently forming and disappearing within it. Using direct numerical simulations of pipe flow at $Re = 2400, 2450, 2500, 2550$, we provide evidence that these laminar gaps form a distinct dynamical state analogous to puffs: a traveling laminar pocket in a turbulent surrounding, stabilized by a shear-dependent self-tuning mechanism. We analyse the mean spatial profile of these gaps and show that their lifetimes are exponentially distributed, suggesting that gap closing corresponds to an escape from a chaotic saddle. Finally, we suggest these laminar gaps become unstable and disappear at a finite Reynolds number, $Re\sim 2900$, which can be interpreted as the onset point of spatially and temporally homogeneous turbulence.

Here, pressure-controlled drainage is formulated as bond percolation with trapping on the pore-network graph, establishing a direct connection between percolation theory and pressure–saturation relations. In two dimensions, the deviation of the residual saturation from its non-vanishing thermodynamic limit obeys a finite-size scaling law with exponent $\delta \approx 0.25$, independent of microscopic details of the lattice. In three dimensions, finite-size corrections decay more rapidly ($\delta \approx 0.75$), while the asymptotic residual saturation remains finite and depends on coordination number. This extends the standard invasion-percolation picture beyond the breakthrough state, where the invading cluster is fractal and the invaded-phase saturation vanishes in the infinite-size limit.

We propose an improved mean-field analysis of cellular automata models of single-lane vehicular traffic. By combining aspects of the Car-Oriented-Mean-Field (COMF) theory and the 2-site cluster method, which have been previously successfully applied to similar models, we aim to capture both short- and long-range correlations more accurately. In contrast to classical mean-field theories, the improved method is well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules. The improved accuracy and new physical insights are illustrated through an application to the VDR model with $v_{\text{max}}=1$.

We propose and numerically validate an efficient single-eigenstate diagnostic for the eigenstate thermalization hypothesis (ETH) based on a perturbed eigenstate quench protocol. By introducing a weak random perturbation to an energy eigenstate to break its stationarity, we characterize the time-averaged subsystem evolution speed as a function of the subsystem-to-total system size ratio. The diagnostic relies on a robust qualitative distinction: eigenstates satisfying ETH exhibit an S-shaped curve with a clear inflection point near half the system size, while ETH-violating eigenstates display a convex J-shaped profile. We benchmark the criterion across paradigmatic one-dimensional spin chains covering chaotic, integrable, many-body localized, and quantum many-body scar regimes, obtaining full agreement with established thermalization phenomenology. Our method circumvents the need for explicit thermal ensemble construction, providing a robust, experimentally feasible probe of eigenstate thermalization at the single-eigenstate level.

We derive an analytical expression for the steady-state quantum statistics of periodically driven quantum systems coupled to a bath using the nonequilibrium Green's function (NEGF) formalism. By embedding Floquet theory into NEGF, we obtain closed expressions for the retarded, advanced, and lesser Green's functions in the Floquet representation, yielding the Floquet Fermi distribution in which the steady-state occupation is expressed as a weighted sum of Fermi functions shifted by integer multiples of the driving frequency. The weights are determined solely by the Fourier components of the micromotion operator, providing a transparent interpretation of Floquet sideband occupations. Our analysis extends beyond the diagonal commuting Hamiltonians treated in earlier work, and further shows that the robust Floquet distribution remains valid for a broad class of weakly coupled bath spectral functions beyond the ideal featureless-bath approximation. Finally, we establish a Floquet version of the Landauer formula for the DC part of the current, in which the equilibrium Fermi functions are replaced by their Floquet-modified counterparts. Together, these results provide a coherent description of Floquet quantum statistics and transport in periodically driven open quantum systems.

We reconstruct the 2PI vertex $\Gamma(k,p;q)$ from Monte Carlo measurements of the connected two-particle correlator for the two-dimensional single-component $\phi^4$ lattice field theory and follow it across the Ising transition. Resolving the vertex in the irreducible representations of the point group $C_{4v}$, we find that the instability is driven by the $A_1$ (ferromagnetic) channel at zero transfer, whose leading eigenvalue of the symmetrized Bethe–Salpeter kernel approaches unity. Substantial $B_1$ (nematic) and $B_2$ (diagonal nematic) contributions cooperate with $A_1$ across all system sizes, highlighting that the soft sector is multidimensional. In real space, the vertex is short-ranged away from criticality while it develops a power-law tail at the critical point. In the ordered phase, the $q=0$ eigenvalue collapses because the ferromagnetic weight has condensed into the (one-particle-reducible) order parameter (or collective coordinate for a finite system), although finite-momentum fluctuations persist. By stripping the crossed-channel ladders, we obtain the fully irreducible vertex, which is a local contact – to a very good approximation. Inserted into the parquet and Schwinger–Dyson equations, this contact reproduces the Monte Carlo self-energy with an accuracy better than one-tenth of a percent. This provides a first-principles benchmark of the dynamical local-vertex approximation (D$\Gamma$A). Additionally, we demonstrate that in the critical region, the physical solution of the parquet equations behaves as a repulsive fixed point, driven initially by a single order-parameter mode.

We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.