Papers

We derive exact finite-size nonperturbative representations of equilibrium modal occupations and related statistics for three representative nonlinear systems: the Majda-McLaughlin-Tabak dispersive-wave model, the Fermi-Pasta-Ulam-Tsingou beta anharmonic chain, and the discrete nonlinear Schrodinger lattice field. Independent simulations confirm the predictions from weak to strong nonlinearity. For DNLS, the theory remains accurate across the weak-coupling quasicondensation crossover, where large low-mode occupations and long-range coherence amplify interaction effects even when the bare nonlinear coefficient is small. The finite-ring DNLS occupations are further resolved into a positive sum of Rayleigh-Jeans channels with distinct correlation lengths, explaining when a single Rayleigh-Jeans law applies and why it fails near quasicondensation. In MMT and DNLS, the exact occupations also determine the mean modal frequencies even when the dynamical spectra broaden or split. The nonperturbative results allow a direct assessment of two representative perturbative approaches. Treating the mean interaction appropriately yields accurate low-order approximations, including at strong nonlinearity. At higher orders, however, the corrections cease to decrease and successive approximations oscillate with increasing amplitude; both finite-order approaches also fail near weak-coupling quasicondensation. Thus neither low-order agreement nor a small bare coupling guarantees a reliable perturbative description. The results establish nonperturbative equilibrium theory for widely used nonlinear wave and lattice models and provide a quantitative basis for modal distributions of energy, particles, and optical power in nonlinear optics, dispersive waves, anharmonic lattices, and cold-atom systems.

Parameterized quantum circuits require repeated measurements to estimate objective gradients, making the number of circuit evaluations a central resource. Simultaneous perturbation stochastic approximation (SPSA) is widely used because it obtains a full gradient estimate from only two cost evaluations, independently of the number of parameters. We analyze the random perturbation for the structured Fourier landscapes generated by quantum circuits. For a finite update width, we derive the exact mode-by-mode response of the mean Rademacher estimator and show that it selectively suppresses modes involving many parameters. For general generators, the filtered mean field need not be conservative. We derive its sampling variance, compare it with Gaussian random-direction smoothing, and formulate the resulting stochastic dynamics through a Fokker–Planck equation. The non-conservative field generates acceleration to the steady state and the global minimum of the cost function by gradually decreasing the parameters in SPSA.

We study a two-dimensional Gaussian Rouse chain divided into two contiguous blocks with different local friction coefficients but identical Hookean elasticity. In quiescent conditions, friction heterogeneity leaves the continuous-time equilibrium Gaussian conformation unchanged while producing distinct block mobilities and a modified generalized relaxation spectrum. The exact friction-weighted translational diffusion coefficient retains the scaling $D_\gamma\propto N^{-1}$, with a friction-dependent prefactor; the corresponding diffusion law and generalized-mode formulation extend beyond the diblock to more general local friction profiles. We then place the chain in an incompressible Batchelor-Kraichnan random flow. Under a common external flow, the high-friction block becomes more extended than the low-friction block. The deformation asymmetry strengthens with friction contrast and develops across the weak- to moderate-flow regime, remaining clearly visible at the strongest finite-time conditions. It also persists when the chain-specific longest-mode Weissenberg number is matched across friction ratios, showing that, within the same finite-time protocol, the effect is not accounted for solely by a shift of the global relaxation timescale. In generalized-mode coordinates, the smooth random strain does not directly mix mode indices and preferentially amplifies the slowest mode. At larger flow strengths, extension distributions broaden markedly and exhibit pronounced temporal drift over the simulated time window. Since all simulated chain-specific longest-mode Weissenberg numbers remain below unity, this drift is interpreted as slow convergence toward the broad, power-law-tailed stationary Hookean regime near the coil-stretch threshold. Overall, friction heterogeneity alone is sufficient to redistribute deformation along an otherwise mechanically uniform polymer.

Lee-Yang theorems are a powerful tool for studying many-body systems, with applications ranging from analyzing phase transitions to proving the efficiency of certain classical and quantum algorithms. In this work, we prove a Lee-Yang zero-freeness theorem for the partition function of a broad class of interacting fermion models, implying the existence of a provably efficient quantum algorithm for estimating their ground-state energies. This class includes several well-known models such as the attractive Hubbard model, repulsive Hubbard model on bipartite graphs, and the interacting Hofstadter model. Our results also rigorously establish the nonexistence of phase transitions in these models in the presence of a nonzero local external field.

The Green-Kubo (GK) method which is used to obtain the shear viscosity of a model liquid in equilibrium molecular dynamics (MD) often requires long simulation times to obtain acceptable statistics. This work extends the GK approach to include spatial correlations. The total shear stress in the GK expression is split into a grid of its components in contiguous volumes. In doing this, the autocorrelation of the total system stress can be rewritten as the cross-correlation of the subvolume stresses. This provides a novel real-space insight into the liquid structure, something previously only treated in Fourier space by liquid-state theory. A novel travelling wave like structure is exposed that is shown to be well fitted by a leading Gaussian pulse added to a second negative Gaussian for the bounce back. The fitting parameters include the wave position, magnitude and width which show deep insights into the liquid property. The wave moves at the speed of sound over short times before decreasing in speed with the square root of time, while the wave packet spreads out also as the square root of time. The magnitude is decreasing with form $t^{-3/2}$, a result with strong significance in the history of MD simulation. These fitted forms mean the entire spatial temporal response of the liquid can be modelled in closed form by fitting to data, with short term requiring MD and the long time and distances approximated by the Gaussian form. By limiting the correlation to localized interactions the longer range contribution, which essentially only contribute to the noise, can be eliminated. This looks like a promising approach to model viscosity by taking short MD runs and fitting the long time behaviour.

The continuity equation serves as a fundamental principle for mass transport in continuous media. While its mathematical structure mirrors that of probability transport and the Liouville equation, an informational interpretation of macroscopic fluid flow is less commonly explored in engineering contexts. This paper treats fluid density as a spatial probability density function, modeling macroscopic motion as the continuous transport of uncertainty. I derive the temporal evolution of Shannon entropy under general flow conditions, establishing how entropy generation depends on macroscopic compressibility and microscopic diffusion. Microscopic diffusion is shown to act as a strictly positive entropy source governed exactly by local Fisher Information. Furthermore, the framework yields an explicit algebraic scaling law characterizing the equilibrium thickness of compressive mixing layers at a local Peclet number of unity. The theoretical model is computationally validated through finite-difference simulations of one-dimensional canonical flows and advection-diffusion within a three-dimensional, spatially varying Arnold-Beltrami-Childress (ABC) flow, yielding a mean relative error of $0.001$. The framework provides an analytical perspective on thermodynamic irreversibility, with potential applications to turbulence modeling, thermal entropy generation in heat exchangers, in-cylinder mixing in internal combustion engines, and aerodynamic flows.

We investigate non-Hermitian quantum phase transitions driven by staggered imaginary Dzyaloshinskii–Moriya (DM) interactions in a transverse-field $XY$ chain. By virtue of a staggered nonunitary transformation, we exactly diagonalize the Hamiltonian. For $D<1$, this procedure maps the non-Hermitian model onto a standard Hermitian $XY$ chain, allowing analytical derivation of the full phase boundaries. The parameter line $D=1$ forms an exceptional boundary with coalesced quasiparticle eigenvalues and eigenvectors, while the entire $D>1$ regime falls into the $\mathcal{RT}$-symmetry-broken phase containing two distinct $z$-ferromagnetic phases. We examine common quantum-information probes and show that conventional measures, such as entanglement entropy, quantum discord, and quantum coherence, fail to capture the $\mathcal{RT}$ symmetry-breaking transition. To address this deficiency, we propose a novel coherence measure $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ based on $\mathcal{RT}$ symmetry and complex-conjugate eigenpair correlations. Embedding intrinsic non-Hermitian information of left and right eigenstates, $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ reliably identifies the $\mathcal{RT}$ symmetry-breaking transition and accurately resolves all magnetic phase boundaries.

Kinetic Ising models are widely used to describe binary opinion dynamics, but their microscopic validity has rarely been tested empirically. Here, we infer the transition probabilities governing opinion updates from a year-long online social network and show that they are accurately described by an Ising heat-bath dynamics. The inferred parameters admit a direct sociological interpretation: the external field quantifies intrinsic bias, the coupling strength measures social influence, and a persistence term captures temporal inertia. We further show that persistence is positively correlated with node degree, while both persistence and interaction strength are strongly correlated with global network heterogeneity and clustering. Using the inferred time-dependent parameters in Monte Carlo simulations on the empirical temporal networks, we accurately reproduce the observed response functions, flip probabilities, and macroscopic opinion dynamics. Within the Twitter climate debate, our results provide direct empirical support for a kinetic Ising description of online opinion formation and establish a quantitative link between microscopic social behavior and evolving network topology.

Diatomic molecules consisting of one spin-1/2 ($\sigma$) and one spin-1 ($S$) atoms are put at each site of the Bethe lattice (BL) of the coordination number $q=3, 4$, or 6. Alongside the ferromagnetic (FM) interactions of individual atoms within a molecule, the molecules are permitted to engage in ferromagnetic interactions with their nearest neighbors (NN) through diverse bilinear interaction parameters $J$. The spin-1 sites are also under the influence of crystal field $D$. The phase diagrams on the ($D, T$) planes for a given $q$ are obtained by investigating the thermal variations of magnetizations for the case with zero external magnetic field $(H)$. It is discovered that the phase diagrams rely on $q$ both qualitatively and quantitatively. The crystal field is also included which operates only on the spin-1 sites. Three separate FM phases are observed with ($\sigma,S$) being $(1/2,1), (1/2,0)$ at the ground state level and a phase region with small magnetization (SM) values at a higher temperature range. In addition to the reentrant behavior in the transition zone from one phase to the other, the model produces first- and second-order phase transitions. Additionally, the impact of $H$ on the magnetization curves is examined, yielding quite intriguing findings.

We develop a multiscale approach for incorporating molecular-scale transport information into computationally efficient models of ion transport through nanopores. A radially varying effective diffusion coefficient profile is fitted to radial conductivity profiles obtained from explicit-water molecular dynamics (MD) simulations. The fitting is performed within the NP+LEMC framework, which combines the Nernst–Planck equation with Local Equilibrium Monte Carlo to account for ion correlations beyond mean-field approximation. We apply the approach to NaCl, CaCl$_2$, and their mixtures in a negatively charged silica nanopore. The resulting diffusion coefficient profiles reproduce the radial current distributions of the MD simulations, including the strong suppression of ionic mobility near the pore wall that cannot be captured by a spatially constant diffusion coefficient inside the pore. NaCl and CaCl$_2$ exhibit qualitatively different transport behavior: the former is cation selective due to enhanced near-wall Na$^+$ conduction, whereas the latter shows weak anion selectivity because strongly bound Ca$^{2+}$ ions have strongly suppressed mobility near the surface. For NaCl–CaCl$_2$ mixtures, preferential Ca$^{2+}$ binding leads to nonlinear changes in ionic conductance. The approach establishes a bridge between experimentally relevant device behavior and computationally efficient reduced models, with explicit-water MD providing the molecular-scale information that can be incorporated into the effective transport coefficients.

In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochastic resetting optimizes these ordered arrivals for all arrival ranks. We construct an exact finite-$N$ reference for non-interacting Brownian searchers and obtain the mean ordered first-passage time $\langle T_{(k)} \rangle$ and its optimal resetting rate $r_k^*$. For searchers with identical initial conditions, $r_k^*$ increases monotonically with arrival rank and, with increasing population size, approaches the known large-$N$ quantile limit where a finite optimum appears only above a critical rank fraction $\phi_c \simeq 0.412$. Spatial heterogeneity qualitatively reorganizes this sequence, shifting its maximum from late to early ranks even without particle interactions. We then compare this baseline with Brownian colloid experiments, interacting active Brownian particles, and a collective autochemotactic search with persistent environmental memory. Across these systems, sensitivity to resetting increases strongly with arrival rank, while deviations from appropriate non-interacting references reveal the influence of direct interactions, finite return overhead, and environmental memory. Our results show that optimal resetting in multiparticle search is governed by the required completion rank and must be evaluated relative to protocol- and geometry-matched baselines.

Equilibrium phase transitions are conventionally categorized into first-order and continuous phase transitions. Far from equilibrium, many new transitions emerge during the real-time evolution of quantum systems. One such transition is the temporal entanglement transition (TET) characterized by the nonanalyticity of the entanglement spectrum. So far, all TETs occur through a linear crossing of the leading Schmidt levels in different symmetry sectors, resembling a first-order transition in equilibrium. A natural question is whether a continuous TET, featured by entanglement spectrum touching, is possible. In a periodically driven transverse $J_1$-$J_2$ Ising chain, we show that two such TETs can merge into a critical touching, where the leading levels meet tangentially without exchanging, realizing the temporal analog of a continuous phase transition. Near the critical frequency, the temporal separation of the two TETs vanishes continuously and its derivative with respect to frequency diverges, a nonanalytic signature that is absent in a single first-order TET. This finite-frequency touching arises from the interplay between a weak symmetry-preserving perturbation of the product initial state and Floquet corrections. Further extending the frequency scan reveals a second critical touching at a higher frequency, and the two critical frequencies enclose a finite window with no TET. These features can be understood from a second-order Floquet Hamiltonian and persist across a broad range of coupling ratios, establishing the critical touching as a distinct form of TET.

We introduce a self-adaptive Floquet system based on a quantum kicked rotor, in which the kicking strength itself becomes a dynamical variable generated self-consistently through cavity-mediated feedback. A superradiant transition gives rise to cavity-mediated kicking and two competing instability channels, symmetric and antisymmetric, which provide a unified organizing principle for the nonequilibrium Floquet phases. For resonant kicking, their competition produces double-kick dynamics that support resonant ballistic transport and an emergent antiresonance with period-quadrupled rotor evolution, arising from a balance between the two instability channels. Remarkably, for incommensurate kicking, the antisymmetric instability stabilizes a robust period-doubled localized phase with persistent subharmonic dynamics despite the underlying incommensurate driving, revealing localized temporal order absent in conventional kicked rotors. As the feedback strength increases, correlated temporal fluctuations progressively suppress quantum interference, driving crossovers from period-doubled localization to irregular localization and eventually to subdiffusive transport. Our results establish a general framework for self-adaptive quantum-chaotic dynamics and demonstrate how dynamical feedback can fundamentally reshape transport, localization, and temporal order in driven quantum systems.

We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+\sigma)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the critical fugacity $z_c$, the universal Binder ratio $Q_N^c$, the correlation-length exponent $\nu$, and the anomalous dimension $\eta$. For $\sigma>1$, the critical fugacity varies smoothly with $\sigma$, while the Binder ratio and the critical exponents remain consistent with the short-range universality class. For $\sigma \le 1$, by contrast, the results clearly depart from short-range behavior, identifying $\sigma=1$ as the boundary between long-range and short-range regimes. In the long-range Wilson-Fisher regime with $1/2 < \sigma \leq 1$, $\eta$ agrees with the long-range Gaussian-fixed-point prediction $\eta_{\mathrm{GFP}}=2-\sigma$, whereas $Q_N^c$ and $\nu$ vary nontrivially with $\sigma$ and exhibit discontinuous jumps at $\sigma=1$. These findings are in good agreement with the recently proposed universality diagram in the $(d,\sigma)$ plane for long-range O$(n)$ models, with the self-avoiding walk corresponding to the $n\to0$ limit.

We revisit the combinatorial loop-equation method for computing planar disc amplitudes in multi-matrix models with polynomial potentials. We develop a procedure which organises the Schwinger-Dyson constraints by the level of their boundary insertions and, when the resulting system closes, produces an algebraic equation for the planar disc function. Using this method we recover the disc partition functions associated with fixed, mixed, and free boundary conditions in the three-state Potts model, previously obtained by saddle-point methods. As a novelty we derive an algebraic equation for the fixed-boundary resolvent of the three-state Potts model with unequal quadratic and cubic couplings. We further show one can compute the disc partition function for several unsolved two- and three-matrix models. These examples demonstrate that loop equations provide a practical route to identifying and solving sectors of multi-matrix models beyond the standard one- and two-matrix cases.

We construct boundary observables that retain memory for a quantified time window in quantum chains whose basis configurations carry a conserved ordered product of matrix labels. Under strong-irreducibility and proximality hypotheses on the label matrices, projective contraction of random matrix products localizes a conserved charge in the root-mean-square over uniform basis configurations. A finite-time inequality then converts readout overlap and reset leakage into a correlation bound: for a conserved reference observable $H$, a readout $F$, accumulated squared leakage $\mathcal B$, and the normalized Hilbert-Schmidt inner product, $\langle F,\Phi(F)\rangle\ge 2\langle H,F\rangle^2/(\|H\|_2^2+\mathcal B)-\|F\|_2^2$. Here $\Phi$ is a sequence of conserving channels and partial resets. The bound holds for each such circuit, without averaging its gates. It yields an exponential memory window in the distance from the noisy region, with quantitative corrections for spatially distributed noise and imperfect conservation. For a thirteen-state elementary-matrix model, exact polynomial certificates give root-mean-square localization error $e^{-r/1400}$ between the charge and its restriction to the last $r$ sites, and limiting variance at least $1/19$ for a rational charge. A related normalized-Gram charge gives an eight-site certificate retaining more than half the specified readout correlation through two boundary-reset rounds. Uniform depolarization imposes an inverse-noise-rate lifetime ceiling. A two-qubit IBM experiment illustrates the general reset inequality; it does not realize the matrix-product chain. We provide proofs, exact certificate programs, and an independent recount of the archived experimental outcomes.

We resolve an existing question concerning dynamical and structural stability of the E {\times} B staircases in magnetically confined fusion plasma. The problem has stirred considerable interest in the literature due to a unique combination of its scientific and practical aspects. Here, we report a new approach to the problem by combining the paradigmatic Hasegawa-Wakatani model of electrostatic drift-wave turbulence with an idea of interaction renormalization, imported from quantum field theory. It is shown based on the Schrödinger-Newton equation with renormalized interaction constant that the plasma staircase is robust and stable as soon as the nonadiabaticity parameter, {\delta}, goes above a certain critical value, and is unstable otherwise. This critical value is an exact result of the interaction model and is found to be {\delta}c = {\pi}. For {\delta} < {\delta}c , the unstable system expands in the radial direction, resulting in a radial second moment that grows with time t as t^(2/3). The results obtained bear important implications with regard to the implementation of arrays of semipermeable transport barriers in tokamaks, suggesting a threshold condition for their generation.

We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction to a highly degenerate flag limit. By constructing a regular $R$-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-$1/2$ XXZ Hamiltonian with anisotropy $\Delta = -1/2$ and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for $L\ge4$, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.

We investigate the discrete-time version of the Kuramoto model with phase lag, which comprises globally-coupled phase oscillators of distributed frequencies that are evolving under a nonlinear map. In the continuum limit of an infinite number of oscillators ($N\to \infty$), we derive the exact Frobenius-Perron equation for the time evolution of the single-oscillator probability density, and study linear stability of the incoherent state. Instability signals onset of synchronization. The corresponding synchronization threshold is obtained analytically for the case of a Lorentzian distribution of the oscillator frequencies. The threshold differs from that of the continuous-time Kuramoto model, reflecting the fundamentally different stability conditions for discrete-time maps and continuous-time flows. Beyond synchronization threshold, we observe several interesting nonlinear phenomena: Unlike the classical Kuramoto model, the discrete-time version exhibits periodic and chaotic states. Numerical simulations of the finite-$N$ system confirm the analytical prediction for the synchronization threshold, while highlighting breakdown of the celebrated Ott-Antonsen ansatz invoked to conveniently study the continuous-time Kuramoto model in terms of a low-dimensional description.

We show how migration between counties in different cities can explain both the population scaling of mean intercity flows and heavy-tailed intercity net-flow distributions. Density-dependent departure and arrival activities determine how mean flows scale with the populations of the origin and destination cities. We assume Gaussian county-pair net flows with standard deviations proportional to their mean directional flows. At a fixed correlation between county-pair net flows, their sum is Gaussian. Averaging this conditional Gaussian density over the correlation distribution can produce an intermediate power law with a Gaussian cutoff. We also present a stochastic model that generates the variance distribution used in this mixture.

A wide range of physical and biological systems are adaptive networks, in which the dynamics of the nodes and of the edges connecting them co-evolve. Mean-field reductions of such systems typically track only the average coupling strength, and therefore cannot determine when the coupling stays effectively homogeneous and when structured connectivity emerges. Here, we present a second-order moment closure that allows us to derive mean-field equations for the coupling-weight variance in networks of heterogeneous phase oscillators with adaptive coupling, starting from uniform coupling weights. In agreement with network simulations, we find a nonlinear, non-monotonic dependence of the relative weight variance on the oscillator heterogeneity that is mediated by the phase coherence. Moreover, we find that deviations from global coupling strongly depend on an interaction between the oscillator heterogeneity and the adaptation rule. Whereas symmetric adaptation causes a strongly coupled core of coherent oscillators to emerge and creates a bistable regime that is absent without adaptation, antisymmetric adaptation leads to antisymmetric coupling within the same core, thereby destabilizing it. Our equations therefore delineate the regimes in which adaptive networks behave like globally coupled systems from those in which more complex coupling patterns form.

We construct a wind-driven forest-fire model in one dimension in which a fire can jump gaps between trees to ignite disjoint downwind forests. The size of a gap that a fire can jump depends on the fire intensity, which increases as the fire propagates through trees and diminishes as the fire jumps gaps. Trees grow on empty sites at rate $r$ and lightning strikes each site with rate $f$. When $f\ll r/L$, where $L$ is the system length, lightning is sufficiently rare that quasi-deterministic dynamics arises where all trees are consumed when a lightning-induced fire occurs. For $f\gg L^{-\mu}$ with $\mu\approx 0.8$, lightning is sufficiently frequent that a steady state is reached, but with unexpected behaviors for the forest- and gap-size distributions. Intermittency arises in between these regimes, with coexisting temporal domains of deterministic and chaotic dynamics.

We investigate the nonequilibrium phase-ordering kinetics of a binary mixture of uniaxial ellipsoidal particles interacting via the anisotropic Gay-Berne potential using large-scale molecular dynamics simulations. Following a temperature quench from the isotropic and homogeneous phase into the coexistence region, the system exhibits two distinct ordering processes occurring on different time scales. At first, rapid orientational ordering leads to the formation and coarsening of nematic domains, characterized by dynamical scaling, generalized Porod-law behavior, and a growth law $\ell(t) \sim t^{1/2}$ consistent with nonconserved order-parameter dynamics. Later, the system undergoes binary phase separation driven by compositional fluctuations. This compositional ordering process shows a transition from diffusive growth $\ell(t) \sim t^{1/3}$ to hydrodynamic regimes, with finite-size scaling analysis indicating asymptotic viscous growth $\ell(t) \sim t$. Despite the presence of global orientational order, the phase-separation kinetics remains effectively isotropic. These results demonstrate a clear separation between orientational and compositional ordering dynamics, governed by distinct conservation laws, and provide a unified framework for understanding phase ordering in anisotropic particle systems.

We study a one-dimensional diffusive particle subject to stochastic resetting to its initial position, in the presence of an imperfect, localized target that can absorb (kill) the particle, modeled by a delta-function killing rate. The central question is how stochastic resetting competes with drift-induced transience and the target's finite reactivity. Exact Laplace-space expressions are derived for the non-normalized propagator and survival probability, for arbitrary diffusion coefficient $D$, resetting rate $r$, and killing strength $k$, first in the absence of drift and then under a constant drift. The long-time behavior separates into distinct regimes. Without resetting, unbiased diffusion exhibits the recurrent algebraic survival law $S(t)\sim t^{-1/2}$, whereas any nonzero drift renders the motion transient with respect to the target and leaves a nonzero ultimate survival probability. By contrast, any $r>0$ and $k>0$ repeatedly renews encounters with the target and restores eventual absorption, yielding an exponential survival law $S(t)\sim A e^{-\theta t}$. The decay rate $\theta$ is given by the dominant (rightmost) pole of the Laplace transform, and the surviving density converges after normalization to an explicit quasi-stationary profile. The driftless and perfectly absorbing limits recover standard resetting results. These formulas provide a unified description of the crossover between recurrence-controlled, transience-controlled, and renewal-controlled survival.

A hot Brownian particle is driven by thermal fluctuations from a nonuniformly heated solvent and therefore obeys a fluctuation-dissipation relation with a frequency-dependent effective temperature. Existing theories assume an incompressible solvent. We show that finite sound speed qualitatively changes this effective temperature in the kinetic regime. Solving the compressible fluctuating-hydrodynamic problem for a heated sphere, we find that the effective noise temperature develops a pronounced acoustic dip when the sound wavelength becomes comparable to the particle radius. The dip occurs because weakly attenuated longitudinal modes carry mechanical energy away from the heated surface before it is dissipated, so that the dissipation is weighted by colder regions of the temperature field. Its position is set by $a\omega/c=\mathcal{O}(1)$, while its depth is controlled by the dimensionless viscous-acoustic attenuation length $a_c/a$. The result identifies an acoustic window in hot Brownian motion in which compressibility lowers, rather than raises, the kinetic noise temperature.

Eigenvector overlaps quantify nonorthogonality and govern the response and dynamics of non-Hermitian systems. We extend the universality of non-Hermitian random matrices to the statistics of these overlaps. We obtain analytical expressions for eigenvector overlaps in the spectral bulk and near the origin, covering ten symmetry classes in the limit of large matrix size. Using fermionic replica nonlinear $\sigma$ models, we relate these overlaps to Hermitian level statistics, symmetry class by symmetry class and topological sector by topological sector. Numerical calculations in various physical models support the universality of the normalized overlaps in the regimes studied. Our work establishes a duality between Hermitian level statistics and non-Hermitian eigenvector overlaps.

Path sampling methods enable the computation of thermodynamic and kinetic properties through Monte Carlo (MC) moves that generate trajectories from short forward and backward molecular dynamics (MD) segments. Recently, the wire-fencing move was developed to achieve near-unity acceptance while also rapidly decorrelating successive paths, two properties that are usually in conflict in conventional MC schemes. However, in large systems, such as biomolecular simulations, the frame-saving frequency is often kept low to reduce storage requirements. Likewise, when evaluating the order parameter is expensive, frames are saved less frequently to reduce the associated cost. In either situation, this can severely limit the number of available shooting points, in extreme situations leaving only a single point, typically the one with the highest order parameter value, accessible for shooting. Repeated shootings may then originate from the same configuration, reducing sampling efficiency. Here, we introduce a multi-resolution variant of the wire-fencing move in which selected subtrajectories are propagated at higher temporal resolution than the stored trajectories. This refinement affects only the MC move and does not alter the structure or storage of the generated paths, but enhances the diffusion of shooting points along the trajectory and thereby improves sampling efficiency. The approach is demonstrated on two model systems and a realistic protein–ligand unbinding process, with the latter showing an estimated efficiency improvement of more than an order of magnitude.

For an underdamped particle driven by a constant non-conservative force across a periodic potential in one spatial dimension at finite temperature, numerical studies have shown that the differential mobility is non-negative. Here, an analytical proof will be given that is based on expressing the differential mobility by the long-time mean position of a marginally stable harmonic oscillator subject to noise in its stiffness.

We study macroscopic thermalization in the ferromagnetic Ising model with a weak generic (highly nonlocal and many-body) random quantum perturbation. We prove that a single typical perturbation makes every initial state $|\Phi(0)\rangle$ in a specified energy shell thermalize: a measurement of a large class of macroscopic observables in the time-evolved state $|\Phi(t)\rangle=e^{-i\widetilde H_Lt}|\Phi(0)\rangle$ yields their thermal equilibrium values, within a prescribed precision and with overwhelming probability, at sufficiently large, typical times $t$. The result covers the full finite-temperature range, including the ordered phase, where we use plus boundary conditions. With periodic boundary conditions in the ordered phase, every energy eigenstate in the shell is shown to be an almost balanced macroscopic Schrödinger-cat state. Moreover, every pure initial state becomes such a cat at sufficiently large, typical times, with each branch in the corresponding macroscopic thermal equilibrium. The proof combines the theory of Roos, Sugimoto, Teufel, Tumulka, and Vogel with rigorous Ising large-deviation estimates.

The self-avoiding trail is an important variant of the self-avoiding walk. In this work, we employ an irreversible Markov chain Monte Carlo algorithm, together with the reversible Berretti-Sokal algorithm for comparison, to simulate self-avoiding trails on the square and simple cubic lattices with periodic boundary conditions. Based on finite-size analyses of the unwrapped end-to-end distance and the Binder ratio, we accurately estimate the critical points on the simple cubic and square lattices to be 0.206\,376\,9(2) and 0.367\,561\,1(1), respectively, improving the precision of previous best estimates by factors of 500 and 70. At the estimated critical point of the simple cubic lattice, we numerically demonstrate that both the critical scaling behaviors of various quantities and the length distributions of self-avoiding trails and walks are consistent with each other. Our accurate numerical results are attributed to the efficiency of the irreversible algorithm, whose advantage over the reversible algorithm is even more pronounced for the self-avoiding trail model than for the self-avoiding walk model.