arXiv subjects

Eli Barkai

Publications and source records attributed to Eli Barkai.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement diagnostics of stochastic-resetting steady states: theory and measurement on superconducting qubits

Stochastic resetting drives quantum systems into nonequilibrium stationary states unreachable under uninterrupted unitary evolution, and their entanglement depends on whether the reset history is resolved or averaged over. We study this interplay in the transverse-field Ising chain, deriving closed-form results for two qubits and evaluating chains of up to 12 qubits exactly. In the two-qubit system, these closed-form results show that phase matching between energy eigenstates produces resonances, and their visibility in the stationary state is determined by the symmetry of the reset state. Measurements on an IBM superconducting processor show the entropies evaluated before and after the reset average closely following noiseless predictions with no fitted parameter, while concurrence lies below prediction across most of the hardware measurements. The two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter. The difference between the two entropies, i. e., the Jensen gap of entanglement entropy, equals the Holevo information that a subsystem retains about the time since the last reset. With a Bell-state reset, this information grows with chain length across a half-chain cut over the sizes studied, without visible saturation at the smaller reset probabilities. Since reset times are sampled and recorded classically, the trajectory-averaged entropy, and with it the Jensen gap, is obtained without postselection, in contrast to monitored circuits, where trajectory-resolved entanglement requires sampling exponentially rare measurement records.

quant-ph↗

arXiv2026

Splitting Probability in Monitored Quantum Dynamics

We consider a continuous-time quantum walk stroboscopically subjected to projective measurements on two distinct targets with sampling time period $τ$. We construct a general renewal framework for the first-detection amplitude at each target, from which we obtain the associated splitting probabilities. For Hamiltonians with reflection symmetry, we further show that each dual-target first-detection amplitude can be viewed as an interference effect between a pair of single-target first-detection amplitudes. This formulation yields exact expressions for the splitting probabilities and gives special sampling times at which they undergo pointwise discontinuous jumps due to a form of ergodicity breaking associated with dark states. As an illustrative example, we apply the framework to a one-dimensional tight-binding lattice chain with nearest-neighbor hopping, and study the splitting probabilities as functions of the initial position and sampling time. Below a critical sampling time, $0<τ< τ_c$ where $τ_c = 2 π/ ΔE$ with $ΔE$ being the energy bandwidth, the splitting probabilities for large system sizes become equal to $1/2$, independent of the initial position, as long as this position does not coincide with target sites. Above the critical sampling time, $τ\geq τ_c$, the splitting probabilities deviate from $1/2$ and develop oscillations as a function of initial position. The wavenumber associated with these oscillations is $Q=2\sin^{-1}(rτ_c/τ)$, where $r$ is a positive integer. We also explore the effects of relative phase and spatial separation between different components of a coherent initial state on the splitting probabilities. Finally, we study how a finite number of measurements modifies the splitting probabilities and broadens the resonances at special sampling times.

cond-mat.stat-mech↗

arXiv2026

Temporal Interference from Topological Transitions in Monitored Quantum Dynamics

Quantum interference is conventionally associated with the coherent superposition of alternative paths. We uncover a temporal form of interference in repeatedly monitored quantum systems, appearing directly as fringes in the stochastic first-detection-time distribution. This temporal interference becomes remarkably long lived near a class of topological transitions at which a pair of dark states emerges in Hilbert space. Close to such transitions, the corresponding quasi-dark modes dominate the late-time dynamics and interfere coherently, producing pronounced temporal fringes whose decay becomes arbitrarily slow upon approaching the transition. We identify the symmetry conditions underlying this mechanism and relate the fringe frequency to the energy spectrum of the Hamiltonian. Our results reveal how the interplay of quantum superposition, topological transitions, and dark-state formation generates long-lived temporal interference in monitored quantum dynamics.

cond-mat.stat-mech↗

arXiv2026

Periodic conditional measurements on a photonic chip

Quantum measurements not only extract information but also reshape quantum evolution through measurement backaction. Here, we investigate periodic conditional measurements, in which coherent evolution is repeatedly interrupted by local measurements. We show that the bright and dark modes of the conditional evolution operator provide a unified spectral description of both the post-selected final state along no-detection trajectories and the statistics of detection events. Using a three-dimensional photonic chip, we demonstrate on-demand state engineering through dark-mode preservation and bright-mode selection, enabling the protection of topological corner states and excited-state shelving. We further observe the predicted transition of the total detection probability on an effectively infinite one-dimensional lattice and identify its microscopic origin in Floquet near-dark modes. These results establish periodic conditional measurements as a general framework for engineering conditional quantum states and manipulating event-detection statistics in monitored quantum dynamics.

quant-ph↗

arXiv2026

Tunable Anomalous Diffusion in Subrecoil-Laser-Cooled Atoms

Laser cooling of atomic motion enables advances in quantum information and precision metrology. However, the spatial spreading of subrecoil-laser-cooled atoms---crucial for understanding cooling mechanisms and atomic confinement---remains largely unexplored. Here, we analyze anomalous diffusion in subrecoil-laser-cooled atoms, where a velocity-dependent fluorescence rate $R(v) \propto |v|^α$ governs transport properties. By tuning $α$, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at $α= 3/2$, diffusion is minimized, leading to optimal atomic confinement. We further identify a conceptual link between subrecoil laser cooling and the Pomeau-Manneville map from nonlinear dynamics, revealing that anomalous diffusion can generically exhibit a nontrivial minimum in spatial spreading---even across seemingly unrelated physical systems.

cond-mat.stat-mech↗

arXiv2026

Transition in Splitting Probabilities of Quantum Walks

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. For large systems and sampling times smaller than a critical value $τ_c = 2π/ΔE$, where $ΔE$ is the energy bandwidth, the splitting probability is universal and equal to $1/2$, independent of the initial condition and the sampling time. Above the critical sampling time, a nonuniversal regime emerges in which the splitting probability deviates from $1/2$ and develops a fluctuating pattern of pronounced peaks and dips dependent on both the sampling time and the initial condition. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle.

cond-mat.stat-mech↗

arXiv2026

Sokoban Random Walk: A Trapping Perspective

We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\rm P}$ number of obstacles. For $N_{\rm P}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\rm P}$. The long-time exponent matches the Balagurov--Vaks--Donsker--Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $ρ$: it is small at both low and high densities, but reaches a peak at a characteristic density $ρ_*$. We estimate $ρ_* \approx 0.55$ for the Sokoban model and $ρ_* \approx 0.675$ for the generalized Sokoban model.

cond-mat.stat-mech↗

arXiv2026

From Continuous-Time Random Walks to Laplace Tails

During Brownian motion, the displacement is normally distributed, a classical fact aligned with the central limit theorem. However, single particle tracking in complex media such as glasses, living cells, and colloidal suspensions often reveals pronounced exponential decay of the displacement distribution, known as Laplace tails. In a short letter, two of us presented the emergence of Laplace tails in the continuous time random walk (CTRW) framework. Here, a detailed complementary study is presented. By exploring the behavior of $Q_t(n)$, the probability that exactly $n$ renewals occur during time $t$, we develop a rate function-like framework for this quantity, valid for finite $t$. We show that $Q_t(n)$ exhibits exponential tails, which in turn give rise to exponential tails of the positional probability density function $P(x,t)$. Favorable comparison to finite-time numerical simulations and asymptotic large deviation rate functions establishes the validity of our results over a wide temporal range.

cond-mat.stat-mech↗

arXiv2026

Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems

Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence times are governed by Anandan-Aharonov phases, yielding fractionally quantized recurrence times. However, the fractional quantization phenomenon in interacting quantum systems remains unexplored. Here, we address this gap by establishing universal lower and upper bounds for recurrence times in interacting many-body spin systems. Notably, we investigate scenarios where these bounds are approached, shedding light on the speed of quantum processes under monitoring. In specific cases, our findings reveal that the complex many-body system can be effectively mapped onto a dynamical system with a single quasi-particle, leading to integer-quantized recurrence times. Our work demonstrates a valuable link between recurrence times and the number of dark states in the system, thus providing a deeper understanding of the intricate interplay between Hilbert-space fragmentation, ergodicity breaking, measurements, and interaction effects. Finally, our findings have been implemented on an IBM quantum computer, revealing resonances and fractional quantization in agreement with theoretical predictions. This demonstrates the resilience of non-equilibrium topological fractional quantization to noise and highlights its potential use for benchmarking quantum devices and probing dark states.

cond-mat.stat-mech↗

arXiv2026

Resonances, Recurrence Times and Steady States in Monitored Noisy Qubit Systems

We study non-equilibrium steady states and recurrence times in noisy, stroboscopically monitored qubit systems using complete measurements. In the noiseless limit, recurrence times are integer-quantized, with dips to lower integers when sampling approaches revival conditions associated with ergodicity breaking. Using an IBM quantum platform, we find that quantization is robust when sampling far from revivals, but breaks down dramatically near revivals: even weak noise produces large deviations and can invert the expected dips into pronounced peaks. To explain this behavior, we formulate a statistical-physics model of monitored noisy circuits in which monitoring drives an effective infinite-temperature steady state while thermal-like relaxation competes to favor a low-temperature limit. We show that the sampling time tunes a crossover between these regimes, near revivals stabilizing low-temperature behavior, and far from revivals restoring infinite-temperature behavior -- with noise strength and detuning acting as coupled small parameters near resonance.

cond-mat.stat-mech↗

arXiv2026

Extreme Values of Infinite-Measure Processes

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in the long-time limit, by a non-normalizable infinite invariant density. Extreme events in such systems emerge in a joint limit where the observation time $t$ is long and the number of variables $N$ is large. We show that the resulting extreme value statistics are controlled by the return exponent $α$ and the infinite invariant measure, and therefore depart from the classical Fréchet, Gumbel, and Weibull universality classes. We illustrate the theory for weakly chaotic intermittent maps, overdamped diffusion in an asymptotically flat potential, and a stochastic model of sub-recoil laser cooling, and show how measurements of extremes can be used to infer the infinite-density structure.

cond-mat.stat-mech↗

arXiv2026

Sokoban Random Walk: From Environment Reshaping to Trapping Crossover

We study the dynamics of a Sokoban random walker moving in a disordered medium with obstacle density $ρ$. In contrast to the classic model of de Gennes with static obstacles that exhibits a percolation transition, the Sokoban walker is capable of modifying its environment by pushing a few surrounding obstacles. Surprisingly, even a limited pushing ability leads to a loss of the percolation transition. Through a combination of a rigorous large-deviation calculation and extensive numerical simulations, we demonstrate that the Sokoban model belongs to the Balagurov-Vaks-Donsker-Varadhan trapping universality class. The survival probability that the walker has not yet been trapped inside a cage exhibits stretched-exponential relaxation at late times. Furthermore, using the average trap size as a proxy, we identify the emergence of a dynamical crossover at a density $ρ_* \approx 0.55$ between two qualitatively different trapping mechanisms: a self-trapping mechanism at low density, where the walker becomes dynamically localized within a self-formed trap, and a pre-existing trapping mechanism at high density, where confinement arises from the initial arrangement of obstacles. This crossover is responsible for the loss of the classical percolation transition.

cond-mat.stat-mech↗

arXiv2025

The Thermodynamic Limit of Extreme First-Passage Times

The statistics of the slowest first-passage time among a large population of $N$ searchers is crucial for determining the completion time of many stochastic processes. Classical extreme-value theory predicts that for diffusing particles in a finite domain of size $L$, the slowest first passage time follows a Gumbel distribution, but a Fréchet distribution in an infinite domain. Here, we study the physically relevant thermodynamic limit where both $N$ and $L$ diverge while the density $ρ= N/L$ remains constant. We obtain an explicit solution for the extreme value in the thermodynamic limit, which recovers the Fréchet and Gumbel distributions in the low- and high-density limits, respectively, and reveals new, nontrivial behavior at intermediate densities. We then extend the framework to compact diffusion on fractal domains, showing that the walk dimension $d_w$ and fractal dimension $d_f$ control the extreme-value statistics via geometry-dependent scaling. The theory yields the full set of moments and finite-density corrections, providing a unified description of slowest-arrival times in confined Euclidean and fractal media.

cond-mat.stat-mech↗

arXiv2025

Strong anomalous diffusion for free-ranging birds

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement moments - do not capture the full complexity of movement behavior. Using high-resolution data from over 70 million localizations of young and adult free-ranging Barn Owls (\textit{Tyto alba}), we reveal strong anomalous diffusion as nonlinear growth of displacement moments. The moment spectrum function $λ_t(q)$ -- defined by $\left<|\bm{x}(t)|^q\right> \sim t^{λ_t(q)}$ -- displays piecewise linearity in $q$, with a critical moment marking the crossover between scaling regimes. This highlights the need of a broad spectrum of displacement moments to characterize movement, which we link to age-specific ecological drivers. Furthermore, a characteristic timescale of five minutes marks an unexpected transition from a convex to a concave $λ_t(q)$. Using two stochastic models - a bounded Lévy walk and a multi-mode behavioral model - we account for the observed phenomena, showing good agreement with data, relating age-specific behavioral states to environmentally confined movement, and demonstrating how Lévy walk-like patterns can arise from underlying behavioral structure. Finally, we discuss the ecological significance of our results, arguing that strong anomalous diffusion may be widespread in animal movement.

q-bio.PE↗

arXiv2025

Quantum Walks: First Hitting Times with Weak Measurements

We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak measurements on a dilated system, enabling minimally invasive monitoring throughout the evolution. To achieve this, we extend the theoretical framework and complement it with both numerical simulations and experimental investigations on an IBM quantum computer. Despite the implementation of a generalized measurement, our modified formalism of weak recurrence provides a description purely within the Hilbert space of the quantum system. Our results reveal that the first hitting time scales inversely with the coupling parameter between the ancilla and the quantum system.

quant-ph↗

arXiv2025

Resonances of recurrence time of monitored quantum walks

The recurrence time is the time a process first returns to its initial state. Using quantum walks on a graph, the recurrence time is defined through stroboscopic monitoring of the arrival of the particle to a node of the system. When the time interval between repeated measurements is tuned in such a way that eigenvalues of the unitary become degenerate, the mean recurrence time exhibits resonances. These resonances imply faster mean recurrence times, which were recorded on quantum computers. The resonance broadening is captured by a restart uncertainty relation [R. Yin, Q. Wang, S. Tornow, E. Barkai, Proc. Natl. Acad. Sci. U.S.A. 122, e2402912121 (2025)]. To ensure a comprehensive analysis, we extend our investigation to include the impact of system size on the widened resonances, showing how the connectivity and energy spectrum structure of a system influence the restart uncertainty relation. Breaking the symmetry of the system, for example time-reversal symmetry breaking with a magnetic flux applied to a ring, removes the degeneracy of the eigenvalues of the unitary, hence modifying the mean recurrence time and the widening of the transitions, and this effect is studied in detail. The width of resonances studied here is related to the finite time resolution of relevant experiments on quantum computers, and to the restart paradigm.

cond-mat.stat-mech↗

arXiv2025

Rare Events and Single Big Jump Effects in Ornstein-Uhlenbeck Processes

Even in a simple stochastic process, the study of the full distribution of time integrated observables can be a difficult task. This is the case of a much-studied process such as the Ornstein-Uhlenbeck process where, recently, anomalous dynamical scaling of large deviations of time integrated functionals has been highlighted. Using the mapping of a continuous stochastic process to a continuous time random walk via the "excursions technique'', we introduce a comprehensive formalism that enables the calculation of the complete distribution of the time-integrated observable $A = \int_0^T v^n(t) dt$, where $n$ is a positive integer and $v(t)$ is the random velocity of a particle following Ornstein-Uhlenbeck dynamics. We reveal an interesting connection between the anomalous rate function associated with the observable $A$ and the statistics of the area under the first-passage functional during an excursion. The rate function of the latter, analyzed here for the first time, exhibits anomalous scaling behavior and a dynamical phase transition, both of which are explored in detail. The case of the anomalous scaling of large deviations, originally associated to the presence of an instantonic solution in the weak noise regime of a path integral approach, is here produced by a so called "big jump effect'', in which the contribution to rare events is dominated by the largest excursion. Our approach, which is quite general for continuous stochastic processes, allows to associate a physical meaning to the anomalous scaling of large deviations, through the big jump principle.

cond-mat.stat-mech↗

arXiv2025

First passage times in compact domains exhibit bi-scaling

The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability density function of first passage times in confined compact processes, applicable to both Euclidean and Fractal domains, diverse geometries, and scenarios with or without external force fields, accommodating Markovian and semi-Markovian random walks. In large systems, first passage time statistics exhibit a bi-scaling behavior, challenging the use of a single time scale. Our theory employs two distinct scaling functions: one for short times, capturing initial dynamics in unbounded systems, and the other for long times is sensitive to finite size effects. The combined framework provides a complete expression for first passage time statistics across all time scales.

cond-mat.stat-mech↗