Abstract We study the nonequilibrium stationary state (NESS) induced by quantum resetting of a system of N noninteracting bosons in a harmonic trap. Our protocol consists of preparing initially the system in the ground state of a harmonic oscillator centered at +a, followed by a rapid quench where the center is shifted to −a and the system is allowed to evolve unitarily up to a random Poissonian time τ distributed via r e − r τ . Then the trap center is reset to +a again and the system is assumed to cool instantaneously to the initial ground state. The system is again allowed to evolve unitarily in the trap centered at −a up to a random time, and the procedure is repeated. Under repeated resetting, the system reaches a NESS where the positions of bosons get strongly correlated due to simultaneous resetting induced by the trap. We fully characterize the steady state by analytically computing several physical observables such as the average density, extreme value statistics, order and gap statistics, and also the distribution of the number of particles in a region [ − L , L ] , known as the full counting statistics (FCS). In particular, we show that in the large N limit, the scaling function describing the FCS exhibits a striking feature: it is supported over a nontrivial finite interval, and moreover is discontinuous at an interior point of the support. Our results are supported by numerical simulations. This is a rare example of a strongly correlated quantum many-body NESS where various observables can be exactly computed.
Abstract We study the nonequilibrium stationary state (NESS) induced by quantum resetting of a system of N noninteracting bosons in a harmonic trap. Our protocol consists of preparing initially the system in the ground state of a harmonic oscillator centered at +a, followed by a rapid quench where the center is shifted to −a and the system is allowed to evolve unitarily up to a random Poissonian time τ distributed via r e − r τ . Then the trap center is reset to +a again and the system is assumed to cool instantaneously to the initial ground state. The system is again allowed to evolve unitarily in the trap centered at −a up to a random time, and the procedure is repeated. Under repeated resetting, the system reaches a NESS where the positions of bosons get strongly correlated due to simultaneous resetting induced by the trap. We fully characterize the steady state by analytically computing several physical observables such as the average density, extreme value statistics, order and gap statistics, and also the distribution of the number of particles in a region [ − L , L ] , known as the full counting statistics (FCS). In particular, we show that in the large N limit, the scaling function describing the FCS exhibits a striking feature: it is supported over a nontrivial finite interval, and moreover is discontinuous at an interior point of the support. Our results are supported by numerical simulations. This is a rare example of a strongly correlated quantum many-body NESS where various observables can be exactly computed.
Abstract We study a system of N noninteracting bosons in a harmonic trap subjected to repeated quantum quenches, where the trap frequency is switched from one value to another after a random time duration drawn from an exponential distribution. Each cycle contains two steps: (i) changing the trap frequency to enable unitary evolution under a Hamiltonian, and (ii) reapplying the original trap at stochastic times to cool the gas back to its initial state. This protocol effectively makes it an open quantum system and drives it into a unique nonequilibrium steady state (NESS). We analytically and numerically characterize the NESS, uncovering a conditionally independent and identically distributed (CIID) structure in the joint probability density function (JPDF) of the positions. The JPDF in the CIID structure is a product of Gaussians with a common random variance, which is then averaged with respect to its distribution, making the JPDF non-factorizable, giving rise to long-range emergent dynamical correlations. The average density profile of the gas shows significant deviations from the initial Gaussian shape. We further compute the order and the gap statistics, revealing universal scaling in both bulk and edge regimes. We also analyze the full counting statistics, exposing rich parameter-dependent structure. Our results demonstrate how stochastic quenches can generate nontrivial correlations in quantum many-body systems
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength and thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system, we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wave function, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wave function in both real and momentum space, and the Tan contact, which unveils the existence of short range two-body correlations. When the system is initialized in its bound state, it is perturbed in the most efficient manner as compared to any other initial configuration. Moreover, starting from an interacting ground state, the two-boson response is enhanced for quenches toward the noninteracting limit.
Stochastic resetting can generate strong correlations in many-body systems through a shared fluctuating environment. Here, we investigate how such dynamically emergent correlations (DEC) coexist with intrinsic (direct) interactions in a weakly repulsive Bose-Einstein condensate described within the Gross-Pitaevskii framework. The condensate undergoes free expansion from an initial Thomas-Fermi state and is stochastically reset to this initial state at a constant rate. We show that the resetting protocol drives the system into a unique nonequilibrium steady state and obtain its density profile, edge statistics, and full counting statistics analytically. The steady-state density retains an inverted-parabolic form within the core, while developing exponentially decaying tails outside it. We further show that resetting induces nontrivial fluctuations of the condensate edge and particle number, yielding exact scaling forms for the edge distribution and the full counting statistics. Our results provide a tractable setting for exploring the interplay between intrinsic repulsive interactions and attractive DEC generated by a common stochastic environment in quantum many-body systems.
We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ``thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.
We study nonequilibrium dynamics of integrable and nonintegrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate r, that project the system to its initial state. We show that the steady-state density matrix of a nonintegrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite r. Consequently a generic observable $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{O}$, whose expectation value receives a contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite r. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles characterized by r. We also study the spread of particle density of a noninteracting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially resolved measurement, the steady state can feature collective behavior similar to what is typically observed at phase transitions. Here we investigate such conditional reset protocol in a system of noninteracting spins, where the reset state is chosen as a magnetization eigenstate, that is selected (conditioned) on the outcome of a previous magnetization measurement. The stationary states that emerge from this protocol are characterized by the density of spins in a given magnetization eigenstate, which is the analog of the order parameter. The resulting stationary phase diagram features multiple nonanalytic points. They are of first-order type for half-integer spin, while multicritical behavior, signalled by both first and second-order discontinuities, is found for integer spin. We also show that the associated dynamics is nonergodic, i.e., which stationary state the system ultimately assumes is determined by the initial state. Interestingly, the mechanism underlying these phenomena does not rely on interactions, but the emergent nonlinear behavior is solely a consequence of correlations induced by the measurement.