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arXiv:2507.03719 · Physical review. E

Entropy production and statistical relaxation of dipolar bosons and fermions in interaction quench dynamics

Barnali Chakrabarti, N. D. Chavda, Frederico V. Prudente

Published Nov 12, 2025• 0 citations
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Abstract

We study the out-of-equilibrium dynamics of dipolar bosons and fermions after a sudden change in the interaction strength from zero to a finite repulsive value. We simulate the interaction quench on the initial state which is the ground state of harmonic potential with noninteracting bosons and fermions. We solve the time-dependent many-boson Schrödinger equation exactly using numerical methods. To understand the many-body dynamics we analyze several measures of many-body information entropy, monitoring their time evolution and assessing their dependence on interaction strength. We establish that for weak interaction quench the dynamics is statistics independent, both dipolar bosons and fermions do not relax, whereas it is significantly different for dipolar bosons from that of dipolar fermions in the stronger interaction quench. While dipolar bosons exhibit concurrent signature of relaxation in all entropy measures, dipolar fermions fail to relax, exhibiting modulated oscillation in all entropy dynamics. For dipolar bosons and larger interaction quench, the many-body information entropy measures dynamically approach the value predicted for the Gaussian orthogonal ensemble of random matrices, implying statistical relaxation and ergodicity. The entire relaxation process and signature of ergodicity are established by three unique features: dynamical delocalization in Hilbert space, violent orbital fragmentation, and saturation of all entropy measures to the maximum entropy states in the long-time dynamics. It highlights the importance of many-body effects with a possible exploration in quantum simulation with ultracold atoms.

DOI
10.1103/2cgx-y8v5

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We study the out-of-equilibrium dynamics of dipolar bosons and fermions after a sudden change in the interaction strength from zero to a finite repulsive value. We simulate the interaction quench on the initial state which is the ground state of harmonic potential with noninteracting bosons and fermions. We solve the time-dependent many-boson Schrödinger equation exactly using numerical methods. To understand the many-body dynamics we analyze several measures of many-body information entropy, monitoring their time evolution and assessing their dependence on interaction strength. We establish that for weak interaction quench the dynamics is statistics independent, both dipolar bosons and fermions do not relax, whereas it is significantly different for dipolar bosons from that of dipolar fermions in the stronger interaction quench. While dipolar bosons exhibit concurrent signature of relaxation in all entropy measures, dipolar fermions fail to relax, exhibiting modulated oscillation in all entropy dynamics. For dipolar bosons and larger interaction quench, the many-body information entropy measures dynamically approach the value predicted for the Gaussian orthogonal ensemble of random matrices, implying statistical relaxation and ergodicity. The entire relaxation process and signature of ergodicity are established by three unique features: dynamical delocalization in Hilbert space, violent orbital fragmentation, and saturation of all entropy measures to the maximum entropy states in the long-time dynamics. It highlights the importance of many-body effects with a possible exploration in quantum simulation with ultracold atoms.
We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N=10N=10N=10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schr\"odinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a nontrivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).
We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide range of interactions. Our key motivation is to characterize relaxation processes where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values via the quantum fidelity and via the production of many-body entropy. The interaction, as a parameter, can induce a phase transition in the ground state of the system from a superfluid (SF) state to a Mott-insulator (MI) state. We show that, for a quench to a weak interaction, the fidelity remains close to unity and the entropy exhibits oscillations. Whereas for a quench to strong interactions (SF to MI transition), the relaxation process is characterized by the first collapse of the quantum fidelity and entropy saturation to an equilibrium value. The dip and the non-analytic nature of quantum fidelity is a hallmark of dynamical quantum phase transitions. We quantify the characteristic time at which the quantum fidelity collapses and the entropy saturates.
Abstract We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic (bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin S . The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving S for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ( t sat ) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.
We investigate the nonequilibrium dynamics of strongly interacting bosons in a finite bichromatic Mott lattice following a sudden quench of the secondary lattice amplitude. The coefficient entropies and second Rényi entropy exhibit pronounced growth toward their Gaussian Orthogonal Ensemble (GOE) predictions from random-matrix theory, consistent with GOE-like statistical spreading in the employed multiconfigurational representation. In striking contrast, experimentally accessible observables, including the momentum distribution, fragmentation, and Glauber correlation functions, remain nearly unchanged throughout the evolution. For the sampled strong quenches, the coefficient entropies, second Rényi entropy, and the NNN-body coefficient spreading collapse onto a common relaxation trajectory that becomes largely independent of the perturbation strength. Our results reveal an emergent hidden ergodic relaxation beneath the persistent local Mott-like order. An effective embedded random-matrix model captures the qualitative crossover from restricted to extensive Hilbert-space spreading, providing an interpretive framework for the observed relaxation dynamics.
We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the weakly interacting (Bose-Hubbard) and strongly interacting (sine-Gordon) regimes. While in a higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in one dimension an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the sine-Gordon model. The present work aims at identifying the quench dynamics in both the Bose-Hubbard and sine-Gordon interaction regimes. We numerically exactly solve the time-dependent Schr\"odinger equation for a small number of atoms and obtain dynamical measures of several key quantities. We investigate the correlation dynamics of first and second order; both exhibit rich many-body features in the dynamics. We conclude that in both cases, dynamics exhibits collapse-revival phenomena, though with different timescales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics especially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. Bose-Hubbard dynamics clearly establishes the possible relaxation to the maximum entropy state. In contrast, the sine-Gordon dynamics is so fast that it does not exhibit any signature of relaxation in the present timescale of computation.
Abstract We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as ( 1 r α ) ( 0.5 < α < 4.0 ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.