The collapse and revival of localized states in many-body systems is a quintessential example of a quantum interference phenomenon that cannot be explained purely within mean-field theories. Historically, the majority of previous work on quantum revivals has been in a Schrödinger mechanics context, typically for effectively 1D systems with a focus on the autocorrelation function as the key detection observable. The general revival subject acquires a far greater complexity in the bosonic many-body context that offers a larger variety of observables and intrinsically implies high dimensionality. Here, the focus is on the simplest nontrivial (i.e., not 1D) bosonic many-body system, namely a symmetric two-site Bose-Hubbard model. The non-equilibrium situation of a coherent initial state prepared on one of the two sites of this integrable 2D system in the strongly self-trapping regime is considered. The revival behaviors emerging from the resulting dynamics within expectation values, coherences, and the autocorrelation function are theoretically derived, and the entanglement behavior is illustrated. Several new features, unknown so far in the Schrödinger context and identified here in terms of five ``puzzles'', are encountered and discussed, among them, a synchronized resurgence behavior, differing revivals times depending on the specific observable, and a manifestation of a precession that appears in the underlying mean field dynamics. These new phenomena can be entirely understood through a comprehensive semiclassical theory, building upon the underlying classical (mean-field) phase-space structure. A quantitative comparison of the latter with semiclassical predictions and quantum perturbative calculations yields an overall excellent agreement and confirms that a full semiclassical theory is pivotal for the understanding of these genuinely quantum many-body interference phenomena.
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The paper asks how collapse and revival dynamics change when a bosonic system involves two dynamical degrees of freedom and is probed through different observables. It studies the symmetric two-site Bose–Hubbard model, initialized in the Glauber coherent state $|\sqrt{\bar N},0\rangle$, in the strongly self-trapping regime. The analysis develops explanations for revival features, several previously reported, in return probabilities, site populations, and coherences; intersite Rényi-2 entanglement is illustrated numerically.
The analytical framework embeds Einstein–Brillouin–Keller quantization into truncated-Wigner propagation to restore revival interference absent from ordinary TWA. Classical action–angle frequencies and their derivatives determine the oscillation, collapse, and revival scales. Predictions are compared with exact quantum dynamics and weak-hopping quantum perturbation theory, including examples with $\bar N=50$–$200$ and dimensionless hopping $\gamma=2J/(\bar N U)=0.14$–$0.25$. Different observables revive at different times near the isolated-site scale $2\pi\hbar/U$. A slow coherence-background decay is connected to mean-field precession. Nonmonotonic return-probability revival heights are explained through synchronization with population oscillations, including correlations with integer versus half-integer time-averaged occupation of the initially empty site.
The treatment assumes integrability, large occupation, and the specified initial state. Perturbative predictions deteriorate at stronger hopping; Gaussian action–angle semiclassics can underestimate return probabilities when the second action is comparable to the effective Planck constant, motivating a quadrature-based correction. Integrability-breaking perturbations and quantitative sensing applications remain open; extension from a dimer to a lattice requires additional dynamical constraints.
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Error found: The claimed quantitative agreement requires qualification because the paper acknowledges significant autocorrelation-amplitude errors near perturbative-regime dips and does not explicitly derive the fully uniform approximation.
The quadrature-Gaussian overlap in Eq. (Imt) is missing an action factor m_alpha in its exponent, invalidating its claimed small-angle correspondence as printed.
The monomer benchmark incorrectly differentiates its classical Hamiltonian, giving erroneous shearing rates and an incorrect analytical revival-time shift as printed.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
The collapse and revival of localized states in many-body systems is a quintessential example of a quantum interference phenomenon that cannot be explained purely within mean-field theories. Historically, the majority of previous work on quantum revivals has been in a Schrödinger mechanics context, typically for effectively 1D systems with a focus on the autocorrelation function as the key detection observable. The general revival subject acquires a far greater complexity in the bosonic many-body context that offers a larger variety of observables and intrinsically implies high dimensionality. Here, the focus is on the simplest nontrivial (i.e., not 1D) bosonic many-body system, namely a symmetric two-site Bose-Hubbard model. The non-equilibrium situation of a coherent initial state prepared on one of the two sites of this integrable 2D system in the strongly self-trapping regime is considered. The revival behaviors emerging from the resulting dynamics within expectation values, coherences, and the autocorrelation function are theoretically derived, and the entanglement behavior is illustrated. Several new features, unknown so far in the Schrödinger context and identified here in terms of five ``puzzles'', are encountered and discussed, among them, a synchronized resurgence behavior, differing revivals times depending on the specific observable, and a manifestation of a precession that appears in the underlying mean field dynamics. These new phenomena can be entirely understood through a comprehensive semiclassical theory, building upon the underlying classical (mean-field) phase-space structure. A quantitative comparison of the latter with semiclassical predictions and quantum perturbative calculations yields an overall excellent agreement and confirms that a full semiclassical theory is pivotal for the understanding of these genuinely quantum many-body interference phenomena.
The paper asks how collapse and revival dynamics change when a bosonic system involves two dynamical degrees of freedom and is probed through different observables. It studies the symmetric two-site Bose–Hubbard model, initialized in the Glauber coherent state ∣Nˉ,0⟩, in the strongly self-trapping regime. The analysis develops explanations for revival features, several previously reported, in return probabilities, site populations, and coherences; intersite Rényi-2 entanglement is illustrated numerically.
The analytical framework embeds Einstein–Brillouin–Keller quantization into truncated-Wigner propagation to restore revival interference absent from ordinary TWA. Classical action–angle frequencies and their derivatives determine the oscillation, collapse, and revival scales. Predictions are compared with exact quantum dynamics and weak-hopping quantum perturbation theory, including examples with Nˉ=50–200 and dimensionless hopping γ=2J/(NˉU)=0.14–0.25. Different observables revive at different times near the isolated-site scale 2πℏ/U. A slow coherence-background decay is connected to mean-field precession. Nonmonotonic return-probability revival heights are explained through synchronization with population oscillations, including correlations with integer versus half-integer time-averaged occupation of the initially empty site.
The treatment assumes integrability, large occupation, and the specified initial state. Perturbative predictions deteriorate at stronger hopping; Gaussian action–angle semiclassics can underestimate return probabilities when the second action is comparable to the effective Planck constant, motivating a quadrature-based correction. Integrability-breaking perturbations and quantitative sensing applications remain open; extension from a dimer to a lattice requires additional dynamical constraints.
Understanding how coherent quantum dynamics give way to correlation-dominated behavior in low-dimensional systems remains a central challenge in quantum many-body physics. Here, we investigate a one-dimensional Bose-Josephson junction confined in a box trap using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). By varying the interaction strength and initial population imbalance, we identify distinct dynamical regimes governed by the competition between coherence and correlation-induced fragmentation. Weak interactions support coherent Josephson oscillations, whereas increasing imbalance leads to damping. At intermediate interaction strength, varying only the initial imbalance induces a crossover from nearly pure coherent oscillations to many-body dephasing with collapse-and-revival dynamics, and ultimately to equilibration accompanied by strong fragmentation and the saturation of many-body observables. In the strongly interacting regime, the system enters a dynamical freezing regime characterized by pronounced fragmentation, well-separated particle-resolved density peaks, and strongly suppressed tunneling. A systematic comparison with the Bose-Hubbard model reveals excellent agreement in the weakly interacting regime, while progressively larger deviations emerge as higher-orbital occupations beyond the two-mode approximation become significant. These results provide a unified picture of the emergence and competition of coherence, many-body dephasing, equilibration, and dynamical freezing, while delineating the regime of validity of the Bose-Hubbard description.
A major goal of the semiclassical theory is to understand and treat a quantum system in the regime of large quantum numbers using information from its classical limit. In this framework, quantum phenomena are addressed through a path integral perspective, i.e. the weighted interference of phases accumulated along classical trajectories. While this formalism has been successful in explaining interference phenomena, for instance, in mesoscopic single-particle quantum systems, the recent extension of the semiclassical theory allows now also the treatment of interacting quantum many-body systems. This thesis aims to contribute to these ongoing efforts to apply semiclassical techniques to quantum many-body systems. It is focused on bosonic quantum many-body systems, where the thermodynamic limit of a large number of particles represents an alternative version of a semiclassical limit. Within the derivation of the corresponding semiclassical theory, mean-field equations, i.e. effective nonlinear wave equations describing the matter wave, re-emerge as Hamilton's equations of motion of an abstract Hamilton function, defining the above thermodynamic limit as the classical limit. Within this thesis, two different topics are studied. The first one deals with the so-called “Out-of-Time-Order Correlator” (OTOC), the expectation value of the squared commutator of two local operators at different times. The OTOC provides a direct probe for the presence of chaos in the classical limit (if any) of a quantum many-body system. This is based on that for short times the OTOC directly relates to the stability of classical solutions upon changes in their initial conditions. One of the defining properties of chaos is that this stability displays an exponential growth, with the rate called the classical Lyapunov exponent. Immediately, this implies an exponential growth of the OTOC for short times, from which the Lyapunov exponent can be extracted. For later times, one observes a saturation of the OTOC as a consequence of unitary quantum time evolution. The Ehrenfest time, the time scale which marks the onset of quantum interference, separates these different dynamical behaviors. In this thesis a thorough understanding of the concept of chaos in the classical limit of quantum many-body systems is provided, and with that the underlying interference mechanisms involved in the early exponential growth and the later saturation of OTOCs are identified. It is found that the pre-Ehrenfest time exponential growth is given through the interference of multiple contributions, all of them essentially following only a single solution of mean-field equations. Conversely the post-Ehrenfest time behavior stems from the contributions of fundamentally different mean-field solutions, which display correlated dynamics only for a limited amount of time, of the order of Ehrenfest time. The second topic covered in this thesis deals with the coherent transport of cold bosonic atoms through an Aharonov-Bohm ring structure. This setup consists of two semi-infinite wave guides attached on the opposite sides of a wave guide ring which is pierced by a synthetic gauge field. Within the ring, the atoms are further subject to both a weak disorder potential and particle-particle interaction. In the non-interacting case, the disorder-averaged transmission probability as a function of the encircled flux displays the well-known Al'tshuler-Aronov-Spivak (AAS) oscillations, i.e. oscillations with a frequency twice as large as Aharonov-Bohm oscillations. This thesis provides further insight into the influence of a weak particle-particle interaction on AAS oscillations, for which numerical results predict an interaction-based inversion of peaks. Here, using semiclassical techniques to solve the corresponding mean-field problem, this inversion is successfully reproduced, and a first indicator of the relevant mechanism leading to the inversion is found through contributions of self-averaging scattering path constellations.
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.
The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space [1]. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect which lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization. We furthermore propose a specific experimental setup in order to detect this many-body coherent backscattering phenomenon with ultracold bosonic atoms.
The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.