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arXiv:2609.19254

Emergent classicality and wavefunction branching in an isolated quantum many-body system

Saúl Pilatowsky-Cameo, Jordan Cotler, Daniel Ranard, C. Jess Riedel

quant-phcond-mat.str-elmath-phSubmitted Sep 16, 2026• Announced Sep 18, 2026• 0 citations
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Abstract

Decoherence in quantum systems is conventionally modeled as the effect of interactions with an external environment. However, such a prescription excludes isolated many-body systems, which are also expected to display classical behavior at macroscopic scales. In isolated systems, decoherence must emerge internally from microscopic degrees of freedom that are invisible to the macroscopic description. Here we explicitly show that classicality can emerge in such a fashion. We consider a weakly disordered, $3$-local chaotic kicked top of $N$ qubits, where the collective spin sector serves as the macroscopic description, while the microscopic permutation sector acts as an internal bath, decohering the collective spin sector. Starting from closed unitary dynamics, we derive and numerically confirm an effective Lindblad equation for the collective spin variables. In the thermodynamic limit these reduced dynamics converge to a classical chaotic Fokker--Planck equation with vanishingly small diffusion on the spherical phase space, producing a quantum-classical correspondence beyond the Ehrenfest time. The chaotic dynamics evolve the pure many-body wavefunction into continuously branching components associated with distinct classical trajectories. These branches acquire nearly orthogonal microscopic records in the permutation sector, preventing quantum interferences and ensuring the corresponding histories remain consistent.

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7+36 pages, 3+5 figures

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Decoherence in quantum systems is conventionally modeled as the effect of interactions with an external environment. However, such a prescription excludes isolated many-body systems, which are also expected to display classical behavior at macroscopic scales. In isolated systems, decoherence must emerge internally from microscopic degrees of freedom that are invisible to the macroscopic description. Here we explicitly show that classicality can emerge in such a fashion. We consider a weakly disordered, 333-local chaotic kicked top of NNN qubits, where the collective spin sector serves as the macroscopic description, while the microscopic permutation sector acts as an internal bath, decohering the collective spin sector. Starting from closed unitary dynamics, we derive and numerically confirm an effective Lindblad equation for the collective spin variables. In the thermodynamic limit these reduced dynamics converge to a classical chaotic Fokker--Planck equation with vanishingly small diffusion on the spherical phase space, producing a quantum-classical correspondence beyond the Ehrenfest time. The chaotic dynamics evolve the pure many-body wavefunction into continuously branching components associated with distinct classical trajectories. These branches acquire nearly orthogonal microscopic records in the permutation sector, preventing quantum interferences and ensuring the corresponding histories remain consistent.
The threshold for quantum-classical correspondence is D∼ℏ43D \sim \hbar^{\frac43}D∼ℏ34​
In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time tE∼log⁡(ℏ−1)t_{\mathrm{E}} \sim \log(\hbar^{-1})tE​∼log(ℏ−1), even in the limit ℏ→0\hbar \to 0ℏ→0. Decoherence by the environment is often invoked to explain the persistence of the quantum-classical correspondence at longer timescales. Recent rigorous results for Lindblad dynamics with phase-space diffusion strength DDD show that quantum and classical evolutions remain close for times that are exponentially longer than the Ehrenfest time whenever D≫ℏ43D \gg \hbar^{\frac43}D≫ℏ34​, in units set by the classical Hamiltonian. At the same time, some heuristic arguments have suggested the weaker condition D≫ℏ2D \gg \hbar^{2}D≫ℏ2 always suffices. Here we construct an explicit Lindbladian that demonstrates that the scaling D∼ℏ43D \sim \hbar^{\frac43}D∼ℏ34​ is indeed the threshold for quantum-classical correspondence beyond the Ehrenfest time. Our example uses a smooth time-dependent Hamiltonian and linear Lindblad operators generating homogeneous isotropic diffusion. It exhibits an ℏ\hbarℏ-independent quantum-classical discrepancy at the Ehrenfest time whenever D≪ℏ43D \ll \hbar^{\frac43}D≪ℏ34​, even for ℏ\hbarℏ-independent "macroscopic" smooth observables.
We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.
We analyze the quantum-to-classical transition of interacting systems from the viewpoint of reduced dynamical closure. Bohmian trajectories are used as a diagnostic of the probability flow generated by the full wavefunction, rather than as an alternative set of quantum predictions. A closed classical or semiclassical description of a retained coordinate can emerge either because interaction-induced correlations are suppressed or because the observable of interest is insensitive to the correlations that remain. Three models are used to isolate distinct mechanisms. In a hard-core collision, the leading tail of a broad relative-coordinate wave packet reaches the boundary before its center and generates spatial nonseparability through reflection and interference. In the Rabi model, the mixed quantum-classical Ehrenfest approximation fails when spin-position covariances prevent the spin dynamics from being determined solely by the mean oscillator coordinate. In an internal-state-dependent force model, the total mean position obeys an exact Ehrenfest equation, while the wavefunction separates into branch-resolved pointer components; mean classicality therefore does not imply branch-level classicality. These examples show that the quantum-to-classical transition of interacting systems is controlled not only by wave-packet localization but also by whether and how interaction-induced correlations enter the reduced equations of motion.
The Lindblad master equation is widely used to describe the reduced dynamics of open quantum systems under Markovian assumptions. Here, we investigate its ability to reproduce the reduced evolution emerging from a microscopic many-body model in which two interacting two-level subsystems are embedded in a larger environment and evolve under fully unitary dynamics. The exact evolution exhibits a clear separation of timescales. At short times, decoherence arises from environmentally induced dephasing, leading to a Gaussian suppression of coherences and a quadratic decay of purity. At intermediate times, collective decoherence channels saturate and a slower, still Gaussian, decay driven by relative environmental fluctuations dominates. At later times the system settles in a complete decohered state. The first two behaviors cannot be reproduced by a Lindblad dynamics with constant coefficients, which always results in an exponential decay: Our work provides a simple example of the breakdown of the effective description relevant in many realistic settings.
Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical level must also be present in the underlying quantum system. In the classical case, the exponential divergence of nearby trajectories in time is described in terms of the Lyapunov exponent. However, in the quantum case, a similar description of chaos is, strictly speaking, impossible due to the absence of trajectories. There are different approaches to remedy this situation, but the universal criterion of quantum chaos is absent. We propose a quantum chaos definition in a manner similar to the classical one using decoherent histories as a quantum analog of trajectories. For this purpose, we consider the model of an open quantum kicked top interacting with the environment, which is a bosonic bath, and illustrate this idea. Here, the environment plays the role of a trajectory-recording device. For the kicked-top model at the classical level, depending on the kick strength, crossover occurs between the integrable and chaotic regimes. We show that for such a model, the production of entropy of decoherent histories is radically different in integrable and chaotic regimes. Thus, the entropy of an ensemble of quantum trajectories can be used as a signature of quantum chaos.
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.