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Register a new userThermalization of a strongly interacting closed spin system: From coherent many-body dynamics to a Fokker-Planck equation
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Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model - in one and two dimensions - for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the non-equilibrium relaxation to it.
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The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.
Relaxation of few-body quantum systems can strongly depend on the initial state when the systems semiclassical phase space is mixed, i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. Time-dependent variational principle (TDVP) allows to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly-entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of quantum many-body scars, i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed-phase space classical variational equations allow to find slowly-thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing towards possible extensions of classical Kolmogorov-Arnold-Moser theorem to quantum systems.
In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small systems long-time state was dubbed ``the non-Abelian thermal state (NATS). We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system. To date, trapped ions have defined the state of the art in terms of achievable coherence times in interacting spin chains. Here, we establish an alternative platform by reporting on the observation of coherent, fully interaction-driven quantum revivals of the magnetization in Rydberg-dressed Ising spin chains of atoms trapped in an optical lattice. We identify partial many-body revivals at up to about ten times the characteristic time scale set by the interactions. At the same time, single-site-resolved correlation measurements link the magnetization dynamics with inter-spin correlations appearing at different distances during the evolution. These results mark an enabling step towards the implementation of Rydberg atom based quantum annealers, quantum simulations of higher dimensional complex magnetic Hamiltonians, and itinerant long-range interacting quantum matter.
We investigate the detailed properties of Observational entropy, introduced by v{S}afr{a}nek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse-grainings, even those that do not commute with each other, without losing any of its properties. It is well-defined out of equilibrium, and for some coarse-grainings it generically rises to the correct thermodynamic value even in a genuinely isolated quantum system. The quantity contains several other entropy definitions as special cases, it has interesting information-theoretic interpretations, and mathematical properties -- such as extensivity and upper and lower bounds -- suitable for an entropy. Here we describe and provide proofs for many of its properties, discuss its interpretation and connection to other quantities, and provide numerous simulations and analytic arguments supporting the claims of its relationship to thermodynamic entropy. This quantity may thus provide a clear and well-defined foundation on which to build a satisfactory understanding of the second thermodynamical law in quantum mechanics.
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