Interscale entanglement production in a quantum system simulating classical chaos

• URL: http://arxiv.org/abs/2201.09217v3
• Date: Sat, 23 Sep 2023 11:33:03 GMT
• Title: Interscale entanglement production in a quantum system simulating classical chaos
• Authors: Taiki Haga and Shin-ichi Sasa
• Abstract summary: We study standard classical chaos in a framework of quantum mechanics. By simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the interscale entanglement entropy becomes positive.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is a fundamental problem how the universal concept of classical chaos emerges from the microscopic description of quantum mechanics. We here study standard classical chaos in a framework of quantum mechanics. In particular, we design a quantum lattice system that exactly simulates classical chaos after an appropriate continuum limit, which is called the "Hamiltonian equation limit". The key concept of our analysis is an entanglement entropy defined by dividing the lattice into many blocks of equal size and tracing out the degrees of freedom within each block. We refer to this entropy as the "interscale entanglement entropy" because it measures the amount of entanglement between the microscopic degrees of freedom within each block and the macroscopic degrees of freedom that define the large-scale structure of the wavefunction. By numerically simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the interscale entanglement entropy becomes positive only when chaos emerges in the Hamiltonian equation limit, and the growth rate of the entropy in the initial stage is proportional to that of the coarse-grained Gibbs entropy of the corresponding classical system.

Related papers

• Non-stabilizerness Entanglement Entropy: a measure of hardness in the classical simulation of quantum many-body systems [0.49157446832511503]
  We introduce the concept of non-stabilizerness entanglement entropy which is basically the minimum residual entanglement entropy for a quantum state. It can serve as a new practical and better measure of difficulty in the classical simulation of quantum many-body systems.
  arXiv  Detail & Related papers  (2024-09-25T13:06:04Z)
• Chaos and magic in the dissipative quantum kicked top [0.0]
  We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. We find that the nonstabilizerness averaged over trajectories, mirrors the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-06-24T12:19:19Z)
• Probing quantum chaos with the entropy of decoherent histories [0.0]
  Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. We propose the quantum chaos definition in the manner similar to the classical one using decoherent histories as a quantum analogue of trajectories. We show that for such a model, the production of entropy of decoherent histories is radically different in integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2023-07-17T21:57:05Z)
• Realizing the entanglement Hamiltonian of a topological quantum Hall system [10.092164351939825]
  Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally quantifies entanglement, has been proposed as a first signature of topological order. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed Hall systems.
  arXiv  Detail & Related papers  (2023-07-12T15:40:06Z)
• Quantum collapse and exponential growth of out-of-time-ordered correlator in anisotropic quantum Rabi model [10.967081346848687]
  We show that the exponential growth of the out-of-time-ordered correlator (OTOC) at early times for the initial states centered both in the chaotic and stable regions of the anisotropic quantum Rabi model. We attribute the exponential growth of the OTOC to quantum collapse which provides a novel mechanism of yielding exponential growth of the OTOC in quantum systems. Our results show that compared with the OTOC, the linear entanglement entropy and Loschmidt echo seem to be more effective to diagnose the signals of quantum chaos in the anisotropic quantum Rabi model.
  arXiv  Detail & Related papers  (2023-05-27T15:23:37Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• A new entanglement measure based dual entropy [7.95085289592294]
  We define $St$-entropy entanglement based on von Neumann entropy and its complementary dual. We prove a new type of entanglement inequality in terms of $St$-entropy entanglement for quantum entangled networks.
  arXiv  Detail & Related papers  (2022-04-15T10:08:12Z)
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
  We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
  arXiv  Detail & Related papers  (2021-09-24T11:19:22Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• Quantum Kolmogorov-Sinai entropy and Pesin relation [0.0]
  A quantum Kolmogorov-Sinai entropy is defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. We show a quantum (Pesin) relation between this entropy and the sum of positive eigenvalues of a matrix describing phase-space expansion.
  arXiv  Detail & Related papers  (2020-10-12T23:08:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.