Closeness of the reduced density matrix of an interacting small system to the Gibbs state

• URL: http://arxiv.org/abs/2003.09258v2
• Date: Thu, 6 Aug 2020 07:56:17 GMT
• Title: Closeness of the reduced density matrix of an interacting small system to the Gibbs state
• Authors: Wen-ge Wang
• Abstract summary: I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case. I also study the RDM which is computed from a typical state of the total system within an energy shell.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form and with a generic interaction strength, when the total system lies in an equilibrium state described by a microcanonical ensemble. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case and the RDM obtained in the uncoupled case. In the eigenbasis of the central system's Hamiltonian, it is shown that the difference between diagonal elements is mainly confined by the ratio of the maximum width of the eigenfunctions of the total system in the uncoupled basis to the width of the microcanonical energy shell; meanwhile, the difference between off-diagonal elements is given by the ratio of certain property of the interaction Hamiltonian to the related level spacing of the central system. As an application, a sufficient condition is given, under which the RDM may have a canonical Gibbs form under system-environment interactions that are not necessarily weak; this Gibbs state usually includes certain averaged effect of the interaction. For central systems that interact locally with many-body quantum chaotic systems, it is shown that the RDM usually has a Gibbs form. I also study the RDM which is computed from a typical state of the total system within an energy shell.

Related papers

• Dynamics of quantum coherence in many-body localized systems [13.711664669643952]
  We show that quantum coherence serves as an effective probe for identifying dephasing, which is a distinctive signature of many-body localization (MBL) Our results provide insights into understanding many-body dephasing phenomena in MBL systems and propose a novel feasible method for identifying and characterizing MBL phases in experiments.
  arXiv  Detail & Related papers  (2024-02-20T03:54:50Z)
• Canonical typicality under general quantum channels [41.94295877935867]
  In the present work we employ quantum channels to define generalized subsystems. We show that generalized subsystems also display the phenomena of canonical typicality. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.
  arXiv  Detail & Related papers  (2023-08-30T21:29:45Z)
• Dispersive Non-reciprocity between a Qubit and a Cavity [24.911532779175175]
  We present an experimental study of a non-reciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity. We show that the qubit-cavity dynamics is well-described in a wide parameter regime by a simple non-reciprocal master-equation model.
  arXiv  Detail & Related papers  (2023-07-07T17:19:18Z)
• Quantifying quantum chaos through microcanonical distributions of entanglement [0.0]
  A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT) We introduce a quantitative metric for quantum chaos which utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of midspectrum eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints) We study this metric in local minimally structured Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed field Ising model (MFIM
  arXiv  Detail & Related papers  (2023-05-19T18:00:05Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians [6.907555940790131]
  In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant.
  arXiv  Detail & Related papers  (2022-02-02T18:05:50Z)
• Preferred basis derived from eigenstate thermalization hypothesis [1.7606558873844536]
  We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned.
  arXiv  Detail & Related papers  (2022-01-17T09:41:39Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Entanglement Emerges from Dissipation-Structured Quantum Self-Organization [12.18859145788751]
  Entanglement is a holistic property of multipartite quantum systems. Dissipative structure theory directs the evolving time arrow of a non-equilibrium system. Entanglement can emerge via the dissipation-structured correlation.
  arXiv  Detail & Related papers  (2021-09-25T08:39:18Z)
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension [0.0]
  Entanglement plays a prominent role in the study of condensed matter many-body systems. We show that the scaling of entanglement with the length of a subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term.
  arXiv  Detail & Related papers  (2021-05-03T10:35:09Z)
• Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath [0.0]
  This work addresses quantum adiabatic decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system-environment interaction Hamiltonian that represents a partition of non-interacting subsystems.
  arXiv  Detail & Related papers  (2019-12-30T16:39:38Z)

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.