Canonical density matrices from eigenstates of mixed systems
- URL: http://arxiv.org/abs/2103.05974v2
- Date: Fri, 16 Dec 2022 19:33:11 GMT
- Title: Canonical density matrices from eigenstates of mixed systems
- Authors: Mahdi Kourehpaz, Stefan Donsa, Fabian Lackner, Joachim Burgd\"orfer,
and Iva B\v{r}ezinov\'a
- Abstract summary: We study the emergence of thermal states in the regime of a quantum analog of a mixed phase space.
Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: One key issue of the foundation of statistical mechanics is the emergence of
equilibrium ensembles in isolated and closed quantum systems. Recently, it was
predicted that in the thermodynamic ($N\rightarrow\infty$) limit of large
quantum many-body systems canonical density matrices emerge for small
subsystems from almost all pure states. This notion of canonical typicality is
assumed to originate from the entanglement between subsystem and environment
and the resulting intrinsic quantum complexity of the many-body state. For
individual eigenstates it has been shown that local observables show thermal
properties provided the eigenstate thermalization hypothesis holds, which
requires the system to be quantum chaotic. In the present paper, we study the
emergence of thermal states in the regime of a quantum analog of a mixed phase
space. Specifically, we study the emergence of the canonical density matrix of
an impurity upon reduction from isolated energy eigenstates of a large but
finite quantum system the impurity is embedded in. Our system can be tuned by
means of a single parameter from quantum integrability to quantum chaos and
corresponds in between to a system with mixed quantum phase space. We show that
the probability for finding a canonical density matrix when reducing the
ensemble of energy eigenstates of the finite many-body system can be
quantitatively controlled and tuned by the degree of quantum chaos present. For
the transition from quantum integrability to quantum chaos we find a continuous
and universal (i.e. size independent) relation between the fraction of
canonical eigenstates and the degree of chaoticity as measured by the Brody
parameter or the Shannon entropy.
Related papers
- Theory of Eigenstate Thermalisation [0.0]
The eigenstate thermalization hypothesis (ETH) of Deutsch and Srednicki suggests that this is possible because each eigenstate of the full quantum system acts as a thermal bath to its subsystems.
Our analysis provides a derivation of statistical mechanics which requires neither the concepts of ergodicity or typicality, nor that of entropy.
arXiv Detail & Related papers (2024-06-03T15:41:16Z) - Steady-state quantum chaos in open quantum systems [0.0]
We introduce the notion of steady-state quantum chaos as a general phenomenon in open quantum many-body systems.
Chaos and integrability in the steady state of an open quantum system are instead uniquely determined by the spectral structure of the time evolution generator.
We study steady-state chaos in the driven-dissipative Bose-Hubbard model, a paradigmatic example of out-of-equilibrium bosonic system without particle number conservation.
arXiv Detail & Related papers (2023-05-24T18:00:22Z) - Quantum Fisher Information for Different States and Processes in Quantum
Chaotic Systems [77.34726150561087]
We compute the quantum Fisher information (QFI) for both an energy eigenstate and a thermal density matrix.
We compare our results with earlier results for a local unitary transformation.
arXiv Detail & Related papers (2023-04-04T09:28:19Z) - 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) - Stochastic entropy production associated with quantum measurement in a
framework of Markovian quantum state diffusion [0.0]
We investigate a two level open quantum system using a framework of quantum state diffusion.
We consider the unpredictability of its reduced density matrix when subjected to an environment-driven process of continuous quantum measurement.
arXiv Detail & Related papers (2023-01-19T17:47:39Z) - Demonstrating Quantum Microscopic Reversibility Using Coherent States of
Light [58.8645797643406]
We propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath.
We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit.
arXiv Detail & Related papers (2022-05-26T00:25:29Z) - Exact emergent quantum state designs from quantum chaotic dynamics [0.0]
We consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis.
We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details.
Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics.
arXiv Detail & Related papers (2021-09-15T18:00:10Z) - Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
We propose a decoherent mechanism for sensing quantum chaos.
The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
arXiv Detail & Related papers (2021-04-13T17:24:08Z) - Taking the temperature of a pure quantum state [55.41644538483948]
Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research.
We propose a scheme to measure the temperature of such pure states through quantum interference.
arXiv Detail & Related papers (2021-03-30T18:18:37Z) - Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
Quantum scars are non-thermal eigenstates characterized by low entanglement entropy.
We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
arXiv Detail & Related papers (2020-11-16T19:05:50Z) - Thermalization of isolated quantum many-body system and the role of entanglement [1.0485739694839669]
We show that entanglement may act as a thermalizing agent, not universally but particularly.
In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are equivalent to the microcanonical and canonical averages of the observable.
arXiv Detail & Related papers (2020-09-22T09:37:38Z)
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.