Undecidability of the fate of relaxation in one-dimensional quantum systems

• URL: http://arxiv.org/abs/2012.13890v2
• Date: Tue, 24 Aug 2021 10:20:34 GMT
• Title: Undecidability of the fate of relaxation in one-dimensional quantum systems
• Authors: Naoto Shiraishi and Keiji Matsumoto
• Abstract summary: We investigate the relaxation dynamics in an isolated quantum many-body system. We prove that the stationary value in quantum many-body systems is incomputable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We investigate the relaxation dynamics in an isolated quantum many-body system. The stationary value of an observable after relaxation is a topic of researches in the field of quantum thermalization, since thermalization is a relaxation phenomena where this stationary value coincides with the equilibrium value. Therefore, computing the stationary value in quantum many-body systems is regarded as an important problem. We, however, prove that the stationary value in quantum many-body systems is incomputable. More precisely, we show that whether the stationary value is in the vicinity of a given value or not is an undecidable problem. Our undecidable result is still satisfied when we restrict our system to a one-dimensional shift-invariant system with nearest-neighbor interaction, our initial state to a product state of a state on a single site, and our observable to a shift-sum of a one-body observable. This result clearly shows that there is no general theorem or procedure to decide the presence or absence of thermalization in a given quantum many-body system.

Related papers

• Emergence of a second law of thermodynamics in isolated quantum systems [0.21990652930491852]
  The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schr"odinger equation. We show that the entropy with respect to a given observable tends towards its equilibrium value in the course of the system's unitary evolution.
  arXiv  Detail & Related papers  (2024-06-03T18:00:01Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• 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)
• Unconventional mechanism of virtual-state population through dissipation [125.99533416395765]
  We report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit. This means that the situation where the virtual state remains unpopulated can be metastable. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.
  arXiv  Detail & Related papers  (2022-02-24T17:09:43Z)
• 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)
• Canonical density matrices from eigenstates of mixed systems [0.0]
  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.
  arXiv  Detail & Related papers  (2021-03-10T10:19:05Z)
• Undecidability in quantum thermalization [0.0]
  We show that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes depending on whether the Turing machine halts.
  arXiv  Detail & Related papers  (2020-12-27T08:34:24Z)
• 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)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)
• Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process [0.0]
  We show new exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales. For any finite-time process with a fixed initial environment, we show that the contraction of the system's distinction exactly quantifies its thermodynamic dissipation.
  arXiv  Detail & Related papers  (2020-02-26T12:10:10Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.