Quantum Chaos on Complexity Geometry

• URL: http://arxiv.org/abs/2004.03501v1
• Date: Tue, 7 Apr 2020 15:53:57 GMT
• Title: Quantum Chaos on Complexity Geometry
• Authors: Bin Yan and Wissam Chemissany
• Abstract summary: We show that complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. We show that the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit.
• Score: 3.800391908440439
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase space. We develop a linear response theory for complexity, and demonstrate that the complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. Two immediate significant results follows: i) the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit, and ii) the linear response of complexity is given by the out-of-time order correlators.

Related papers

• Krylov complexity for 1-matrix quantum mechanics [0.0]
  This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM) We analyze the Lanczos coefficients derived from the correlation function, revealing their linear growth even in this integrable system. Our findings in both ground and thermal states of 1-MQM provide new insights into the nature of complexity in quantum mechanical models.
  arXiv  Detail & Related papers  (2024-06-28T18:00:03Z)
• Universal Early-Time Growth in Quantum Circuit Complexity [0.0]
  We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times. We are able to extract the early-time behavior and dependence on the lattice spacing of complexity of field theories in the limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.
  arXiv  Detail & Related papers  (2024-06-18T18:27:36Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Krylov complexity in quantum field theory, and beyond [44.99833362998488]
  We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
  arXiv  Detail & Related papers  (2022-12-29T19:00:00Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Growth of entanglement of generic states under dual-unitary dynamics [77.34726150561087]
  Dual-unitary circuits are a class of locally-interacting quantum many-body systems. In particular, they admit a class of solvable" initial states for which, in the thermodynamic limit, one can access the full non-equilibrium dynamics. We show that in this case the entanglement increment during a time step is sub-maximal for finite times, however, it approaches the maximal value in the infinite-time limit.
  arXiv  Detail & Related papers  (2022-07-29T18:20:09Z)
• Krylov complexity from integrability to chaos [0.0]
  We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. We investigate the integrable XXZ spin chain, enriched with an integrability breaking deformation that allows one to interpolate between integrable and chaotic behavior. We find that the chaotic system indeed approaches the RMT behavior in the appropriate symmetry class.
  arXiv  Detail & Related papers  (2022-07-15T18:51:13Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Quantum Circuit Complexity of Primordial Perturbations [0.0]
  We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. Our analysis serves to highlight how different models achieve the same end result for the perturbations via different routes.
  arXiv  Detail & Related papers  (2020-12-09T08:30:07Z)
• Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos [0.0]
  We take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix.
  arXiv  Detail & Related papers  (2020-11-09T19:33:57Z)

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.