Quantum space-time Poincaré inequality for Lindblad dynamics

• URL: http://arxiv.org/abs/2406.09115v2
• Date: Sat, 13 Jul 2024 13:09:32 GMT
• Title: Quantum space-time Poincaré inequality for Lindblad dynamics
• Authors: Bowen Li, Jianfeng Lu,
• Abstract summary: We derive explicit and constructive exponential decay estimates for the convergence in the noncommutative $L2$-norm. Our analysis relies on establishing a quantum analog of space-time Poincar'e inequalities. A number of concrete examples are provided as applications of our theoretical results.
• Score: 15.031583573428481
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the mixing properties of primitive hypocoercive Lindblad dynamics. By extending the variational framework originally developed for underdamped Langevin dynamics, we derive fully explicit and constructive exponential decay estimates for the convergence in the noncommutative $L^2$-norm. Our analysis relies on establishing a quantum analog of space-time Poincar\'{e} inequalities. To complement these hypocoercive estimates, we also analyze the limiting behavior of the spectral gap for Lindblad dynamics with a large coherent contribution, providing sharper convergence rate estimates in this asymptotic regime. A number of concrete examples are provided as applications of our theoretical results.

Related papers

• Algebraic and Statistical Properties of the Ordinary Least Squares Interpolator [3.4320157633663064]
  We provide results for the minimum $ell$-norm OLS interpolator. We present statistical results such as an extension of the Gauss-Markov theorem. We conduct simulations that further explore the properties of the OLS interpolator.
  arXiv  Detail & Related papers  (2023-09-27T16:41:10Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems [98.34292831923335]
  Motivated by the problem of online correlation analysis, we propose the emphStochastic Scaled-Gradient Descent (SSD) algorithm. We bring these ideas together in an application to online correlation analysis, deriving for the first time an optimal one-time-scale algorithm with an explicit rate of local convergence to normality.
  arXiv  Detail & Related papers  (2021-12-29T18:46:52Z)
• Lindbladian dissipation of strongly-correlated quantum matter [0.9290757451344674]
  The Sachdev-Ye-Kitaev Lindbladian is a paradigmatic solvable model of dissipative many-body quantum chaos. Analytical progress is possible by developing a mean-field theory for the Liouvillian time evolution on the Keldysh contour.
  arXiv  Detail & Related papers  (2021-12-22T18:17:52Z)
• 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)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes [0.0]
  We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians. We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differential-difference equations.
  arXiv  Detail & Related papers  (2021-07-06T15:02:58Z)
• Statistical mechanics of one-dimensional quantum droplets [0.0]
  We study the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions.
  arXiv  Detail & Related papers  (2021-02-25T15:30:30Z)

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.