Bounds in Nonequilibrium Quantum Dynamics

Abstract

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb-Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.

87 pages, 11 figures. Commissioned review paper submitted to International Journal of Modern Physics B, (close to) final version

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Cited by in corpus (32)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Speed limits and locality in many-body quantum dynamics
• Quantum speed limits on operator flows and correlation functions
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Speed limits of the trace distance for open quantum system
• Exact universal bounds on quantum dynamics and fast scrambling
• Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
• Optimal Hamiltonian simulation for time-periodic systems
• Estimation of Hamiltonian parameters from thermal states
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
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• Limits on the Evolutionary Rates of Biological Traits
• A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
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• Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition