Quench Dynamics of Isolated Many-Body Quantum Systems

Abstract

We study isolated quantum systems with two-body interactions after a quench. In these systems, the energy shell is a Gaussian of width $\sigma$, and it gives the maximum possible spreading of the energy distribution of the initial states. When the distribution achieves this shape, the fidelity decay can be Gaussian until saturation. This establishes a lower bound for the fidelity decay in realistic systems. An ultimate bound for systems with many-body interactions is also derived based on the analysis of full random matrices. We find excellent agreement between numerical and analytical results. We also provide the conditions under which the short-time dynamics of few-body observables is controlled by $\sigma$. The analyses are developed for systems, initial states, and observables accessible to experiments.

6 pages, 4 figures, version as published

References in corpus (18)

• Many-Body Physics with Ultracold Gases
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Fluctuation theorems: Work is not an observable
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Dynamics of Loschmidt echoes and fidelity decay
• Microscopic observation of magnon bound states and their dynamics
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Loschmidt Echo
• Controlling and Detecting Spin Correlations of Ultracold Atoms in Optical lattices
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Time Fluctuations in Isolated Quantum Systems of Interacting Particles
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
• Enlarging and cooling the Néel state in an optical lattice
• Dynamics of thermalisation in small Hubbard-model systems
• Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems
• Interaction-disorder competition in a spin system evaluated through the Loschmidt Echo
• Equilibration times in clean and noisy systems

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