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Register a new userQuantum hydrodynamics from local thermal pure states
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We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum ($ell$TPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the $ell$TPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic relaxation obeying the Fouriers law. We further prove the second law of thermodynamics and the quantum fluctuation theorem, which are also validated numerically. The $ell$TPQ formulation gives a useful theoretical basis to describe the emergent hydrodynamic behavior of quantum many-body systems furnished with a numerical efficiency, being applicable to both the non-relativistic and relativistic regimes.
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By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in an one dimensional free Fermi gas or Tonks gas (Bose gas with infinite repulsion).
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