Abstract
We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies. These hamiltonians arise, respectively, in harmonic traps, and the c = 1 Matrix Model description of two dimensional string theory with time dependent string coupling. We show how the dynamics is determined by a single function of time which satisfies a generalized Ermakov-Pinney equation. The quench protocols we consider asymptote to constant masses and frequencies at early times, and cross or approach a gapless potential. In a right side up harmonic oscillator potential we determine the scaling behavior of the one point function and the entanglement entropy of a subregion by obtaining analytic approximations to the exact answers. The results are consistent with Kibble-Zurek scaling for slow quenches and with perturbation calculations for fast quenches. For cis-critical quench protocols the entanglement entropy oscillates at late times around its initial value. For end-critical protocols the entanglement entropy monotonically goes to zero inversely with time, reflecting the spread of fermions over the entire line. For the inverted harmonic oscillator potential, the dual collective field description is a scalar field in a time dependent metric and dilaton background.
Highlights
A common way to study non-equilibrium properties of quantum field theories is to subject them to a quantum quench, i.e. introduce an explicit time dependence to parameters which appear in the lagrangian
We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies
We provide exactly solvable quench protocols for fermions with a fixed mass m in a harmonic oscillator potential with time dependent frequencies
Summary
A common way to study non-equilibrium properties of quantum field theories is to subject them to a quantum quench, i.e. introduce an explicit time dependence to parameters which appear in the lagrangian. We will solve the quantum mechanical time evolution of such a system for interesting time dependent frequencies of the CCP and ECP type and calculate the early time response of one point functions as well as entanglement entropies for a sub-region for arbitary quench rates to find the scaling behavior in various regimes. For the ECP the entanglement entropy monotonically goes to zero as a power law in time, reflecting the fact that the particles can spread all over space Such solvable systems have played a major role in providing insight into scaling properties of quantum quench in continuum relativistic theories and in spin systems which can be reduced to lattice versions of relativistic fermions [33,34,35, 42, 43].
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