Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory.

摘要: We investigate a class of exactly solvable quantum quench protocols with finite rate in systems one dimensional non-relativistic fermions external harmonic oscillator or inverted potentials, time dependent masses and frequencies. These hamiltonians arise, respectively, traps, the $c=1$ Matrix Model description two string theory coupling. show how dynamics is determined by single function which satisfies generalized Ermakov-Pinney equation. The we consider asymptote to constant frequencies at early times, cross approach gapless potential. In right side up potential determine scaling behavior point entanglement entropy subregion obtaining analytic approximations exact answers. results are consistent Kibble-Zurek for slow quenches perturbation calculations fast quenches. For cis-critical oscillates late times around its initial value. end-critical monotonically goes zero inversely time, reflecting spread over entire line. potential, dual collective field scalar metric dilaton background.