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

Understand

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.