# Total Energy Dynamics and Asymptotics of the Momentum Distribution Following an Interaction Quench in a Two-component Fermi Gas

## TL;DR

This paper investigates the energy dynamics and momentum distribution asymptotics in a two-component Fermi gas after an interaction quench, addressing divergence issues and analyzing the evolution of Tan's contact across different quench protocols.

## Contribution

It introduces a method to remove divergences in energy calculations and derives the time evolution of Tan's contact during interaction ramps.

## Key findings

- Divergences in energy dynamics can be regularized for arbitrary interaction protocols.
- Tan's contact exhibits rapid oscillations and reaches a stationary value after a sudden quench.
- In the adiabatic limit, the contact grows quadratically and saturates to equilibrium.

## Abstract

The absence of a characteristic momentum scale in the pseudo-potential description of atomic interaction in ultracold (two-component Fermi) gases is known to lead to divergence in perturbation theory. Here we show that they also plague the calculation of the dynamics of the total energy following a quantum quench. A procedure to remove the divergence is devised, which provides finite answers for the time-evolution of the total energy after a quench in which the interaction strength is ramped up according to an arbitrary protocol. An important result of this analysis is the time evolution of the asymptotic tail of the momentum distribution (related to Tan's contact) and the contact for a linear interaction ramp are obtained, as a function of the interaction ramp time in the crossover from the sudden quench to the adiabatic limit are reported. In sudden quench limit, the contact, following a rapid oscillation, reaches a stationary value which is different from the equilibrium one. In the adiabatic limit, the contact grows quadratically in time and later saturates to its equilibrium value for the final value of the scattering length.