Complex scaling flows in the quench dynamics of interacting particles

TL;DR

This paper develops analytical solutions describing the universal scaling behavior of interacting many-body quantum systems immediately after a sudden quench to resonant interactions, revealing new insights into their nonequilibrium dynamics.

Contribution

It introduces a new class of complex scaling solutions for the wave function post-quench, enabling exact analysis of observable dynamics in various interacting systems.

Findings

Exact scaling solutions for wave functions after a quench

Universal scaling properties of correlations at short times

Application to fermions, bosons, and three-body systems

Abstract

Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables such as the pair correlation function, the contact and the fidelity. We give explicit examples of the nonequilibrium dynamics for two trapped fermions or bosons quenched to unitarity, for ideal Bose polarons, and for resonantly interacting, Borromean three-body systems. These solutions reveal universal scaling properties of interacting many-body systems that arise from the buildup of correlations at short times after the quench.