# Critical behavior at dynamical phase transition in the generalized Bose-Anderson model

## TL;DR

This paper investigates the critical properties of a dynamical phase transition in a generalized Bose-Anderson model, revealing power-law behaviors and non-Lyapunov instabilities near the critical quench amplitude.

## Contribution

It provides a numerically exact analysis of the critical dynamics in the mean-field limit, highlighting the role of irreversibility and memory effects in the transition.

## Key findings

- Relaxation constant follows a power law near criticality
- Asymptotic frequency shows power-law dependence on detuning
- Critical evolution exhibits non-Lyapunov power-law instability

## Abstract

Critical properties of the dynamical phase transition in the quenched generalized Bose-Anderson impurity model are studied in the mean-field limit of an infinite number of channels. The transition separates the evolution toward ground state and toward the branch of stable excited states. We perform numerically exact simulations of a close vicinity of the critical quench amplitude. The relaxation constant describing the asymptotic evolution toward ground state, as well as asymptotic frequency of persistent phase rotation and number of cloud particles at stable excited state are power functions of the detuning from the critical quench amplitude. The critical evolution (separatrix between the two regimes) shows a non-Lyapunov power-law instability arising after a certain critical time. The observed critical behavior is attributed to the irreversibility of the dynamics of particles leaving the cloud and to memory effects related to the low-energy behavior of the lattice density of states.