Non-adiabacity and large flucutations in a many particle Landau Zener problem

TL;DR

This paper investigates how interactions and slow external driving cause broad quantum fluctuations in many-particle systems, leading to non-adiabatic behavior even at slow driving rates, contrasting with single-particle expectations.

Contribution

It introduces a comprehensive analysis of many-body Landau-Zener dynamics, revealing the profound effects of interactions and fluctuations on quantum state evolution.

Findings

Broad particle distributions in Hilbert space for all driving rates

Strong amplification of quantum fluctuations due to interactions

Difficulty in achieving full ground state occupancy at slow driving

Abstract

We consider the behavior of an interacting many particle system under slow external driving -- a many body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are 'non-adiabatic' in that even at very slow driving it is exceedingly difficult to push the center of the distribution towards the limit of full ground state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.