Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

TL;DR

This paper introduces an exact analytical method for solving the Landau-Zener problem with waiting at the minimum gap, extending it to many-body systems and discussing experimental implications.

Contribution

It develops a time-reversal based technique to solve a variant of the Landau-Zener problem with waiting, providing exact excitation probabilities and applying it to many-body quantum critical systems.

Findings

Derived exact excitation probability as a function of waiting time

Numerical validation of analytical results

Analyzed residual energy in many-body quantum critical systems

Abstract

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem which involves waiting at the minimum gap for a time t_w; we find an exact expression for the excitation probability as a function of t_w. We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally we discuss possible experimental realizations of this work.