Quantum dynamics by the constrained adiabatic trajectory method

TL;DR

The paper introduces the constrained adiabatic trajectory method (CATM) for solving the time-dependent Schrödinger equation by constraining dynamics to a single Floquet eigenstate, simplifying calculations especially for large systems.

Contribution

The paper develops the CATM, a novel approach that constrains quantum dynamics to a single Floquet state using an artificial absorbing potential, facilitating easier computation.

Findings

CFS eigenvalue is well isolated, aiding computation.

CATM effectively handles large systems.

Method's properties and limitations are demonstrated through examples.

Abstract

We develop the constrained adiabatic trajectory method (CATM) which allows one to solve the time-dependent Schr\"odinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are explored through simple examples.