Transition Probability for Class of Two Level System Time Dependent Hamiltonians

TL;DR

This paper derives a simplified formula for transition probabilities in certain two-level quantum systems with time-dependent Hamiltonians, applicable under specific asymptotic conditions.

Contribution

It introduces a new, simplified expression for transition probabilities in two-level systems with time-dependent Hamiltonians, valid under specific asymptotic conditions.

Findings

Transition probability simplifies to a form depending only on Hamiltonian parameters at large times.

Applicable when the approach to the infinite time limit is non-trivial and at least as fast as 1/t.

Provides a practical method for calculating transition probabilities in time-dependent two-level systems.

Abstract

Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for large t, the transition probability takes a particularly simple form depending only on the value of Hamiltonian parameters in this limit.