Quantum Dynamics in Noisy Backgrounds: from sampling to dissipation and fluctuations
Abstract
We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian, which evolves the quantum state with a dissipative dynamics. We also show that if the integration over the noisy field is done for the time evolution of the density matrix, a gain contribution from the fluctuations, can be accessed in addition to the loss one from the non-hermitian Hamiltonian dynamics. We illustrate our study by computing analytically the effective non-Hermitian Hamiltonian, which we found to be the complex frequency harmonic oscillator, with a known evolution operator. It leads to space and time localisation, a common feature of noisy quantum systems in general applications.
Cite
@article{arxiv.1512.06456,
title = {Quantum Dynamics in Noisy Backgrounds: from sampling to dissipation and fluctuations},
author = {O. Oliveira and W. de Paula and T. Frederico and M. S. Hussein},
journal= {arXiv preprint arXiv:1512.06456},
year = {2016}
}