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Quantum Dynamics in Noisy Backgrounds: from sampling to dissipation and fluctuations

Authors: O. Oliveira, W. de Paula, T. Frederico, M. S. Hussein

Ref.: Braz. J. Physics 46, 384 (2016)

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.

DOI: 10.1007/s13538-016-0425-4

URL: arxiv.org