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arXiv · 1512.06456

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

O. Oliveira·W. de Paula·T. Frederico·M. S. Hussein
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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.

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O. Oliveira, W. de Paula, T. Frederico, M. S. Hussein. 2015-12-20. Quantum Dynamics in Noisy Backgrounds: from sampling to dissipation and fluctuations. https://doi.org/10.1007/s13538-016-0425-4

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