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Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

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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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Acknowledgments

The authors acknowledge financial support from the Brazilian agencies FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico). OO acknowledges financial support from grant 2014/08388-0 from São Paulo Research Foundation (FAPESP). MSH acknowledges support from CAPES/ITA-PVS Fellowship program, and FAPESP/CEPID-CEPOF.

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Authors and Affiliations

  1. CFisUC, Department of Physics, University of Coimbra, 3004 516, Coimbra, Portugal

    O. Oliveira

  2. Instituto Tecnológico de Aeronáutica, DCTA, 12228-900, São José dos Campos, Brazil

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

  3. Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970, São Paulo, SP, Brazil

    M. S. Hussein

  4. Instituto de Estudos Avançados, Universidade de São Paulo, Caixa Postal 66318, 05314-970, São Paulo, SP, Brazil

    M. S. Hussein

Authors
  1. O. Oliveira
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  2. W. de Paula
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  3. T. Frederico
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  4. M. S. Hussein
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Corresponding author

Correspondence to W. de Paula.

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Oliveira, O., Paula, W.d., Frederico, T. et al. Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations. Braz J Phys 46, 384–392 (2016). https://doi.org/10.1007/s13538-016-0425-4

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  • DOI: https://doi.org/10.1007/s13538-016-0425-4

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