Nonlinear Schrödinger equation with chaotic, random, and nonperiodic nonlinearity

Cardoso, Wesley B.; Leão, Salviano A.; Avelar, A. T.; Bazeia, D.; Hussein, M. S.

doi:10.1016/j.physleta.2010.09.037

Cited by 6 publications

(1 citation statement)

References 32 publications

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“…the Gross-Pitaevskii equation, to investigate nonlinear photonics, Langmuir waves in plasmas among other systems -see e.g. [20,21] and references there in. Furthermore, besides the linear coupling in ξ, the functional integration can also be performed exactly up to quadratic terms g 1 ξ + g 2 ξ 2 /2, where g 1 and g 2 represent possible quantum operators.…”

Section: Discussion and Summarymentioning

confidence: 99%

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

et al. 2016

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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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Section: Discussion and Summarymentioning

confidence: 99%