The dissipative quantum systems are treated using Klein-Kramers equation, combined with the Gaussian kernel trajectory ensemble, for time evolution of Wigner function $ρ_ω(q, p, t)$ in phase space. The entangled trajectory molecular dynamics approach is used to obtain trajectory solutions for the Klein-Kramers equation with three models: free particle, damped harmonic oscillator and metastable potential. It is found that the performance of semiclassical Wigner propagation is effectively for the relaxation of damped harmonic oscillator and dissipative decay of a metastable state. In addition, the energy of trajectory ensemble decays faster with smaller friction value and changes slightly with variable temperature parameters.The dissipative quantum systems are treated using Klein-Kramers equation, combined with the Gaussian kernel trajectory ensemble, for time evolution of Wigner function $ρ_ω(q, p, t)$ in phase space. The entangled trajectory molecular dynamics approach is used to obtain trajectory solutions for the Klein-Kramers equation with three models: free particle, damped harmonic oscillator and metastable potential. It is found that the performance of semiclassical Wigner propagation is effectively for the relaxation of damped harmonic oscillator and dissipative decay of a metastable state. In addition, the energy of trajectory ensemble decays faster with smaller friction value and changes slightly with variable temperature parameters.

The Journal of Atomic and Molecular SciencesJul 1, 20160 citations

Quantum damped oscillator I: dissipation and resonances

Chruscinski, D, Jurkowski, J

Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

Jan 1, 200527 citations

Quantum theory of the damped harmonic oscillator

Hermann Grabert, Ulrich Weiß, Peter Talkner A

The European Physical Journal BMar 1, 1984272 citations

The quantum damped harmonic oscillator

Chung‐In Um, Kyu-Hwang Yeon, Thomas F. George

Physics ReportsMay 1, 2002194 citations

The dissipative quantum systems are treated using Klein-Kramers equation, combined with the Gaussian kernel trajectory ensemble, for time evolution of Wigner function

ρ_ω(q, p, t)

in phase space. The entangled trajectory molecular dynamics approach is used to obtain trajectory solutions for the Klein-Kramers equation with three models: free particle, damped harmonic oscillator and metastable potential. It is found that the performance of semiclassical Wigner propagation is effectively for the relaxation of damped harmonic oscillator and dissipative decay of a metastable state. In addition, the energy of trajectory ensemble decays faster with smaller friction value and changes slightly with variable temperature parameters.