With use of the Wigner representation, the Kramers equation for a Brownian particle in a potential field of external force is extended to the quantum mechanical case. As a simple application of the equation, the rate of jump over a potential barrier is estimated to the lowest order approximation in $\hbar$ . The rate increases due to the quantum mechanical effect by the factor $1{+}(\beta\hbar\omega)^{2}\omega^{2}/6(\eta^{2}{+}\omega^{2}$ ), where ω, η and β are the angular frequency of the particle in the potential well, viscosity and the inverse of temperature, respectively.With use of the Wigner representation, the Kramers equation for a Brownian particle in a potential field of external force is extended to the quantum mechanical case. As a simple application of the equation, the rate of jump over a potential barrier is estimated to the lowest order approximation in $\hbar$. The rate increases due to the quantum mechanical effect by the factor $1{+}(\beta\hbar\omega)^{2}\omega^{2}/6(\eta^{2}{+}\omega^{2}$), where ω, η and β are the angular frequency of the particle in the potential well, viscosity and the inverse of temperature, respectively.

Journal of the Physical Society of JapanFeb 1, 198011 citations

Quantum rate theory: basic methods

WORLD SCIENTIFIC eBooksOct 1, 20210 citations

Analysis of laser-amplifier noise: A review of the method and its application to optical communications

Kazuro Kikuchi

This study summarizes the theory of laser-amplifier noise based on the master equation, the quantum-mechanical Langevin equation, and the rate equation. The three approaches are used differently depending on the application. Laser-amplifier noise in the direct-detection receiver is described by the master equation. Meanwhile, the quantum-mechanical Langevin equation is most effective for analyzing noise appearing in coherent optical communication systems. The rate equation approach provides a clear understanding of the intensity-noise characteristics of laser oscillators, including the amplitude squeezing.This study summarizes the theory of laser-amplifier noise based on the master equation, the quantum-mechanical Langevin equation, and the rate equation. The three approaches are used differently depending on the application. Laser-amplifier noise in the direct-detection receiver is described by the master equation. Meanwhile, the quantum-mechanical Langevin equation is most effective for analyzing noise appearing in coherent optical communication systems. The rate equation approach provides a clear understanding of the intensity-noise characteristics of laser oscillators, including the amplitude squeezing.

Jun 7, 20230 citations

Analysis of laser-amplifier noise: A review of the method and its application to optical communications

Kazuro Kikuchi

Jun 6, 20230 citations

Rate equations in quantum electronics

J.E. Carroll

Cambridge University Press eBooksFeb 6, 19860 citations

\hbar

. The rate increases due to the quantum mechanical effect by the factor

1{+}(\beta\hbar\omega)^{2}\omega^{2}/6(\eta^{2}{+}\omega^{2}

), where ω, η and β are the angular frequency of the particle in the potential well, viscosity and the inverse of temperature, respectively.