Quantum Brownian motion

Previously, stochastic Schrodinger equations for a quantum Brownian motion have been derived only for the particle component through approximated equations, such as the master equation obtained by the Markovian approximation [18]. In contrast, our stochastic Schrodinger equation is exact. Moreover, our stochastic equation includes both the particle and the field components, so it does not rely on integrating out the field bath modes. 

The resulting dissipation model, first introduced in Refs. 20-22, has later been popularized by A.O. Caldeira and A.J. Leggett, who applied it to the quantum mechanical tunneling of a macroscopic variable [23,24]. This model (also put forward at the same time in Refs. 25-27 for the description of quantum Brownian motion) is now referred to as the Caldeira-Leggett dissipation model. It is widely used for the description of the dynamics of classical as well as... 

We now turn to quantum Brownian motion as described by the generalized Langevin equation (22), with the symmetrized correlation function of the random force as given by Eq. (20). 

N. Pother and A. Mauger, Aging effects in free quantum Brownian motion. Physica A 282, 77 (2000). 

H. Grabert, P. Schramm, and G. L. Ingold, Quantum Brownian motion The functional integral approach. Phys. Rep. 168, 115 (1988). 

Quantum Brownian Motion in a Two-Level Spin-Bath.185... 

QUANTUM BROWNIAN MOTION IN A TWO-LEVEL SPIN-BATH... 

Quantum Brownian Motion in a Spin-Bath and for the FD relation (Equation 9.30)... 

Barik, D., D. Banerjee, and D. S. Ray. 2009. Quantum Brownian Motion in c-Numbers Theory and Application. NY Nova-Science Publishers. 

Caldeira, A. O., and A. J. Leggett. 1983a. Path integral approach to quantum Brownian motion. PhysicaA Statistical Mechanics and its Applications 121 (3) 587-616. 

Nucleation, quantum Brownian motion, and the third law of thermodynamics... 

P. Hanggi, G.L. Tngold Fundamental aspects of quantum Brownian motion Chaos 15(2005)111... 

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