We study the small mass limit (or: the Smoluchowski–Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz–Drude cutoff, we derive the Heisenberg–Langevin equations for the particle’s observables using a quantum stochastic calculus approach. We set the mass of the particle to equal m= m0ϵ, the reduced Planck constant to equal ħ= ϵ and the cutoff frequency to equal Λ= EΛ/ ϵ, where m0 and EΛ are positive constants, so that the particle’s de Broglie wavelength and the largest energy scale of the bath are fixed as ϵ→ 0. We study the limit as ϵ→ 0 of the rescaled model and derive a limiting equation for the (slow) particle’s position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.
CITATION STYLE
Lim, S. H., Wehr, J., Lampo, A., García-March, M. Á., & Lewenstein, M. (2018). On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion. Journal of Statistical Physics, 170(2), 351–377. https://doi.org/10.1007/s10955-017-1907-7
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