On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

Abstract

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 = m0ǫ, the reduced Planck constant to equal = ǫ and the cutoff frequency to equal Λ = EΛ/ǫ, 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 ǫ → 0. We study the limit as ǫ → 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.

Using Polarons for sub-nK Quantum Nondemolition Thermometry in a Bose-Einstein Condensate

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Quantum partition of energy for a free Brownian particle: Impact of dissipation

“…Lately, kinetic energy of a trappped Fermi gas has been considered [11]. Many other aspects of quantum Brownian motion has been intensively studied in last few years [12][13][14][15][16][17][18][19][20]. However, the previous results have not been directly related to the energy equipartition theorem.…”

Partition of energy for a dissipative quantum oscillator

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