TY - JOUR

T1 - On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

AU - Lim, Soon Hoe

AU - Wehr, Jan

AU - Lampo, Aniello

AU - García-March, Miguel Ángel

AU - Lewenstein, Maciej

N1 - Funding Information:
Acknowledgements S. Lim and J. Wehr were partially supported by NSF Grant DMS 1615045. This work has been funded by a scholarship from the Programa Másters d’Excel-léncia of the Fundació Catalunya-La Pedrera, ERC Advanced Grant OSYRIS (ERC-2013-AdG Grant 339106), EU IP SIQS (FP7-ICT-2011-9600645), EU PRO QUIC (H2020-FETProAct-2014 641122), EU STREP EQuaM (FP7/2007-2013, No. 323714), Fundació Cellex, the Spanish MINECO (SEVERO OCHOA GRANT SEV-2015-0522, FISICATEAMO FIS2016-79508-P), and Generalitat de Catalunya (SGR 874 and CERCA/Program).

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Heisenberg–Langevin equation

KW - Noise-induced drifts

KW - Quantum Brownian motion

KW - Quantum stochastic calculus

KW - Small mass limit

KW - Smoluchowski–Kramers limit

UR - http://www.scopus.com/inward/record.url?scp=85034836913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034836913&partnerID=8YFLogxK

U2 - 10.1007/s10955-017-1907-7

DO - 10.1007/s10955-017-1907-7

M3 - Article

AN - SCOPUS:85034836913

VL - 170

SP - 351

EP - 377

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -