On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion |
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Authors: | Soon Hoe Lim Jan Wehr Aniello Lampo Miguel Ángel García-March Maciej Lewenstein |
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Institution: | 1.Department of Mathematics and Program in Applied Mathematics,University of Arizona,Tucson,USA;2.ICFO-Institut de Ciències Fotòniques,The Barcelona Institute of Science and Technology,Castelldefels (Barcelona),Spain;3.ICREA,Barcelona,Spain |
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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 \(m = m_{0} \epsilon \), the reduced Planck constant to equal \(\hbar = \epsilon \) and the cutoff frequency to equal \(\varLambda = E_{\varLambda }/\epsilon \), where \(m_0\) and \(E_{\varLambda }\) are positive constants, so that the particle’s de Broglie wavelength and the largest energy scale of the bath are fixed as \(\epsilon \rightarrow 0\). We study the limit as \(\epsilon \rightarrow 0\) 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. |
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