Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

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2014-06

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Abstract

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density → ∞). Our estimates allow us to interchange the thermodynamic with the mean-field limit. © 2014 Springer-Verlag Berlin Heidelberg.

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10.1007/s00220-014-1987-z

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Deckert, DA, J Fröhlich, P Pickl and A Pizzo (2014). Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas. Communications in Mathematical Physics, 328(2). 10.1007/s00220-014-1987-z Retrieved from https://hdl.handle.net/10161/17115.

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