A quantum diffusion law

Abstract

We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and temperature, each with its own characteristic rate of spreading. As with earlier analyses, we find logarithmic spreading in the quantum regime, indicating that this behavior is robust. A consistent R(t) must satisfy the key physical requirements of Wightman positivity and passivity, and we prove that ours does so. We also prove in general that these two conditions are equivalent when the FDT holds. Given current technology, our diffusion law can be tested in a laboratory with ultra cold atoms.

arXiv commentsubmitted for publication

References in corpus (4)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• All Optical Formation of an Atomic Bose-Einstein Condensate
• Brownian motion at absolute zero
• Moving mirrors and the fluctuation-dissipation theorem

Cited by in corpus (5)

• Quantum Brownian Motion: Drude and Ohmic Baths as Continuum Limits of the Rubin Model
• Measurements and analysis of response function of cold atoms in optical molasses
• Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field
• Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour
• Effect of light-assisted tunable interaction on the position response function of cold atoms