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Journal of Physics A Mathematical and General

A quantum pipette

Pavel Exner

Published Sep 21, 1995• 24 citations
Publisher

Abstract

Curved quantum waveguides are known to bind particles. We show that a number of charged fermions in such a trap can be tuned by an external electrostatic field; if the latter is slowly increased, the bent duct can serve as a single particle ejector up to the spin degeneracy.
DOI
10.1088/0305-4470/28/18/021

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We consider N fermionic particles in a harmonic trap initially prepared in a thermal equilibrium state at temperature β^{-1} and examine the probability density function (pdf) of the work done by a magnetic field slowly varying in time. The behavior of the pdf crucially depends on the number of particles N but also on the temperature. At high temperatures (β≪1) the pdf is given by an asymmetric Laplace distribution for a single particle, and for many particles it approaches a Gaussian distribution with variance proportional to N/β(2). At low temperatures the pdf becomes strongly peaked at the center with a variance that still linearly increases with N but exponentially decreases with the temperature. We point out the consequences of these findings for the experimental confirmation of the Jarzynski equality such as the low probability issue at high temperatures and its solution at low temperatures, together with a discussion of the crossover behavior between the two temperature regimes.