Exact Solution of Bogoliubov Equations for Bosons in One-Dimensional Piecewise Constant Potential

2009/09/07 by Daisuke Takahashi, Takahashi, Daisuke
Physics and Astronomy · #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #cond-mat.quant-gas

paper · pdf · doi:10.48550/arxiv.0909.1068

12 pages, 7 figures, 1 table; misprints fixed

arxiv created 2009/09/08 · arxiv updated 2009/12/01

Abstract

We show that Bogoliubov equations in one-dimensional systems with piecewise constant potentials can be always solved. In particular, we analyze in detail the case where the condensate wavefunction is a real-valued function, and give the explicit expressions for wavefunctions of Bogoliubov excitations. By means of these solutions, we consider transmission and reflection properties of Bogoliubov excitations for two types of potential, namely, a rectangular barrier and a potential step. The results yield simple and exact examples of anomalous tunneling effect and quantum evaporation.

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