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

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

2009-09-07

arxiv.org/abs/0909.1068v2

Physics

Condensed Matter

Quantum Gases

12 pages, 7 figures, 1 table; misprints fixed

Scientific paper

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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