Open AccessStationary and Dynamical Solutions of the Gross-Pitaevskii Equation for a Bose-Einstein Condensate in a PT symmetric Double Well
Author(s) -
Holger Cartarius,
Dennis Dast,
Daniel Haag,
Günter Wunner,
Rüdiger Eichler,
Jörg Main
Publication year - 2013
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/1797
Subject(s) - gross–pitaevskii equation , bose–einstein condensate , eigenvalues and eigenvectors , hamiltonian (control theory) , physics , wave function , stationary state , quantum mechanics , function (biology) , classical mechanics , mathematical physics , mathematics , mathematical optimization , evolutionary biology , biology
We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional and a fully three-dimensional setup are used. Stationary states are determined and the propagation of wave function is investigated using the time-dependent Gross-Pitaevskii equation. Due to the nonlinearity of the Gross-Pitaevskii equation the potential dependson the wave function and its solutions decide whether or not the Hamiltonian itself is PT symmetric. Stationary solutions with real energy eigenvalues fulfilling exact PT symmetry are found as well as PT broken eigenstates with complex energies. The latter describe decaying or growing probability amplitudes and are not true stationary solutions of the time-dependent Gross-Pitaevskii equation. However, they still provide qualitative information about the time evolution of the wave functions.