Acta Polytechnica. 2014, vol. 54, no. 2http://hdl.handle.net/10467/666022024-03-29T04:57:00Z2024-03-29T04:57:00ZSTABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTSLöhle, AndreasCartarius, HolgerHaag, DanielDast, DennisMain, JörgWunner, Günter Wunnerhttp://hdl.handle.net/10467/989342022-01-04T13:23:17Z2014-01-01T00:00:00ZSTABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS
Löhle, Andreas; Cartarius, Holger; Haag, Daniel; Dast, Dennis; Main, Jörg; Wunner, Günter Wunner
A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a PT symmetric external potential. If the strength of the in- and outcoupling is increased two PT broken states bifurcate from the PT symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a PT symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.
2014-01-01T00:00:00ZEXACT RENORMALIZATION GROUP FOR POINT INTERACTIONSTurgut Teoman, Osman Teoman TurgutEröncel , Cemhttp://hdl.handle.net/10467/671312017-02-09T09:24:57Z2014-01-01T00:00:00ZEXACT RENORMALIZATION GROUP FOR POINT INTERACTIONS
Turgut Teoman, Osman Teoman Turgut; Eröncel , Cem
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble nonabelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
2014-01-01T00:00:00ZLAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACEPrešnajder , PeterGáliková , VeronikaKováčik , Samuelhttp://hdl.handle.net/10467/671302022-01-04T13:06:25Z2014-01-01T00:00:00ZLAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE
Prešnajder , Peter; Gáliková , Veronika; Kováčik , Samuel
The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM). The considered noncommutative configuration space has such a “fuzzy”structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.
2014-01-01T00:00:00ZA SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLEOhya , Satoshihttp://hdl.handle.net/10467/671292022-01-04T13:06:00Z2014-01-01T00:00:00ZA SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLE
Ohya , Satoshi
We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. Making use of the real-time prescription of AdS/CFT correspondence and ladder equations of the Lie algebra so(2,2) ∼= sl(2,R)L⊕sl(2,R)R, we show that the finite-temperature two-point functions in momentum space satisfy linear recurrence relations with respect to the left and right momenta. These recurrence relations are exactly solvable and completely determine the momentum-dependence of retarded and advanced two-point functions of finite-temperature conformal field theory.
2014-01-01T00:00:00Z