SISSA Open Science

Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates

Show simple item record Michelangeli, Alessandro Olgiati, Alessandro 2017-04-03T06:33:45Z 2017-04-03T06:33:45Z 2017-04-03
dc.description.abstract We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates. en_US
dc.language.iso en en_US
dc.relation.ispartofseries SISSA;07/2017/MATE
dc.subject effective non-linear evolution equations en_US
dc.subject many-body quantum dynamics en_US
dc.subject pseudo-spinor Bose- Einstein condensates en_US
dc.subject partial trace en_US
dc.subject reduced density matrix en_US
dc.subject Gross-Pitaevskii scaling en_US
dc.subject cubic NLS en_US
dc.subject coupled nonlinear Schrödinger system en_US
dc.title Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.identifier.sissaPreprint 07/2017/MATE
dc.relation.firstpage 1 en_US
dc.relation.lastpage 39 en_US

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search SISSA Open Science


My Account