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

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dc.contributor.areaMathematicsen_US
dc.contributor.authorMichelangeli, Alessandro
dc.contributor.authorOlgiati, Alessandro
dc.date.accessioned2017-04-03T06:33:45Z
dc.date.available2017-04-03T06:33:45Z
dc.date.issued2017-04-03
dc.description.abstractWe 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.identifier.sissaPreprint07/2017/MATE
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35279
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;07/2017/MATE
dc.relation.lastpage39en_US
dc.subjecteffective non-linear evolution equationsen_US
dc.subjectmany-body quantum dynamicsen_US
dc.subjectpseudo-spinor Bose- Einstein condensatesen_US
dc.subjectpartial traceen_US
dc.subjectreduced density matrixen_US
dc.subjectGross-Pitaevskii scalingen_US
dc.subjectcubic NLSen_US
dc.subjectcoupled nonlinear Schrödinger systemen_US
dc.titleGross-Pitaevskii non-linear dynamics for pseudo-spinor condensatesen_US
dc.typePreprinten_US
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