Titel
Quantum Gross-Pitaevskii Equation
Autor*in
Jutho Haegeman
Universiteit Gent
Vid Stojevic
Universiteit Gent
... show all
Abstract
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
Stichwort
Bogoliubov-de Gennes equationsContinuous matrix product statesEntanglementGross-Pitaevskii equationMatrix product states (MPS)One-dimensional Bose gasOne-dimensional systemsTime-dependent variational principle (TDVP)
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
SciPost Physics
Band
3
Ausgabe
1
Publication
Stichting SciPost
Erscheinungsdatum
2017
Zugänglichkeit
Rechte
Rechteangabe
Copyright J. Haegeman et al
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