Quantum Gross-Pitaevskii Equation
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
SciPost Phys. 3, 006 (2017) · published 28 July 2017
- doi: 10.21468/SciPostPhys.3.1.006
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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.
Cited by 12
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Jutho Haegeman,
- 2 Damian Draxler,
- 1 3 Vid Stojevic,
- 4 J. Ignacio Cirac,
- 5 Tobias Osborne,
- 1 2 Frank Verstraete
- 1 Universiteit Gent / Ghent University
- 2 Universität Wien / University of Vienna
- 3 London Centre for Nanotechnology [LCN]
- 4 Max-Planck-Institut für Quantenoptik / Max Planck Institute of Quantum Optics [MPQ]
- 5 Leibniz Universität Hannover / University of Hannover
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Engineering and Physical Sciences Research Council [EPSRC]
- European Research Council [ERC]
- Fonds Wetenschappelijk Onderzoek (FWO) (through Organization: Fonds voor Wetenschappelijk Onderzoek - Vlaanderen / Research Foundation - Flanders [FWO])