Journal
SCIPOST PHYSICS
Volume 3, Issue 1, Pages -Publisher
SCIPOST FOUNDATION
DOI: 10.21468/SciPostPhys.3.1.006
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Funding
- Research Foundation Flanders
- EPSRC [EP/L001578/1, EP/I031014/1]
- Austrian FWF SFB grant FoQuS
- Austrian FWF SFB grant ViCoM
- cluster of excellence [EXC 201]
- European grant SISQ
- European grant QUTE
- European grant QFTCMPS
- EPSRC [EP/I031014/1, EP/K02163X/1, EP/L001578/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K02163X/1, EP/I031014/1, EP/L001578/1] Funding Source: researchfish
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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.
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