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arXiv · 1501.06575

Quantum Gross-Pitaevskii Equation

Jutho Haegeman·Damian Draxler·Vid Stojevic·J. Ignacio Cirac·Tobias J. Osborne·Frank Verstraete
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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.

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Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete. 2015-01-26. Quantum Gross-Pitaevskii Equation. https://doi.org/10.21468/scipostphys.3.1.006

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