Quantum Gross-Pitaevskii Equation

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Date: 
2015-05-26
Author(s): 

J. Haegeman, D. Draxler, V. Stojevic, J. I. Cirac, T. J. Osborne, F. Verstraete

Reference: 

arXiv:1501.06575

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum field theories. This generalization is obtained by applying the Dirac-Frenkel time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of the 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 one-dimensional systems.