Quantum Gross-Pitaevskii Equation
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.
Keywords
Cite
@article{arxiv.1501.06575,
title = {Quantum Gross-Pitaevskii Equation},
author = {Jutho Haegeman and Damian Draxler and Vid Stojevic and J. Ignacio Cirac and Tobias J. Osborne and Frank Verstraete},
journal= {arXiv preprint arXiv:1501.06575},
year = {2018}
}
Comments
4.{\epsilon} pages + references and 4 pages supplementary material (small revisions + extended discussion of periodic potential example)