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Title: Quantum Gross-Pitaevskii Equation
Author(s): Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
As Contributors: Jutho Haegeman
arxiv Link:
Date submitted: 2017-05-16
Submitted by: Haegeman, Jutho
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Quantum Physics


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.

Current status:

Publication decision taken: accept

List of changes

We have extended the discussion of the periodic potential example. We clearly indicate how our framework improves upon the mean field prediction (Bogoliubov theory), which is also shown in the plot. We also discuss the underlying physics that shows up in the response amplitude, namely the signature of the low-lying excitations in the system, which are known to be Lieb's Type I and Type II excitations. Whereas Bogoliubov theory can only access the first type, our method also captures the effect of the second type, which is important at stronger interactions.