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Quantum Gross-Pitaevskii Equation

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

Submission summary

As Contributors: Jutho Haegeman · Frank Verstraete
Arxiv Link: http://arxiv.org/abs/1501.06575v5 (pdf)
Date submitted: 2017-05-16 02:00
Submitted by: Haegeman, Jutho
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Atomic, Molecular and Optical Physics - Theory
  • Quantum Physics
Approach: Theoretical

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.

Ontology / Topics

See full Ontology or Topics database.

Bogoliubov-de Gennes equations Continuous matrix product states Entanglement Gross-Pitaevskii equation Matrix product states (MPS) One-dimensional Bose gas One-dimensional systems Time-dependent variational principle (TDVP)

Published as SciPost Phys. 3, 006 (2017)



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.

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