Quantum Gross-Pitaevskii Equation

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung

Autoren

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

Organisationseinheiten

Externe Organisationen

  • Universiteit Gent
  • Universität Wien
  • Max-Planck-Institut für Quantenoptik (MPQ)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
FachzeitschriftSciPost Physics
Jahrgang3
Ausgabenummer6
PublikationsstatusVeröffentlicht - 26 Jan. 2015

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.

Zitieren

Quantum Gross-Pitaevskii Equation. / Haegeman, Jutho; Draxler, Damian; Stojevic, Vid et al.
in: SciPost Physics, Jahrgang 3, Nr. 6, 26.01.2015.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung

Haegeman, J, Draxler, D, Stojevic, V, Cirac, JI, Osborne, TJ & Verstraete, F 2015, 'Quantum Gross-Pitaevskii Equation', SciPost Physics, Jg. 3, Nr. 6. https://doi.org/10.21468/SciPostPhys.3.1.006
Haegeman, J., Draxler, D., Stojevic, V., Cirac, J. I., Osborne, T. J., & Verstraete, F. (2015). Quantum Gross-Pitaevskii Equation. SciPost Physics, 3(6). https://doi.org/10.21468/SciPostPhys.3.1.006
Haegeman J, Draxler D, Stojevic V, Cirac JI, Osborne TJ, Verstraete F. Quantum Gross-Pitaevskii Equation. SciPost Physics. 2015 Jan 26;3(6). doi: 10.21468/SciPostPhys.3.1.006
Haegeman, Jutho ; Draxler, Damian ; Stojevic, Vid et al. / Quantum Gross-Pitaevskii Equation. in: SciPost Physics. 2015 ; Jahrgang 3, Nr. 6.
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TY - JOUR

T1 - Quantum Gross-Pitaevskii Equation

AU - Haegeman, Jutho

AU - Draxler, Damian

AU - Stojevic, Vid

AU - Cirac, J. Ignacio

AU - Osborne, Tobias J.

AU - Verstraete, Frank

N1 - Funding information: We acknowledge discussions with C. Lubich and A. Daley. Research supported by the Research Foundation Flanders (JH), the EPSRC under grant numbers EP/L001578/1 and EP/I031014/1 (VS), the Austrian FWF SFB grants FoQuS and ViCoM, the cluster of excellence EXC 201 “Quantum Engineering and Space-Time Research” and the European grants SISQ, QUTE and QFTCMPS.

PY - 2015/1/26

Y1 - 2015/1/26

N2 - 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.

AB - 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.

KW - quant-ph

KW - cond-mat.quant-gas

KW - hep-th

KW - math-ph

KW - math.MP

KW - nlin.PS

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JO - SciPost Physics

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