Quantum Gross-Pitaevskii Equation
Copyright policy )Quantum Gross-Pitaevskii Equation
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.
- University College London United Kingdom
- Max Planck Institute for Biology Germany
- Universität Wien Austria
- University of Hannover Germany
- Universität Wien Austria
BOSONS, DYNAMICS, High Energy Physics - Theory, QC1-999, FOS: Physical sciences, Time-dependent variational principle (TDVP), Pattern Formation and Solitons (nlin.PS), IMPENETRABLE BOSONS, Entanglement, One-dimensional systems, Vortrex, Matrix product states (MPS), SYSTEMS, TONKS-GIRARDEAU GAS, BOSE-EINSTEIN CONDENSATION, Density - Matrix Renormalisation, Impenetrable Bosons, DENSITY-MATRIX RENORMALIZATION, Mathematical Physics, Traps, Continuous matrix product states, VORTEX, Quantum Physics, NONLINEAR SCHRODINGER-EQUATIONS, Bose-Einstein Condensation, Physics, 103036 Theoretische Physik, Bogoliubov-de Gennes equations, TRAPS, Mathematical Physics (math-ph), One-dimensional Bose gas, Nonlinear Sciences - Pattern Formation and Solitons, Dynamics, 103036 Theoretical physics, Physics and Astronomy, STATES, High Energy Physics - Theory (hep-th), GAS, Quantum Gases (cond-mat.quant-gas), Nonlinear Schrodinger- Equations, Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), Gross-Pitaevskii equation, Tonks - Girardeau Gas
BOSONS, DYNAMICS, High Energy Physics - Theory, QC1-999, FOS: Physical sciences, Time-dependent variational principle (TDVP), Pattern Formation and Solitons (nlin.PS), IMPENETRABLE BOSONS, Entanglement, One-dimensional systems, Vortrex, Matrix product states (MPS), SYSTEMS, TONKS-GIRARDEAU GAS, BOSE-EINSTEIN CONDENSATION, Density - Matrix Renormalisation, Impenetrable Bosons, DENSITY-MATRIX RENORMALIZATION, Mathematical Physics, Traps, Continuous matrix product states, VORTEX, Quantum Physics, NONLINEAR SCHRODINGER-EQUATIONS, Bose-Einstein Condensation, Physics, 103036 Theoretische Physik, Bogoliubov-de Gennes equations, TRAPS, Mathematical Physics (math-ph), One-dimensional Bose gas, Nonlinear Sciences - Pattern Formation and Solitons, Dynamics, 103036 Theoretical physics, Physics and Astronomy, STATES, High Energy Physics - Theory (hep-th), GAS, Quantum Gases (cond-mat.quant-gas), Nonlinear Schrodinger- Equations, Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), Gross-Pitaevskii equation, Tonks - Girardeau Gas
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