Rigorous derivation of the Gross-Pitaevskii equation.

Phys Rev Lett

Institute of Mathematics, University of Munich, Theresienstrasse 39, D-80333 Munich, Germany.

Published: January 2007

The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.98.040404DOI Listing

Publication Analysis

Top Keywords

gross-pitaevskii equation
8
rigorous derivation
4
derivation gross-pitaevskii
4
equation time-dependent
4
time-dependent gross-pitaevskii
4
equation describes
4
describes dynamics
4
dynamics initially
4
initially trapped
4
trapped bose-einstein
4

Similar Publications

A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schrödinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to the rotation of rigid bodies and centrifugal force.

View Article and Find Full Text PDF

We have theoretically realized a photonic time crystal in a homogeneous spinor exciton-polariton condensate subject to a cavity strain induced energy splitting between the x- and y-polarized polaritons with distinct loss rates. Numerical modeling based on the time-dependent open dissipative Gross-Pitaevskii equation results in the phase transition from linearly-polarized spinor condensate at low pump powers into a circularly-polarized one and then a photonic time crystal at higher pump powers. This phenomenon occurs only under the condition that the lower-energy x-polarized condensate has a higher loss rate than the y-polaried condensate, which can exist intrinsically in the semiconductor microcavities.

View Article and Find Full Text PDF

The generation of patterns by breaking the spatial symmetry in external confinement is a captivating area of physics. The emergence of patterns is a fundamental inquiry spanning various disciplines such as nonlinear optics, condensed matter physics, and fluid dynamics. The article investigates the generation of a variety of patterns in a one-dimensional binary mixture of Bose-Einstein condensate forming quantum droplets.

View Article and Find Full Text PDF

Maxwell Relation between Entropy and Atom-Atom Pair Correlation.

Phys Rev Lett

September 2024

School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia.

For many-particle systems with short-range interactions, the local (same point) particle-particle pair correlation function represents a thermodynamic quantity that can be calculated using the Hellmann-Feynman theorem. Here we exploit this property to derive a thermodynamic Maxwell relation between the local pair correlation and the entropy of an ultracold Bose gas in one dimension (1D). To demonstrate the utility of this Maxwell relation, we apply it to the computational formalism of the stochastic projected Gross-Pitaevskii equation (SPGPE) to determine the entropy of a finite-temperature 1D Bose gas from its atom-atom pair correlation function.

View Article and Find Full Text PDF

Ultrafast dynamics of exciton-polariton fluids at non-zero momenta.

J Phys Condens Matter

July 2024

State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, People's Republic of China.

In this study, we have explored the ultrafast formation and decay dynamics of exciton-polariton fluids at non-zero momenta, non-resonantly excited by a small-spot femtosecond pump pulse in a ZnO microcavity. Using the femtosecond angle-resolved spectroscopic imaging technique, multidimensional dynamics in both the energy and momentum degrees of freedom have been obtained. Two distinct regions with different decay rate in the energy dimension and various decay-channels in the momentum dimension can be well-resolved.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!