Beyond mean field: On the role of pair excitations in the evolution of condensates

Abstract

This paper (published in 2013) introduces a refinement of the equations for the pair excitation function used in our previous work with D. Margetis. The new equations are Euler-Lagrange equations, and the solutions conserve energy and the number of particles.

arXiv admin note: text overlap with arXiv:1509.05911

References in corpus (3)

• Rigorous Derivation of the Gross-Pitaevskii Equation
• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy

Cited by in corpus (11)

• Pair excitations and the mean field approximation of interacting Bosons, II
• Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions $d\le 3$
• Dynamics of Large Boson Systems with Attractive Interaction and a Derivation of the Cubic Focusing NLS in ${\mathbb{R}}^3$
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• Uniform in $N$ Global Well-posedness of the Time-Dependent Hartree-Fock-Bogoliubov Equations in ${\mathbb{R}}^{1+1}$
• Bosonization of Fermionic Many-Body Dynamics
• Global estimates for the Hartree-Fock-Bogoliubov equations
• Uniform in $N$ estimates for a Bosonic system of Hartree-Fock-Bogoliubov type
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• Many-body excitations in trapped Bose gas: A non-Hermitian view