Low-dimensional stochastic projected Gross-Pitaevskii equation
نویسندگان
چکیده
منابع مشابه
Stochastic Fluctuations in the Gross-pitaevskii Equation
Abstract. We study from a mathematical point of view a model equation for Bose Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of solutions in 1D and 2D in the energy space. The blowup phenomenon is also discussed...
متن کاملThe stochastic Gross–Pitaevskii equation: II
We provide a derivation of a more accurate version of the stochastic Gross– Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a ‘high temperature’ master equation for a Bose gas, which include...
متن کاملNumerical method for evolving the dipolar projected Gross-Pitaevskii equation.
We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic-oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low-energy c -field region of the system. We ...
متن کاملStationary periodic solutions of the two-dimensional Gross-Pitaevskii equation
Stationary periodic solutions of the two-dimensional Gross-Pitaevskii equation are obtained and analyzed for different parameter values in the context of the problem of a supersonic flow of a Bose-Einstein condensate past an obstacle. The asymptotic connections with the corresponding periodic solutions of the Korteweg-de Vries and nonlinear Schrödinger equations are studied and typical spatial ...
متن کاملRigorous derivation of the Gross-Pitaevskii equation.
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review A
سال: 2015
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.92.033631