C W Gardiner and M J Davis 2003 J. Phys. B: At. Mol. Opt. Phys. 36 4731 doi:10.1088/0953-4075/36/23/010
C W Gardiner1 and M J Davis2
Show affiliationsWe 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 includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cut-off (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross–Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.
Issue 23 (14 December 2003)
Received 9 August 2003
Published 11 November 2003
C W Gardiner and M J Davis 2003 J. Phys. B: At. Mol. Opt. Phys. 36 4731
Achim Kempf and Paulo J S G Ferreira 2004 J. Phys. A: Math. Gen. 37 12067
K J Falconer 1988 J. Phys. A: Math. Gen. 21 L737
H De Bie and F Sommen 2007 J. Phys. A: Math. Theor. 40 10441
Y Abou-Ali et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2855
Andrew L Goertzen et al 2004 Phys. Med. Biol. 49 5251
Joost M Bakker et al 2006 J. Phys. B: At. Mol. Opt. Phys. 39 S1111
Alfred Scharff Goldhaber and M L Horner 2007 J. Phys. A: Math. Theor. 40 14343
Andy Adler et al 2008 Physiol. Meas. 29 S101
D J Baker et al 2007 Phys. Scr. 75 615