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
Natalie M Cann and Ajit J Thakkar 2002 J. Phys. B: At. Mol. Opt. Phys. 35 421
C H Keitel et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 L75
Ruth E Hoffmeyer et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 3675
M R Koblischka and R J Wijngaarden 1995 Supercond. Sci. Technol. 8 199
E Bonetti et al 1991 Supercond. Sci. Technol. 4 S196
M J Martínez-Pérez et al 2009 Supercond. Sci. Technol. 22 125020
T Nomura et al 2008 Supercond. Sci. Technol. 21 125028
Yuhu Zhai and Mark D Bird 2008 Supercond. Sci. Technol. 21 115010
Jie Yang et al 2008 Supercond. Sci. Technol. 21 082001