Two-Dimensional Gross-Pitaevskii Equation With Space-Time White Noise

被引：1

作者：

de Bouard, Anne ^{[1
]}

Debussche, Arnaud ^{[2
,3
]}

Fukuizumi, Reika ^{[4
]}

机构：

[1] Ecole Polytech, CMAP, CNRS, IP Paris, F-91128 Palaiseau, France

[2] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

[3] Inst Univ France, Paris, France

[4] Tohoku Univ, Grad Sch Informat Sci, Res Ctr Pure & Appl Math, Sendai, Miyagi 9808579, Japan

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 12期

关键词：

GLOBAL WELL-POSEDNESS; SCHRODINGER-OPERATORS; DYNAMICS;

D O I：

10.1093/imrn/rnac137

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg-Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.

引用

页码：10556 / 10614

页数：59

共 50 条

[21] Approximation of a two-dimensional Gross-Pitaevskii equation with a periodic potential in the tight-binding limit
Gilg, Steffen
Schneider, Guido
MATHEMATISCHE NACHRICHTEN, 2024, 297 (10) : 3870 - 3886
[22] Numerical method for the projected Gross-Pitaevskii equation in an infinite rotating two-dimensional Bose gas
Doran, R.
Billam, T. P.
PHYSICAL REVIEW E, 2020, 102 (03)
[23] Scattering for the Gross-Pitaevskii equation
Gustafson, Stephen
Nakanishi, Kenji
Tsai, Tai-Peng
MATHEMATICAL RESEARCH LETTERS, 2006, 13 (2-3) : 273 - 285
[24] VORTEX RING PINNING FOR THE GROSS-PITAEVSKII EQUATION IN THREE-DIMENSIONAL SPACE
Wei, Juncheng
Yang, Jun
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (06) : 3991 - 4047
[25] Wilson loops in two-dimensional space-time regarded as white noise
Becker, C
JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 134 (02) : 321 - 349
[26] The stochastic Gross-Pitaevskii equation
Gardiner, CW
Anglin, JR
Fudge, TIA
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS, 2002, 35 (06) : 1555 - 1582
[27] ROTONS AND THE GROSS-PITAEVSKII EQUATION
ICHIYANAGI, M
PHYSICS LETTERS A, 1980, 79 (01) : 95 - 97
[28] Wellposedness of the cubic Gross-Pitaevskii equation with spatial white noise on R2
Mackowiak, Pierre
NONLINEARITY, 2025, 38 (03)
[29] The equation of state of one-dimensional Gross-Pitaevskii equation
Prayitno, T. B.
CONFERENCE OF THEORETICAL PHYSICS AND NONLINEAR PHENOMENA (CTPNP) 2014 - FROM UNIVERSE TO STRING'S SCALE, 2014, 539
[30] Conserved energies for the one dimensional Gross-Pitaevskii equation
Koch, Herbert
Liao, Xian
ADVANCES IN MATHEMATICS, 2021, 377

← 1 2 3 4 5 →