Complex Langevin method: When can it be trusted?

被引：154

作者：

Aarts, Gert ^{[1
]}

Seiler, Erhard ^{[2
]}

Stamatescu, Ion-Olimpiu ^{[3
,4
]}

机构：

[1] Swansea Univ, Dept Phys, Swansea, W Glam, Wales

[2] Max Planck Inst Phys & Astrophys, Werner Heisenberg Inst, D-80805 Munich, Germany

[3] Heidelberg Univ, Inst Theoret Phys, D-6900 Heidelberg, Germany

[4] FEST, Heidelberg, Germany

来源：

PHYSICAL REVIEW D | 2010年 / 81卷 / 05期

关键词：

MONTE-CARLO; SIMULATIONS; EQUATIONS;

D O I：

10.1103/PhysRevD.81.054508

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

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页数：13

相关论文

共 28 条

[1]

AARTS G, ARXIV09120617, P74012

[2] Stochastic quantization at finite chemical potential [J].

Aarts, Gert ;

Stamatescu, Ion-Olimpiu .

JOURNAL OF HIGH ENERGY PHYSICS, 2008, (09)

[3] Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas [J].

Aarts, Gert .

JOURNAL OF HIGH ENERGY PHYSICS, 2009, (05)

[4] Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential [J].

Aarts, Gert .

PHYSICAL REVIEW LETTERS, 2009, 102 (13)

[5] NUMERICAL PROBLEMS IN APPLYING THE LANGEVIN EQUATION TO COMPLEX EFFECTIVE ACTIONS [J].

AMBJORN, J ;

YANG, SK .

PHYSICS LETTERS B, 1985, 165 (1-3) :140-146

[6] THE COMPLEX LANGEVIN EQUATION AND MONTE-CARLO SIMULATIONS OF ACTIONS WITH STATIC CHARGES [J].

AMBJORN, J ;

FLENSBURG, M ;

PETERSON, C .

NUCLEAR PHYSICS B, 1986, 275 (03) :375-397

[7]

[Anonymous], 1977, Grundlagen der mathematischen Wissenschaften

[8] LANGEVIN SIMULATIONS OF LATTICE FIELD-THEORIES [J].

BATROUNI, GG ;

KATZ, GR ;

KRONFELD, AS ;

LEPAGE, GP ;

SVETITSKY, B ;

WILSON, KG .

PHYSICAL REVIEW D, 1985, 32 (10) :2736-2747

[9] Making sense of non-Hermitian Hamiltonians [J].

Bender, Carl M. .

REPORTS ON PROGRESS IN PHYSICS, 2007, 70 (06) :947-1018

[10] Simulating nonequilibrium quantum fields with stochastic quantization techniques [J].

Berges, J ;

Stamatescu, IO .

PHYSICAL REVIEW LETTERS, 2005, 95 (20)