Localised distributions in complex Langevin dynamics

Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution and relate the results to the recently derived criteria for correctness. We demonstrate analytically that if the distribution has support only on a strip in the complexified configuration space, correct results are expected.

Note:

7 pages, 8 figures, talk given at the 31st International Symposium on Lattice Field Theory (Lattice 2013), July 29-August 3 2013, Mainz, Germany

action: complex
numerical calculations
stochastic
toy model
Langevin equation: complex

References(16)

Figures(8)

[1]

Complex Langevin dynamics and other approaches at finite chemical potential

Gert Aarts
(
- Swansea U.
)

- PoS LATTICE2012 (2012) 017
•
e-Print:
- 1302.3028

[2]

Controlling complex Langevin dynamics at finite density

Gert Aarts
(
- Swansea U.
)
,
Lorenzo Bongiovanni
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Denes Sexty
(
- Heidelberg U.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U. and
- Heidelberg, FEST
)

- Eur.Phys.J.A 49 (2013) 89
•
e-Print:
- 1303.6425
•
DOI:
- 10.1140/epja/i2013-13089-4

[3]

The Complex Langevin method: When can it be trusted?

Gert Aarts
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U.
)

- Phys.Rev.D 81 (2010) 054508
•
e-Print:
- 0912.3360
•
DOI:
- 10.1103/PhysRevD.81.054508

[4]

Complex Langevin: Etiology and Diagnostics of its Main Problem

Gert Aarts
(
- Swansea U.
)
,
Frank A. James
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U. and
- Heidelberg, FEST
)

- Eur.Phys.J.C 71 (2011) 1756
•
e-Print:
- 1101.3270
•
DOI:
- 10.1140/epjc/s10052-011-1756-5

[5]

Temporal breakdown and Borel resummation in the complex Langevin method

A. Duncan
(
- Pittsburgh U.
)
,
M. Niedermaier
(
- Pittsburgh U.
)

- Annals Phys. 329 (2013) 93-124
•
e-Print:
- 1205.0307
•
DOI:
- 10.1016/j.aop.2012.09.011

[5]

Temporal breakdown and Borel resummation in the complex Langevin method

A. Duncan
(
- Pittsburgh U.
)
,
M. Niedermaier
(
- Pittsburgh U.
)

- Annals Phys. 329 (2013) 93-124
•
e-Print:
- 1205.0307
•
DOI:
- 10.1016/j.aop.2012.09.011

[6]

Localised distributions and criteria for correctness in complex Langevin dynamics

Gert Aarts
(
- Swansea U.
)
,
Pietro Giudice
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)

- Annals Phys. 337 (2013) 238-260
•
e-Print:
- 1306.3075
•
DOI:
- 10.1016/j.aop.2013.06.019

[6]

Localised distributions and criteria for correctness in complex Langevin dynamics

Gert Aarts
(
- Swansea U.
)
,
Pietro Giudice
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)

- Annals Phys. 337 (2013) 238-260
•
e-Print:
- 1306.3075
•
DOI:
- 10.1016/j.aop.2013.06.019

[7]

Journal of Stat. Phys. 39 (1985) 53,

J.R. Klauder
,
W.P. Petersen

[8]

Numerical Problems in Applying the Langevin Equation to Complex Effective Actions

Jan Ambjorn
(
- Bohr Inst.
)
,
S.K. Yang
(
- Bohr Inst.
)

- Phys.Lett.B 165 (1985) 140,
- IN *DAMGAARD, P.H. (ED.), HUEFFEL, H. (ED.): STOCHASTIC QUANTIZATION*, 406-412. (PHYS. LETT. B165 (1985) 140-146) AND COPENHAGEN UNIV. - NBI-HE-85-27 (85,REC.OCT.) 15p
•
DOI:
- 10.1016/0370-2693(85)90708-7