### Abstract

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.

Original language | English |
---|---|

Pages (from-to) | 3936-3941 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 60 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1999 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*60*(4), 3936-3941. https://doi.org/10.1103/PhysRevE.60.3936

**Spectrum of stochastic evolution operators : Local matrix representation approach.** / Cvitanović, Predrag; Søndergaard, Niels; Palla, Gergely; Vattay, G.; Dettmann, C. P.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 60, no. 4, pp. 3936-3941. https://doi.org/10.1103/PhysRevE.60.3936

}

TY - JOUR

T1 - Spectrum of stochastic evolution operators

T2 - Local matrix representation approach

AU - Cvitanović, Predrag

AU - Søndergaard, Niels

AU - Palla, Gergely

AU - Vattay, G.

AU - Dettmann, C. P.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.

AB - A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.

UR - http://www.scopus.com/inward/record.url?scp=0002058641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002058641&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.60.3936

DO - 10.1103/PhysRevE.60.3936

M3 - Article

AN - SCOPUS:0002058641

VL - 60

SP - 3936

EP - 3941

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

ER -