### Abstract

A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems. The corresponding Fokker-Planck equation is shown to be a diffusion-type equation and is solved analytically at any finite fictitious time. The solution generally depends on the choice of initial distribution and has no equilibrium limit. An interesting connection to the ordinary Feynman measure, which in this case is not normalizable, is clarified.

Original language | English |
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Pages (from-to) | 98-103 |

Number of pages | 6 |

Journal | Physics Letters B |

Volume | 333 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1994 Jul 28 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Analytical solution to the Fokker-Planck equation with a bottomless action.** / Nakazato, Hiromichi.

Research output: Contribution to journal › Article

*Physics Letters B*, vol. 333, no. 1-2, pp. 98-103. https://doi.org/10.1016/0370-2693(94)91013-8

}

TY - JOUR

T1 - Analytical solution to the Fokker-Planck equation with a bottomless action

AU - Nakazato, Hiromichi

PY - 1994/7/28

Y1 - 1994/7/28

N2 - A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems. The corresponding Fokker-Planck equation is shown to be a diffusion-type equation and is solved analytically at any finite fictitious time. The solution generally depends on the choice of initial distribution and has no equilibrium limit. An interesting connection to the ordinary Feynman measure, which in this case is not normalizable, is clarified.

AB - A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems. The corresponding Fokker-Planck equation is shown to be a diffusion-type equation and is solved analytically at any finite fictitious time. The solution generally depends on the choice of initial distribution and has no equilibrium limit. An interesting connection to the ordinary Feynman measure, which in this case is not normalizable, is clarified.

UR - http://www.scopus.com/inward/record.url?scp=4243665650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243665650&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(94)91013-8

DO - 10.1016/0370-2693(94)91013-8

M3 - Article

VL - 333

SP - 98

EP - 103

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -