### Abstract

We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises Ginzburg-Landau-type field theories defined on finite intervals, perturbed by thermal or other classical spatiotemporal noise. The second class comprises systems in which a single degree of freedom is perturbed by both thermal and quantum noise. Each class possesses a transition in its escape behavior, at a critical value of interval length and temperature, respectively. It is shown that there exists a mapping from one class of problems to the other, and that their respective transitions can be understood within a unified theoretical context. We consider two applications within the first class: thermally induced breakup of monovalent metallic nanowires, and stochastic reversal of magnetization in thin ferromagnetic annuli. Finally, we explore the depth of the analogy between the two classes of problems, and discuss to what extent each case exhibits the characteristic signs of critical behavior at a sharp second-order phase transition.

Original language | English (US) |
---|---|

Pages (from-to) | 242-252 |

Number of pages | 11 |

Journal | Brazilian Journal of Physics |

Volume | 35 |

Issue number | 2 A |

State | Published - Jun 2005 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Brazilian Journal of Physics*,

*35*(2 A), 242-252.

**Fluctuations, classical activation, quantum tunneling, and phase transitions.** / Stein, D. L.

Research output: Contribution to journal › Article

*Brazilian Journal of Physics*, vol. 35, no. 2 A, pp. 242-252.

}

TY - JOUR

T1 - Fluctuations, classical activation, quantum tunneling, and phase transitions

AU - Stein, D. L.

PY - 2005/6

Y1 - 2005/6

N2 - We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises Ginzburg-Landau-type field theories defined on finite intervals, perturbed by thermal or other classical spatiotemporal noise. The second class comprises systems in which a single degree of freedom is perturbed by both thermal and quantum noise. Each class possesses a transition in its escape behavior, at a critical value of interval length and temperature, respectively. It is shown that there exists a mapping from one class of problems to the other, and that their respective transitions can be understood within a unified theoretical context. We consider two applications within the first class: thermally induced breakup of monovalent metallic nanowires, and stochastic reversal of magnetization in thin ferromagnetic annuli. Finally, we explore the depth of the analogy between the two classes of problems, and discuss to what extent each case exhibits the characteristic signs of critical behavior at a sharp second-order phase transition.

AB - We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises Ginzburg-Landau-type field theories defined on finite intervals, perturbed by thermal or other classical spatiotemporal noise. The second class comprises systems in which a single degree of freedom is perturbed by both thermal and quantum noise. Each class possesses a transition in its escape behavior, at a critical value of interval length and temperature, respectively. It is shown that there exists a mapping from one class of problems to the other, and that their respective transitions can be understood within a unified theoretical context. We consider two applications within the first class: thermally induced breakup of monovalent metallic nanowires, and stochastic reversal of magnetization in thin ferromagnetic annuli. Finally, we explore the depth of the analogy between the two classes of problems, and discuss to what extent each case exhibits the characteristic signs of critical behavior at a sharp second-order phase transition.

UR - http://www.scopus.com/inward/record.url?scp=22544442775&partnerID=8YFLogxK

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M3 - Article

VL - 35

SP - 242

EP - 252

JO - Brazilian Journal of Physics

JF - Brazilian Journal of Physics

SN - 0103-9733

IS - 2 A

ER -