Finite Temperature Theory of Metastable Anharmonic Potentials
| dc.creator | Zoli, Marco | |
| dc.date | 2008-04-03 | |
| dc.date | 2008-04-04 | |
| dc.date.accessioned | 2026-07-07T09:33:38Z | |
| dc.date.available | 2026-07-07T09:33:38Z | |
| dc.description | The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low $T$ up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lamè equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed. | |
| dc.description | European Physical Journal B EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2008 | |
| dc.identifier | https://arxiv.org/abs/0804.0582 | |
| dc.identifier | http://arxiv.org/abs/0804.0582 | |
| dc.identifier | Eur. Phys. J. B 62, 221â?"231 (2008) | |
| dc.identifier | doi:10.1140/epjb/e2008-00148-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159203 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Finite Temperature Theory of Metastable Anharmonic Potentials | |
| dc.type | text |