Unstable state decay in non-Markovian heat baths and weak signals detection

• Published in: Physica A Vol. 529; p. 121493
• Main Authors: Jiménez Aquino, José Inés, Sánchez Salas, Norma, Ramírez de la Piscina Millán, Laureano, Romero Bastida, M
• Format: Journal Article Publication
• Language: English
• Published: Elsevier B.V 01.09.2019
• Subjects: Decay of an unstable state; Equacions diferencials estocàstiques; Equacions diferencials i integrals; Generalized Langevin equation; Matemàtiques i estadística; Mean first passage time; Nonlinear relaxation time; Stochastic differential equations; Weak signals detection; Àrees temàtiques de la UPC; Decay of an unstable state; Weak signals detection; Nonlinear relaxation time; Generalized Langevin equation; Mean first passage time
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.121493

The statistics of the first passage and nonlinear relaxation times are used to characterize the decay process of an unstable state for an electrically charged Brownian particle embedded in non-Markovian heat baths under the action of an external electric field. The relaxation process is described, in the overdamped regime, by a Generalized Langevin Equation (GLE) characterized by an arbitrary friction memory kernel, and a bistable potential profile. By applying the quasideterministic approach, the statistics of the mean first passage time is calculated through the exact analytical solution of the GLE with arbitrary memory kernel in the linear regime of the bistable potential. To characterize the relaxation process including the nonlinear contributions of the bistable potential, we use the specific Ornstein–Uhlenbeck friction memory kernel to exactly calculate the nonlinear statistics of the mean first passage time as well as the nonlinear relaxation time. Both characteristic times are applied for possible detection of weak signals in the unstable state decay process.