Holon Physics Seminar 14.3.17
Beyond the Linear Response: Well Dynamics in the Kramers Model
Prof. Ilya Rips, HIT
March 14, 2017 | 14:00 | Room 424/8
Abstract:
The linear response theory has been the standard treatment of the problem of a system interacting with the medium.
The later is represented by the bath of harmonic oscillators (classical or quantum). Within the linear response theory the coupling between the system and the bath is taken to be linear in the oscillator coordinates. The problem of calculation of the energy loss (gain) of the system reduces to calculation of the transition probabilities for the forced quantum harmonic oscillator (Feynman 1950, Schwinger 1953).
Calculation of the corrections to the linear-response theory result is an extremely difficult physical problem. A method for calculating these corrections is suggested that is based on taking into account the coupling term that is quadratic in the coordinates of the bath oscillators. The equations of motion for the oscillators reduce in this case to the forced oscillator with the time-dependent frequency (TDF-oscillator).
This problem is also solvable in quantum mechanics (Husimi 1953), when the corresponding quantum scattering problem can be solved. The use of the generating function for the transition probabilities for the forced TDF–oscillator together with the perturbation approach allows to calculate the lowest order corrections to the linear-response theory results. I will present the results of my recent paper [Phys. Rev. E95, 012119 (2017)].
In it the approach has been applied to analysis of the decay of the metastable state within the framework of the quantum Kramers model in the weak-to-intermediate dissipation strength regime.
The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. Lowest order corrections to the linear-response results for the energy loss and for the rate have been calculated for the cubic and the quartic potentials with Ohmic (Markovian) dissipation. The range of validity of the approach has been determined, which includes the Kramers turnover region.
The main physical effect of the correction to the linear response theory result is the reduction of the average energy loss and its dispersion (up to ~10-20 %). Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers.
