Time-convolutionless master equation for mesoscopic electron-phonon systems

Abstract

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to a Ohmic and super-Ohmic baths, as well as for a a model of charge-transfer dynamics between semiconducting organic polymers.

Fourier’s law of heat conduction: Quantum mechanical master equation analysis

“…In this case the second assumption does not hold, and we cannot derive Eq. (9) and the subsequent result (12). Thus, interestingly, in order to derive Fourier's law, the system spectrum should be anharmonic, in accordance with classical results [1,2].…”

“…The time-convolutionless generator K(t) is in general an extremely complicated object, calculated using perturbative expansions [9]. Though the time-local master equation (2) is less well known than the Nakajima-Zwanzig equation [10,11], it is easy to show that these forms are equivalent [12]. In order to project the diagonal part of the total density ρ tot (t) we use the following projection [11,12] …”

Noise-induced quantum coherence drives photo-carrier generation dynamics at polymeric semiconductor heterojunctions

“…The model can provide the necessary input for describing the dynamics of a polymerbased photovoltaic cell [33][34][35] . A similar lattice model for a bulk heterojunction was presented recently by Troisi that includes many of the features of our model, but does not include explicit phonons and electronic transitions between states are introduced via the semiclassical Marcus theory 36 .…”

Non-Markovian quantum jumps in excitonic energy transfer

“…Formally exact dynamics for the system is described by the Nakajima-Zwanzig equation with time convolution 5,6 and the time-convolutionless ͑TCL͒ equations. [7][8][9][10][11] The first is equivalent to the chronological ordering prescription while the second corresponds to a partial ordering prescription of the time ordering in a system-bath cumulant expansion. 7,12,13 Under certain conditions, the convolution kernel can be transformed into the TCL kernel by including the appropriate backward propagation for the density matrix.…”

“…7,12,13 Under certain conditions, the convolution kernel can be transformed into the TCL kernel by including the appropriate backward propagation for the density matrix. 10,14 The time-dependent Redfield equation is derived from a second-order approximation in the system-bath interaction Hamiltonian. 14 Further imposing the Markov approximation leads to the standard time-independent Redfield equation.…”