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Master equation
About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.
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TL;DR: In this article, the authors calculate the asymptotic behavior of the moments of the first-passage time and survival probability for random walks on an exactly self-similar tree, and on a quasi-self-similar comb, by applying an exact decimation approach to the master equations.
Abstract: The authors calculate the asymptotic behaviour of the moments of the first-passage time and survival probability for random walks on an exactly self-similar tree, and on a quasi-self-similar comb, by applying an exact decimation approach to the master equations. For the hierarchical comb, a transition from ordinary to anomalous diffusion occurs at R=2, where R is the ratio of teeth length in successive iterations of the structure. In the anomalous regime (R>2), the positive integer moments of the first-passage time, (tq), scale as Ltau q, with tau q=1+(2q-1)ln R/ln 2, where L is the linear distance from input to output. The asymptotic behaviour of the survival probability is studied using both scaling theory and by a direct solution of the master equations. They find that the characteristic time, t*, in the asymptotic exponential decay of the survival probability, exp(-t/t*), scales as t* approximately Ltau *=, with tau *=ln R2/ln 2, i.e. tau * is distinct from tau 1. However, substantial corrections to this asymptotic form for tau * exist, and these are needed to account for the recent simulation data of Havlin and Matan (1988).
92 citations
TL;DR: In this article, the authors proposed several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields.
Abstract: We propose several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms. The schemes could be realized in one step without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields. When the Rydberg-Rydberg-interaction (RRI) strength and the parameters of the driving fields satisfy some certain conditions, the effective Rabi oscillation between the two-excitation Rydberg state and the ground state would be generated, which is out of the Rydberg blockade regime and essential for our scheme. In addition, the individual addressing of the atoms is not required. And the schemes can work under strong or weak RRI strength. The imperfections induced by the variation of RRI strength and spontaneous emission are discussed through solving the master equation numerically.
92 citations
TL;DR: In this paper, a theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported, and the rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state are calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952).
Abstract: A theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported. The rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state have been calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952). High-lying vibrational states and dissociative states were explicitly included but rotational energy transfer was neglected. The transition probabilities calculated from the SSH theory were fed into the master equation, which was integrated numerically to determine the population distribution of the vibrational states as well as bulk thermodynamic properties. The results show that: (1) the transition rates have a minimum near the middle of the bound vibrational levels, causing a bottleneck in the vibrational relaxation and dissociation rates; (2) high vibrational states are always in equilibrium with the dissociative state; (3) for the heating case, only the low vibrational states relax according to the Landau-Teller theory; (4) for the cooling case, vibrational relaxation cannot be described by a rate equation; (5) Park's (1985, 1988) two-temperature model is approximately valid; and (6) the average vibrational energy removed in dissociation is about 30 percent of the dissociation energy.
91 citations
TL;DR: In this paper, a spin dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead (NM-QD-FM) was studied and the spin-resolved currents in the presence of an external bias and an intra-dot Coulomb interaction.
Abstract: We report a study of spin dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead (NM-QD-FM). We use the master equation approach to calculate the spin-resolved currents in the presence of an external bias and an intra-dot Coulomb interaction. We find that for a range of positive external biases (current flow from the normal metal to the ferromagnet) the current polarization $\wp=(I_\uparrow-I_\downarrow)/(I_\uparrow+I_\downarrow)$ is suppressed to zero, while for the corresponding negative biases (current flow from the ferromagnet to the normal metal) $\wp$ attains a relative maximum value. The system thus operates as a rectifier for spin--current polarization. This effect follows from an interplay between Coulomb interaction and nonequilibrium spin accumulation in the dot. In the parameter range considered, we also show that the above results can be obtained via nonequilibrium Green functions within a Hartree-Fock type approximation.
91 citations
TL;DR: In this article, the authors considered the quantum-mechanical version of the Kramers turnover problem and derived an expression for the quantum escape rate in the thermally activated tunneling regime.
Abstract: The quantum-mechanical version of the Kramers turnover problem is considered. The multidimensional character of the problem is taken into account via transformation to normal modes. This eliminates the coupling to the bath near the barrier top allowing the use of a simple harmonic transmission coefficient for the barrier dynamics. The well dynamics is described by a continuum form of a master equation for the energy in the unstable normal mode. Within first-order perturbation theory, the equations of motion for the stable normal modes have the form of a forced oscillator. The transition probability kernel is found using the known solution for the quantum forced oscillator problem. An expression for the quantum escape rate is derived. It encompasses all previously known limiting results in the thermally activated tunneling regime. The depopulation factor, which accounts for the nonequilibrium energy distribution is evaluated. The quantum transition probability kernel is broader than the classical and is skewed towards lower energies. Interplay between these two effects, together with a positive tunneling contribution, determines the relative magnitude of the quantum rate compared to the classical one. The theory is valid for arbitrary dissipation. Its use is illustrated for the case of a cubic potential with Ohmic (Markovian) dissipation.
91 citations