Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.

New Formulation of Stochastic Theory and Quantum Mechanics

Abstract: The theory of stochastic motion is formulated from a new point of view. It is shown that the fundamental equations of the theory reduce to Schrodinger's equation for specific values of certain parameters. A generalized Fokker‐Planck‐Kolmogorov equation is obtained; with other values of the parameters, certain approximations reduce this to the Smoluchowski equation for Brownian movement. In particular, the potential function in the Schrodinger equation differs in the two cases. The usual uncertainty relations appear in a natural way in the theory, but in a broader context. A single theory thus covers both similarities and differences between quantum‐mechanical and Brownian motion. Furthermore, possibilities for broadening nonrelativistic quantum mechanics are brought out and, as an example, the possible corrections due to non‐Markoffian terms are briefly studied.

Non-equilibrium quantum theory for nanodevices based on the Feynman–Vernon influence functional

Abstract: In this paper, we present a non-equilibrium quantum theory for transient electron dynamics in nanodevices based on the Feynman-Vernon influence functional. Applying the exact master equation for nanodevices we recently developed to the more general case in which all the constituents of a device vary in time in response to time-dependent external voltages, we obtained non-perturbatively the transient quantum transport theory in terms of the reduced density matrix. The theory enables us to study transient quantum transport in nanostructures with back-reaction effects from the contacts, with non-Markovian dissipation and decoherence being fully taken into account. For a simple illustration, we apply the theory to a single-electron transistor subjected to ac bias voltages. The non-Markovian memory structure and the nonlinear response functions describing transient electron transport are obtained.

Coherent quantum transport in disordered systems: I. The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems

Abstract: Excitonic transport in static-disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken–Strobl–Reineker model. For short times, non-diffusive behavior is observed that can be characterized as the free-particle dynamics on the length-scale bounded by the Anderson localized system. Over longer time scales, the environment-induced dephasing is sufficient to overcome the Anderson localization caused by the disorder and allow for transport to occur which is always seen to be diffusive. In the limiting regimes of weak and strong dephasing quantum master equations are developed, and their respective scaling relations imply the existence of a maximum in the diffusion constant as a function of the dephasing rate that is confirmed numerically. In the weak dephasing regime, it is demonstrated that the diffusion constant is proportional to the square of the localization length which leads to a significant enhancement of the transport rate over the classical prediction. Finally, the influence of noise and disorder on the absorption spectrum is presented and its relationship to the transport properties is discussed.

Quantum heat current under non-perturbative and non-Markovian conditions: Applications to heat machines.

Abstract: We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)—which have a purely quantum mechanical origin—the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat curren...

Collective spontaneous emission from a line of atoms

Abstract: We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the $k\mathrm{th}$ emitted photon, $k=1,\dots{},N.$ We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.