Search results for "master equation"
showing 10 items of 103 documents
Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide
2018
We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to discuss the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit …
Nonlinear response theory for Markov processes II: Fifth-order response functions
2017
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012)). For sinusoidal fields the $5\om$-component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurence of such a hump as compared to a …
Nucleation in physical and nonphysical systems
2003
Abstract The aggregation of particles out of an initially homogeneous situation is well known in physics. Depending on the system under consideration and its control parameters, the cluster formation in a supersaturated (metastable or unstable) situation has been observed in nucleation physics as well as in other branches. We investigate the well-known example of condensation (formation of liquid droplets) in an undercooled vapour to conclude that the formation of bound states as a phase transition is related to transportation science. We present a comparison of nucleation in an isothermal–isochoric container with traffic congestion on a circular one-lane freeway. The analysis is based, in …
Levy flights in confining environments: Random paths and their statistics
2013
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…
Fractional master equations and fractal time random walks
1995
Fractional master equations containing fractional time derivatives of order 0\ensuremath{\le}1 are introduced on the basis of a recent classification of time generators in ergodic theory. It is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks. The corresponding waiting time density \ensuremath{\psi}(t) is obtained exactly as \ensuremath{\psi}(t)=(${\mathit{t}}^{\mathrm{\ensuremath{\omega}}\mathrm{\ensuremath{-}}1}$/C)${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremath{\omega}}}$(-${\mathit{t}}^{\mathrm{\ensuremath{\omega}}}$/C), where ${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremat…
Giant Quantum Oscillators from Rydberg Atoms: Atomic Coherent States and Their Squeezing from Rydberg Atoms
1989
This paper summarises work since about 1979 by all the authors indicated: RKB is given prominence only because he bears the responsibility for the present paper. All the work has proved relevant to Rydberg atoms. Here we lay particular stress on recent results for squeezing by Rydberg atoms.
Electrical fluctuations in monolayer-protected metal nanoclusters
2008
Abstract Monolayer-protected clusters (MPCs) are formed by a neutral or charged metallic core surrounded by an organic ligand monolayer. We estimate the electric potential fluctuations of a MPC in an electrolyte solution by using the equilibrium fluctuation–dissipation theorem and the non-linear Poisson–Boltzmann equation extended to account for ion penetration in the monolayer. Significant fluctuations are predicted because the MPC capacitance is small (approximately 1 aF). We study also the non-equilibrium case of a MPC sandwiched between two electrodes and estimate the current noise considering the nanocluster as a single electron transistor and using a theoretical approach based on the …
Adatom Island Diffusion on Metal Fcc(100) Surfaces
2001
We study the energetics and atomic mechanisms of diffusion of adatom islands on fcc(100) metal surfaces. For small islands, we perform detailed microscopic calculations using semi-empirical embedded-atom model and glue potentials in the case of Cu and Al, respectively. Combining systematic saddle-point search methods and molecular statics simulations allows us to find all the relevant transition paths for island motion. In particular, we demonstrate that there are novel many-body mechanisms such as internal row shearing which can, in some cases, control the island dynamics. Next, we show how using the master equation formalism, diffusion coefficients for small islands up to about five atoms…
A new mathematical tool for an exact treatment of open quantum system dynamics
2005
A new method to obtain an operatorial exact solution of a wide class of Markovian master equations is presented. Its key point is the existence of a constant of motion partitioning the Hilbert space into finite-dimensional subspaces. The consequent possibility of representing the reduced density operator as a block diagonal matrix is shown. Each “block operator” evolves under the action of a non-unitary operator explicitly derived. Our mathematical approach is illustrated applying it to simple physical systems.