Search results for "Master equation"
showing 10 items of 103 documents
Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale
2020
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our mo…
Optimal Control of Dissipative Quantum Systems
2008
We study the control of finite dimensional quantum systems by external laser fields. After examining the concrete example of the diatomic molecular alignment in dissipative media, we are interested in the problem of optimal control, where the objective is to bring the system from an initial state into a given final state while minimizing a cost functional. The Pontryagin maximum principle (PMP) provides necessary conditions for optimality, by establishing that any optimal trajectory is the extremal solution of an extended problem of Hamiltonian structure. In this context, we perform the analysis of two particular systems. The first one is a dissipative 2-level system, for which we determine…
Nonresonant hole burning spectroscopy of the relaxor ferroelectric PLZT
2002
Abstract The polydispersive dielectric response of a lanthanum-modified lead zirconate titanate relaxor ferroelectric was studied using nonresonant hole burning (NHB) spectroscopy. The dynamic heterogeneity of this material was evidenced by the fact that it was possible to burn frequency-dependent spectral holes. The maximum position of the spectral holes depended on the square root of the pump frequency Ω . The refilling of the spectral holes was monitored subsequent to excitation using various pump frequencies. The refilling data could be collapsed onto a master curve by re-scaling them, again, using Ω −0.5 as scaling factor. The refilling time was found to be much longer than the time sc…
EXACT SOLUTIONS FOR A CLASS OF FRACTAL TIME RANDOM WALKS
1995
Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied. This class of fractal time processes is characterized by a dynamical critical exponent 0<ω≤1, and is equivalently described by a fractional master equation with time derivative of noninteger order ω. Exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques. The Greens functions are expressible in terms of general H-functions. For ω<1 they are singular at the origin and exhibit a stretched Gaussian form at infinity. Changing the order ω interpolates smoothly between ordinary diffusion ω=1 and completely localized behavior in the …
Single-layer metal-on-metal islands driven by strong time-dependent forces
2012
Non-linear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semi-empirical lattice model and use master equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of int…
The kinetics of defect aggregation: A novel lattice formalism
1995
We introduce a stochastic model for the A + B → O reaction on a discrete lattice. The system may include mono- and bimolecular steps (i. e. reaction and diffusion steps). The resulting infinite chain of equations is truncated at a certain level via a modified Kirkwood approximation.
The energy minimization problem for two-level dissipative quantum systems
2010
In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.
Thermalization of Levy flights: Path-wise picture in 2D
2013
We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy stable noise which, under the sole influence of external (force) potentials $\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such behavior is excluded within standard ramifications of the Langevin approach to L\'{e}vy flights. In the present paper we address the response of L\'{e}vy noise not to an external conservative force field, but directly to its potential $\Phi (x)$. We prescribe a priori the target pdf $\rho_*$ in the Boltzmann form $\sim \exp[- \Phi (x)]$ and next select the L\'evy noise of interest. Given suitable initial data, this allows to infer a reliable path-wise approxima…
Two-Color Single-Photon Emission from In As Quantum Dots: Toward Logic Information Management Using Quantum Light
2014
In this work, we propose the use of the Hanbury-Brown and Twiss interferometric technique and a switchable two-color excitation method for evaluating the exciton and noncorrelated electron-hole dynamics associated with single photon emission from indium arsenide (InAs) self-assembled quantum dots (QDs). Using a microstate master equation model we demonstrate that our single QDs are described by nonlinear exciton dynamics. The simultaneous detection of two-color, single photon emission from InAs QDs using these nonlinear dynamics was used to design a NOT AND logic transference function. This computational functionality combines the advantages of working with light/photons input/output device…
A 1D coupled Schrödinger drift-diffusion model including collisions
2005
We consider a one-dimensional coupled stationary Schroedinger drift-diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone). We give boundary conditions at the classic-quantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.