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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: Using an existing expression for the state-to-state rotational transition rate coefficients, which is derived from the experimental data taken at temperatures equal to or below 1500 K, the master equation for rotational states is integrated with time for N 2.
Abstract: Using an existing expression for the state-to-state rotational transition rate coefficients, which is derived from the experimental data taken at temperatures equal to or below 1500 K, the master equation for rotational states is integrated with time for N 2 . The postshock temperature considered is from 400 to 128,000 K. From the numerical solutions of the master equation, the effective collision numbers and characteristic relaxation times are determined
118 citations
TL;DR: In this paper, the authors compare second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix.
Abstract: In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.
118 citations
TL;DR: In this article, the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments is quantified by relating it to the decay rates of various complementary measures of the quantum nature of a state, such as the purity, some non-classicality indicators in phase space, and, for two-mode states, entanglement measures and total correlations between the modes.
Abstract: We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some non-classicality indicators in phase space, and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wavepackets.
117 citations
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TL;DR: The quantum dynamical Yang-Baxter equation as mentioned in this paper is a generalization of the ordinary quantum Yang-baxter equation, considered in a physical context by Gervais and Neveu, and later from a mathematical viewpoint by Felder.
Abstract: This paper contains a systematic and elementary introduction to a new area of the theory of quantum groups -- the theory of the classical and quantum dynamical Yang-Baxter equations. It arose from a minicourse given by the first author at MIT in the Spring of 1999, when the second author extended and improved his lecture notes of this minicourse.
The quantum dynamical Yang-Baxter equation is a generalization of the ordinary quantum Yang-Baxter equation, considered in a physical context by Gervais and Neveu, and later from a mathematical viewpoint by Felder. Felder attached to every solution of this equation a quantum group, and also considered the classical analogue of the quantum dynamical Yang-Baxter equation -- the classical dynamical Yang-Baxter equation. Since then, the theory of dynamical Yang-Baxter equations and the corresponding quantum groups was systematically developed in many papers. By now, this theory has many applications, in particular to integrable systems and representation theory.
The goal of this paper is to discuss this theory and some of its applications.
117 citations
01 Dec 2006
TL;DR: The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering.
Abstract: Computation of Invariant Manifolds.- A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory.- A Versatile Algorithm for Computing Invariant Manifolds.- Covering an Invariant Manifold with Fat Trajectories.- "Ghost" ILDM-Manifolds and Their Identification.- Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays.- Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form.- Coarse-Graining and Ideas of Statistical Physics.- Basic Types of Coarse-Graining.- Renormalization Group Methods for Coarse-Graining of Evolution Equations.- A Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining.- Finite Difference Patch Dynamics for Advection Homogenization Problems.- Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation.- Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory.- Kinetics and Model Reduction.- Exactly Reduced Chemical Master Equations.- Model Reduction in Kinetic Theory.- Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics.- Dynamics of the Plasma Sheath.- Mesoscale and Multiscale Modeling.- Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition.- Lattice Boltzmann Method and Kinetic Theory.- Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation.- Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework.- Diagnostic Goal-Driven Reduction of Multiscale Process Models.- Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations.- An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation.- A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems.
117 citations