scispace - formally typeset
Search or ask a question
Topic

Master equation

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


Papers
More filters
Journal ArticleDOI
TL;DR: A pedagogical treatment of the formalism of continuous quantum measurement is presented, using the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables.
Abstract: We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.

456 citations

Journal ArticleDOI
TL;DR: A general theory of chemical kinetics, developed over the past 7 years, is presented, capable of answering questions about how reaction rate is a nonlinear function of the thermodynamic driving force, the free energy of reaction, expressed in terms of variational chemical potentials.
Abstract: Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li$_x$FePO$_4$

440 citations

Journal ArticleDOI
TL;DR: In this paper, an expansion in powers of some parameter is needed in order to solve the master equation by a systematic approximation method, and the appropriate parameter is the reciprocal size of the system.
Abstract: In order to solve the master equation by a systematic approximation method, an expansion in powers of some parameter is needed. The appropriate parameter is the reciprocal size of the system, defin...

439 citations

Journal ArticleDOI
TL;DR: Decoherence provides physical justification of surface hopping, obviating the need for ad hoc surface hopping rules and providing an improvement over the most popular surface hopping technique.
Abstract: A simple surface hopping method for nonadiabatic molecular dynamics is developed. The method derives from a stochastic modeling of the time-dependent Schrodinger and master equations for open systems and accounts simultaneously for quantum mechanical branching in the otherwise classical (nuclear) degrees of freedom and loss of coherence within the quantum (electronic) subsystem due to coupling to nuclei. Electronic dynamics in the Hilbert space takes the form of a unitary evolution, intermittent with stochastic decoherence events that are manifested as a localization toward (adiabatic) basis states. Classical particles evolve along a single potential energy surface and can switch surfaces only at the decoherence events. Thus, decoherence provides physical justification of surface hopping, obviating the need for ad hoc surface hopping rules. The method is tested with model problems, showing good agreement with the exact quantum mechanical results and providing an improvement over the most popular surface hopping technique. The method is implemented within real-time time-dependent density functional theory formulated in the Kohn-Sham representation and is applied to carbon nanotubes and graphene nanoribbons. The calculated time scales of non-radiative quenching of luminescence in these systems agree with the experimental data and earlier calculations.

437 citations

Journal ArticleDOI
TL;DR: This work considers an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products and considers the situation where some of the chemical eigenvalues approach the energy relaxation time scale and how to modify the phenomenological rate coefficients.
Abstract: We consider an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products. Within this formulation the dynamical phase space consists of only the microscopic populations of the various isomers making up the reactive complex, while the bimolecular reactants and products are treated equally as sources and sinks. This reformulation yields compact expressions for the phenomenological rate coefficients describing all chemical processes, i.e., internal isomerization reactions, bimolecular-to-bimolecular reactions, isomer-to-bimolecular reactions, and bimolecular-to-isomer reactions. The applicability of the detailed balance condition is discussed and confirmed. We also consider the situation where some of the chemical eigenvalues approach the energy relaxation time scale and show how to modify the phenomenological rate coefficients so that they retain their validity.

425 citations


Network Information
Related Topics (5)
Quantum
60K papers, 1.2M citations
94% related
Hamiltonian (quantum mechanics)
48.6K papers, 1M citations
94% related
Ground state
70K papers, 1.5M citations
92% related
Phase transition
82.8K papers, 1.6M citations
89% related
Excited state
102.2K papers, 2.2M citations
87% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023140
2022344
2021431
2020460
2019420
2018427