Showing papers on "Master equation published in 1996"
TL;DR: Different couplings between a single ion trapped in a harmonic potential and an environment are designed and the variation of the laser frequencies and intensities allows one to design the coupling and select the master equation describing the motion of the ion.
Abstract: We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.
615 citations
TL;DR: It is shown that under certain conditions the resonant transport in mesoscopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms.
Abstract: It is shown that under certain conditions the resonant transport in mesoscopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms. Detailed microscopic derivation from the many-body Schr\"odinger equation is presented. Special attention is paid to the Coulomb blockade and quantum coherence effects in coupled quantum dot systems. The distinction between classical and quantum descriptions of resonant transport is clearly manifested in the modified rate equations. \textcopyright{} 1996 The American Physical Society.
341 citations
TL;DR: In this paper, a model of an irreversible quantum heat engine is presented, which is composed of a three-level system simultaneously coupled to hot and cold heat baths, and driven by an oscillating external field.
Abstract: The manifestations of the three laws of thermodynamics are explored in a model of an irreversible quantum heat engine. The engine is composed of a three‐level system simultaneously coupled to hot and cold heat baths, and driven by an oscillating external field. General quantum heat baths are considered, which are weakly coupled to the three‐level system. The work reservoir is modeled by a classical electro‐magnetic field of arbitrary intensity, which is driving the three‐level system. The first law of thermodynamics is related to the rate of change of energy obtained from the quantum master equation in the Heisenberg picture. The fluxes of the thermodynamic heat and work are then directly related to the expectation values of quantum observables. An analysis of the standard quantum master equation for the amplifier, first introduced by Lamb, is shown to be thermodynamically inconsistent when strong driving fields are used. A generalized master equation is rigorously derived, starting from the underlying quantum dynamics, which includes relaxation terms that explicitly depend upon the field. For weak fields the generalized master equation reduces to the standard equation. In very intense fields the amplifier splits into two heat engines. One engine accelerates as the field intensifies, while the other slows down and eventually switches direction to become a heat pump. The relative weight of the slower engine increases with the field intensity, leading to a maximum in power as a function of the field intensity. The amplifier is shown to go through four ‘‘phases’’ as the driving field is intensified, throughout all of which the second law of thermodynamics is generally satisfied. One phase corresponds to a ‘‘refrigeration window’’ which allows for the extraction of heat out of a cold bath of temperatures down to the absolute zero. This window disappears at absolute zero, which is conjectured to be a dynamical manifestation of the third law of thermodynamics.
166 citations
TL;DR: In this article, the authors mainly focus on the time development of the survival probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum.
Abstract: The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called “survival” probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann’s projection postulate in quantum measurement theory are critically overviewed fro...
163 citations
TL;DR: In this article, the dynamics of an N-level system linearly coupled to a field of massless bosons at positive temperature were investigated using complex deformation techniques, and time-dependent perturbation theory was developed.
Abstract: We investigate the dynamics of anN-level system linearly coupled to a field of mass-less bosons at positive temperature. Using complex deformation techniques, we develop time-dependent perturbation theory and study spectral properties of the total Hamiltonian. We also calculate the lifetime of resonances to second order in the coupling.
139 citations
TL;DR: This paper gives an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function.
Abstract: Hu, Paz, and Zhang [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases. \textcopyright{} 1996 The American Physical Society.
125 citations
TL;DR: In this paper, a simple example of a four-stroke engine operated in finite-time is analyzed subject to a fixed cycle time, and the time allocation between the hot and cold branches that maximizes the work output is considered.
Abstract: A simple example of a four‐stroke engine operated in finite‐time is analyzed. The working medium consists of noninteracting two‐level systems or harmonic oscillators. The cycle of operation is analogous to a four‐stroke Otto cycle. The only source of irreversibility is due to the finite rate of heat transfer between the working medium and the cold and hot baths. The dynamics of the working medium is governed by a master equation. The engine is shown to settle to a stable limit cycle for given contact periods with the hot and cold baths. The operation of the engine is analyzed subject to a fixed cycle time. The time allocation between the hot and cold branches that maximizes the work output is considered. Analytical results are obtained when the relaxation is very slow, very fast, or when the relaxation rates along the hot and cold branches are equal. Numerical results are presented for the general case. A maximization of the power with respect to the cycle time leads to a finite optimal cycling frequency provided the adiabatic branches are allotted finite durations.
122 citations
TL;DR: In this article, a mesoscopic description of surface chemical reactions, aimed to provide a link between microscopic lattice models and reaction−diffusion equations, is formulated, which is needed when large populations of nanoscale structures are considered or patterns characterized by a combination of macroscopic and microscopic lengths are investigated.
Abstract: A mesoscopic description of surface chemical reactions, aimed to provide a link between microscopic lattice models and reaction−diffusion equations, is formulated. Such a description is needed when large populations of nanoscale structures are considered or patterns characterized by a combination of macroscopic and microscopic lengths are investigated. By using the example of an adsorbate with attractive lateral interactions between molecules, the mesoscopic evolution equation for fluctuating coverages is derived from the microscopic master equation of the respective kinetic lattice model. This stochastic equation is applied to study phenomena of pattern formation related to adsorbate phase transitions.
110 citations
98 citations
TL;DR: It is shown that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius.
Abstract: We consider a \ensuremath{\lambda}${\mathrm{\ensuremath{\varphi}}}^{4}$ theory in Minkowski spacetime. We compute a ``coarse-grained effective action'' by integrating out the field modes with a wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients of this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. \textcopyright{} 1996 The American Physical Society.
94 citations
TL;DR: In this article, the quantum dynamics of an exciton boser or laser were analyzed and it was shown that the line width reduction obtained in a boser is limited by the strength of the exciton-exciton interactions.
TL;DR: In this paper, a fully Galilean covariant zero spin Markovian evolution was shown to reduce to the free motion perturbed by a covariant stochastic process with independent stationary increments in the classical phase space.
Abstract: Quantum Markovian master equations with generally unbounded generators, having physically relevant symmetries, such as Weyl, Galilean or boost covariance, are characterized. It is proven in particular that a fully Galilean covariant zero spin Markovian evolution reduces to the free motion perturbed by a covariant stochastic process with independent stationary increments in the classical phase space. A general form of the boost covariant Markovian master equation is discussed and a formal dilation to the Langevin equation driven by quantum Boson noises is described.
TL;DR: In this paper, a concept of semiclassically concentrated states was developed on the basis of the Maslov germ theory and a Schrodinger-type equation is shown to be equivalent to a closed finite system of ordinary differential equations.
TL;DR: In this paper, rate constants for the unimolecular decomposition of allyl, ethyl, n-propyl, and n-hexyl radicals have been determined on the basis of the solution of the time-dependent master equation with specific rate constants from RRKM calculations.
Abstract: This paper deals with the high-temperature decomposition of reactive intermediates with low reaction thresholds. If these intermediates are created in situ, for example, through radical chain processes, their initial molecular distribution functions may be characteristic of the bath temperature and, under certain circumstances, peak at energies above the reaction threshold. Such an ordering of reaction thresholds and distribution functions has some similarities to that found during chemical activation. This leads to consequences that are essenially the inverse (larger rate constants than those deduced from steady-state distributions) of the situation for stable compounds under shock-heated conditions and hence reduces falloff effects. To study this behavior, rate constants for the unimolecular decomposition of allyl, ethyl, n-propyl, and n-hexyl radicals have been determined on the basis of the solution of the time-dependent master equation with specific rate constants from RRKM calculations. The time req...
TL;DR: In this article, a completely discretized version of the 2D Toda lattice is used to reveal classical integrable structures in quantum models solved by Bethe ansatz.
Abstract: The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter's T-Q relation.
TL;DR: In this article, a non-Lindblad master equation without Lindblad form was shown to violate the positivity of the density operator in the Ornstein Uhlenbeck process both at high and low temperatures.
Abstract: Master equations without Lindblad form can in principle violate the positivity of the density operator. However, when such a master equation arises through systematic adiabatic elimination of fast variables from underlying microscopic dynamics, the violation can at worst arise on time scales one has coarsegrained over when performing the adiabatic elimination and can thus simply be ignored. Examples of non-Lindblad master equations are shown to arise for the Ornstein Uhlenbeck process both at high and low temperatures and for a single-mode laser operated near threshold.
TL;DR: It is shown that for two quite different models with low-energy cutoffs—a collection of two-level systems and a system described by the energy master equation—the frequency-dependent specific heat becomes universal at low temperatures, i.e., independent of both energy distribution and temperature.
Abstract: A derivation of the fluctuation-dissipation ~FD! theorem for the frequency-dependent specific heat of a system described by a master equation is presented The FD theorem is illustrated by a number of simple examples, including a system described by a linear Langevin equation, a two-level system, and a system described by the energy master equation It is shown that for two quite different models with low-energy cutoffs—a collection of two-level systems and a system described by the energy master equation—the frequency-dependent specific heat in dimensionless units becomes universal at low temperatures, ie, independent of both energy distribution and temperature These two models give almost the same universal frequencydependent specific heat, which compares favorably to experiments on supercooled alcohols
TL;DR: In this paper, the status of stochastic theories of homogeneous chemical systems operating in the multiple steady state region is clarified using microscopic simulation. But the results demonstrate the failure of the Langevin approach, but show excellent agreement with the master equation formulation.
Abstract: Microscopic simulation is used to clarify the status of stochastic theories of homogeneous chemical systems operating in the multiple steady state region. The results demonstrate the failure of the Langevin approach, but show excellent agreement with the master equation formulation.
TL;DR: In this article, the authors define various nonequilibrium concepts: relative entropy, dissipation during the relaxation to the stationary state, path entropy, cost for maintaining the system in a none-ilibrium state, fluctuation-dissipation theory, and finally a tree integral formula for the stationary states.
Abstract: For a nonequilibrium system characterized by its state space, by a dynamics defined by a transfer matrix and by a reference equilibrium dynamics given by a detailed‐balance transfer matrix, we define various nonequilibrium concepts: relative entropy, dissipation during the relaxation to the stationary state, path entropy, cost for maintaining the system in a nonequilibrium state, fluctuation‐dissipation theory, and finally a tree integral formula for the stationary state.
TL;DR: In this paper, the Nesbet algorithm was applied to the full iterative solution of the two-dimensional master equation for thermal unimolecular reactions, and an efficient algorithm for computing thermal rate coefficients in the falloff regime for reactions such as simple fission dissociations, radical−radical recombinations, and ion−molecule reactions wherein microcanonical dissociation rate coefficients are sensitive to both the vibrational energy and the angular momentum of the excited species.
Abstract: The application of the Nesbet algorithm to the full iterative solution of the two-dimensional master equation for thermal unimolecular reactions is presented. This leads to an efficient algorithm for computing thermal rate coefficients in the falloff regime for reactions such as simple fission dissociations, radical−radical recombinations, and ion−molecule reactions wherein microcanonical dissociation rate coefficients are sensitive to both the vibrational energy and the angular momentum of the excited species.
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TL;DR: Theoretical advances in the area of the glass transition have led to various experimental detections of the onset of microscopic inhomogeneity near T g, and the calorimetric characterization of a β-glass transition well below T g.
Abstract: Key advances in the area of the glass transition include various experimental detections of the onset of microscopic inhomogeneity near T g , and the calorimetric characterization of a β-glass transition well below T g . Theoretical advances include development of master equation approaches, alternative formulations of the mode coupling equations, and microheterogeneity-based interpretations of the origin of strong and fragile liquid characteristics.
TL;DR: In this article, the dynamics of the driven dissipative two-state system is formulated in terms of an exact nonconvolutive master equation, and the kernel is expressed as power series in the intersite coupling, in which the lowest order corresponds to the familiar noninteracting-blip approximation.
Abstract: The dynamics of the driven dissipative two-state system is formulated in terms of an exact nonconvolutive master equation. The kernel is expressed as power series in the intersite coupling, in which the lowest order corresponds to the familiar noninteracting-blip approximation. We use this formalism to calculate the kernel systematically in all orders of the intersite coupling for weak damping, and we solve the affiliated master equation for high-frequency driving in analytic form. Our approach finds straightforward generalization to any multistate dissipative tight-binding system.
TL;DR: In this paper, a reduced version of the quantum hydrodynamic model for semiconductors is formulated, which is shown to be equivalent to a non-standard integro-differential equation.
Abstract: A third order quantum perturbation of the stress tensor, and a relaxation approximation to represent averaged collisions, are employed as perturbations of the isentropic model for a collisionless plasma. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. As formulated, the model is a reduced version of the quantum hydrodynamic model for semiconductors. Existence is demonstrated for the model, which is shown to be equivalent to a non-standard integro-differential equation. An unusual boundary condition, with the important physical interpretation of specifying the quantum potential at the (current) inflow boundary, is identified as essential for the theory.
TL;DR: In this article, a generalized Forster theory is presented which includes reorientation of the interacting molecules, and a formal solution to the stochastic master equation is given, which is used to formulate the time-dependent fluorescence anisotropy.
Abstract: A generalized Forster theory is presented which includes reorientation of the interacting molecules. The stochastic master equation is, for the first time, derived from the stochastic Liouville equation, so that it accounts for the molecular origin to the stochastic transitions rates. A formal solution to the stochastic master equation is given. This equation is compared with its truncated cumulant expansion. The second‐order cumulant contains the correlation function 〈κ2(0)κ2(t)〉, where κ denotes the orientational dependence on dipole–dipole coupling. The solution of the master equation is used to formulate the time‐dependent fluorescence anisotropy, which is the relevant observable of energy transfer within donor–donor (dd) pairs, or bichromophoric molecules. Depending on symmetry of the local orientational distributions of the donor molecules, and their rates of reorientation, the fluorescence anisotropy decay becomes more or less complicated. Different simplifying conditions are given. The orientation...
TL;DR: In this article, the incoherent dynamics of a two-level system coupled to a thermal bath and driven by a strong external periodic field is studied, and analytical expressions for the effective rate constant and apparent energy bias of the TLS in a fast oscillating periodic field are derived.
TL;DR: In this paper, it was shown that the incorporation of the rigid symmetries to the solution of the master equation through the introduction of a constant ghost for each global symmetry can be obstructed already at the classical level whenever the theory possesses higher order conservation laws.
TL;DR: In this paper, both quantum and classical stochastic evolution equations are derived for the statistical state of a system subject to continuous observation of a position variable, which can also be interpreted as a conditional evolution equation for observations which give no information about the measured system but indicate the size of the random perturbations induced by the environment coupling.
Abstract: Quantum and classical stochastic evolution equations are derived for the statistical state of a system subject to continuous observation of a position variable. In the classical case this results in a stochastic Fokker - Planck equation for the conditional state of the system conditioned on observation records. In the quantum case a stochastic master equation results, or a stochastic Schrodinger equation if the system starts in a pure state. In both cases the resulting equations are nonlinear. A simple modification of the model results in a linear stochastic Schrodinger equation which can also be interpreted as a conditional evolution equation for observations which give no information about the measured system but indicate the size of the random perturbations induced by the environment coupling.
TL;DR: In this article, a photon assisted tunnelling (PAT) through a quantum dot with zero-dimensional (0D) states is described, which allows electrons to reach previously inaccessible energy states by absorbing or emitting photons from a microwave signal.
Abstract: We report photon-assisted tunnelling (PAT) through a quantum dot with zero-dimensional (0D) states. PAT allows electrons to reach previously inaccessible energy states by absorbing or emitting photons from a microwave signal. We discuss a model based on a master equation for a quantum dot with 0D states and include PAT processes. Simulations are compared with measurements.