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1.
We present the continued fraction solution for the stationary probability of discrete master equations of one-variable processes. After we elucidate the method for simple birth and death processes we focus the study on processes which introduce at least two-particle jumps. Consequently, these processes do in general not obey a detailed balance condition. The outlined method applies as well to solutions of eigenmodes of the stochastic operator. Further we derive explicit continued fraction solutions for the Laplace transform of conditional probabilities. All the various continued fraction coefficients are given directly in terms of the transition rates and they obey recursion relations. The method is illustrated for the stationary solution of a simple nonlinear chemical reaction scheme originated by Nicolis.  相似文献   

2.
In this paper we continue to extend our previous investigation of continued fraction (CF) solutions for the stationary probability of discrete one-variable master equations which generally do not satisfy detailed balance. We derive explicit expressions, directly in terms of the elementary transition rates, for the continued fraction recursion coefficients. Further, we derive several approximate CF-solutions, i.e., we deduce non-systematic and systematic truncation error estimates. The method is applied to two master equations with two-particle jumps for which we derive the exact probability solution and make a comparison with approximate solutions. The investigation is also extended to the case of master equations with multiple birth and death transitions of maximal orderR.Supported in part by Deutsche Forschungsgemeinschaft and by National Science Foundation Grant CHE78-21460  相似文献   

3.
We present two different approximation schemes for determining non-perturbatively the quenched master field of large-N field theories. The first method is variational and involves minimizing the trace of the squared master-field equation. The second method is based on solving the master-field equation exactly in a truncated basis of stochastic matrices. Either method, when applied to matrix γθ4 theory in D = 0 and 1 dimensions, gives results of n-point functions and the mass-gap which are in extremely close agreement with the known exact values.  相似文献   

4.
Recent mathematical developments on approximate diffusionlike solutions to the master equation are summarized. The technique is applied to two master equations of physical interest-one that describes the phenomenon of superradiance and a second that characterizes generation-recombination noise in semiconductors. For this second case, some previously obtained equilibrium results are found and the extension of these results to finite times is given.  相似文献   

5.
An approximative method of solving master equations based on information-gain minimization is applied for the Schlögl's model systems showing nonequilibrium phase transitions. The time evolution of the mean value and of the fluctuation of the relevant stochastic variable is discussed.  相似文献   

6.
A scheme is presented by which we can obtain static electrovac exterior solutions from the stationary gravitational fields given by Kerr and Tomimatsu and Sato. A five-parameter solution of the combined Einstein-Maxwell equations is given that describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds and angular momentum. These are generated by using Kinnersley's method from Wang's electrovac solutions, which, in turn, were generated from the gravitational fields of Tomimatsu and Sato for =2–3. All the solutions are asymptotically flat.  相似文献   

7.
The time relaxation behavior of the solutions of certain classes of discrete master equations is studied in the limit of an infinite number of states. Depending on the range of the transition matrix, a relaxation behavior is found reaching from at –1/2 law for short range, over enhanced relaxation to an exponential relaxation for the extreme long-range case. The behavior in the limit of a continuous family of states is also discussed.  相似文献   

8.
The discrete self-trapping equation is a model coupled oscillator system with applications in many areas including the dynamics of small molecules and the study of solitions on alpha-helix proteins. Some simple stability criteria for stationary solutions of this equation are presented, together with some example calculations.  相似文献   

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10.
Steady state solutions of master equations with one variable are constructed. The method of solution is based on a transformation of the original equation for the probability into one for a slowly varying function. The method is of general applicability and is particularly useful in obtaining solutions in the case where detailed balance does not hold. Examples of such systems in chemical reaction models and the two photon laser are discussed.On leave from the University of Waikato, Hamilton, New Zealand  相似文献   

11.
The Weyl axially symmetric electrovac formalism for coincident gravitational and electrostatic equipotential surfaces is used to generate charged versions of some axially symmetric vacuum fields. The metric for two separated charged Curzon particles held in equilibrium by a strut is found and the condition for the removal of the strut is discussed. Kinnersley transformations applied to the two-particle metric yield spin but line singularities invariably appear along the symmetry axis and the metric is asymptotically NUT-like. It is shown that any Kinnersley transformation applied to a static axially symmetric asymptotically flat vacuum metric generates another asymptotically flat metric only if the latter is static. Moreover, the transformed metric is always undercharged (q 2<m 2) if it is asymptotically flat. A necessary and sufficient condition for asymptotic flatness in terms of the relevant parameters is found. A generalization of the Kinnersley transformation scheme is presented and illustrated by an example.  相似文献   

12.
We introduce transition factors and derive equations for them which are equivalent to the originalN-dimensional discrete master equation. After transition to continuous variables we obtain nonlocal partial differential equations for these transition factors which are slowly varying variables. Finally we consider a chemical reaction system. Using this method the corresponding master equation is exactly solvable in a very simple manner.  相似文献   

13.
14.
The phonon dynamics of a harmonic oscillator coupled to a steady reservoir is studied. In the Markovian limit, the equilibrium is reached through a progressive loss of memory process which involves the moments of the initial distribution. The relationship to the non-Markovian equations of motion and its resolvent poles is settled. As a particular model of the coupling mechanism is adopted, the possibility of non-Gibbsian equilibrium distribution arises, which is analyzed focusing upon the dependence of various parameters of the system on an effective equilibrium temperature.  相似文献   

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16.
A class of approximate stationary solutions of the Einstein-Maxwell equations are obtained by expanding the metric in powers of a certain parameter and solving explicitly the first few orders in terms of four harmonic functions. These solutions, to the order considered, reduce to the Weyl, Bonnor, and Perjés-Israel-Wilson solutions, respectively, for suitable choice of the harmonic functions. They also contain a subclass that is asymptomatically flat and has realistic arbitrary spinning sources.  相似文献   

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18.
We give a rigorous proof that under certain technical conditions the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit. This is sufficient to show that a number of open systems obey an exponential decay law in the weak coupling limit for a rescaled time variable. The theory is applied to a fairly general finite dimensional system weakly coupled to an infinite free heat bath.  相似文献   

19.
As a first step in the search of an analytical study of mechanical denaturation of DNA in terms of the sequence, we study stable, stationary solutions in the discrete, finite, and homogeneous Peyrard-Bishop DNA model. We find and classify all the stationary solutions of the model, as well as analytic approximations of them, both in the continuum and in the discrete limits. Our results explain the structure of the solutions reported by Theodorakopoulos et al. [Phys. Rev. Lett. 93, 258101 (2004)] and provide a way to proceed to the analysis of the generalized version of the model incorporating the genetic information.  相似文献   

20.
We consider a special class of stationary rotating charged dust solutions of Einstein's field equations without cosmological constant. In these space-times, the motion of freely falling particles and of light rays can be visualized by the motion of charged particles in an appropriate model magnetic field. Any curl-free magnetostatic field, given on an open subset of Euclidean 3-space, can serve as a model magnetic field for a charged dust solution in this sense. The simplest example, corresponding to a homogeneous model magnetic field, is given by Som-Raychaudhuri space-time. Some other examples are worked out.  相似文献   

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