Stochastic theory of nonlinear nonequilibrium processes

Arguments about the stochastic nature of the changes in thermodynamic parameters are used to construct a nonlinear version of the nonequilibrium thermodynamics of scalar processes, with account taken of crossover effects. The formalism is generalized to the case of vector processes. A cyclic chemical reaction in an ideal gas is treated as an example.Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 55–63, September, 1970.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Stochastic processes in cosmology

The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state.     

Stochastic processes in rheology

Various stochastic differential equations arising in rheology are presented. Their phenomenological derivation and some of their results are outlined. Rheology appears as a source of stochastic problems and as a test for the applicability of methods developed in the theory of stochastic processes.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Stochastic coupled cluster theory

We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.     

Stochastic processes and multihadron production

Acta physica Academiae Scientiarum Hungaricae - Statistical multihadron production models are considered in a stochastic framework. The predictions of the stochastic quark model of hadron clusters...     

Stochastic processes on quantum logics

Stochastic processes on quantum logics are defined and the properties of a Brownian motion process are studied. A stochastic integral with respect to this Brownian motion process is constructed.     

Stochastic time-dependent current-density-functional theory

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state |Psi0> and the particle-bath interaction operator, two external vector potentials A(r,t) and A'(r,t) that produce the same ensemble-averaged current density, j(r,t), must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.     

Stochastic processes of a quantum state

Starting from a quantum state represented by its wave function (x), satisfying the Schrödinger equation, we determine stochastic processes which provide the same time evolution for the probability density(x)=¦(x)¦². The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.     

Stochastic processes in conformal Riemann-Cartan-Weyl gravitation

We construct the Riemann-Cartan geometries with torsion generated by the action of the conformal Weyl group. We study the wave operators associated to these structures, which, in addition to the usual Laplace-Beltrami operator, have a term which is a gradient vector field conjugate to the one-form given by the torsion potential derived from the Weyl group, and which we associate with a relativistic extension of the drift vector field in Nelson's construction of stochastic mechanics. In fact, our construction is valid for configuration spaces of any dimension. We sketch the construction of the stochastic processes on space-time generated by these operators, where the invariant measure is found to be defined by the conformal structure. We discuss briefly the relation with the theory of Dirichlet forms and D. Bohm's quantum potential in the theory of hidden variables, which in this setting acquire a gauge-geometric status previously unknown.     

Stochastic processes associated with quantum systems

Stochastic processes have been useful in constructing and studying states in Quantum Field Theory (e.g., the Erice Lectures [3], Simon [2], Glimm and Jaffle [6] and in Quantum Statistical Mechanics (e.g., Ginibre [5], Høegh-Khron [7], Fröhlich [4], Driessler, Landau and Perez [2]). By analytically continuing into imaginary time, we may in certain cases replace the non-commulative algebra of observables of the quantum system by a commulative algebra consisting of functions of a stochastic process.In this article we are going to discuss an appropriate mathematical framework for this connection between quantum systems and stochastic processes.     

Stochastic representation of nearly-Gaussian,nonlinear processes

The use of polynomial functionals of the white noise process is discussed for the treatment of nonlinear random processes. It is noted that such treatments are useful for nearly-Gaussian processes. Applications of such representations to nonlinear systems and to nonlinear fluid mechanics problems (turbulence) are reviewed.     

HCCI燃烧过程化学发光光谱研究

在一台经改装单缸光学发动机机上,进行不同喷油策略和进气温度条件下均质压燃(HCCI)燃烧化学发光光谱实验研究。实验保证循环供油量一定,燃用正庚烷作为燃料,转速600 r.min-1,进气压力0.1MPa,控制2个不同的进气温度:95和125℃。化学发光光谱研究结果表明,低温反应阶段化学发光很弱,主要源于甲醛光谱;低温反应后期-负温度系数区-高温反应初始阶段主要发光来源还是甲醛光谱;高温反应阶段发光主要来源于CO—O*连续谱,同时在CO—O*连续谱上出现OH,HCO,CH,HCHO谱峰;高温反应后期化学发光明显减弱。与-30°ATDC喷油相比,-300°ATDC喷油时CO—O*连续谱发光强度更大,HCO和OH生成量更多,燃烧反应进行程度更深。较高进气温度下CO—O*连续谱发光强度更大,HCO和OH生成量更多。     

Stochastic interpretations of nonrelativistic quantum theory

A critique of the causla and classical stochastic interpretations of nonrelativistic quantum mechanics is presented. The only way that the classical stochastic formulation can be made compatible with the theory of quantum measurement is to extend the probability measure density for fluctuating paths to the complex domain. In doing so, we obtain the generalized stochiastic formulation in which the methods of classical probability theory can be used to describe the quantum mechanical phenomenon of interfering alternatives. Illustrative examples from quantum theory are used to show the complete compatibility between the traditional and generalized stochastic interpretations of quantum mechanics. Work supported in part by a contribution from the CNR.     

Stochastic quantization of supersymmetric field theory

The Parisi-Wu stochastic quantization method is applied to supersymmetric field theory. The Langevin equation, which reproduces the Green functions of euclidean field theory, is written in terms of superfields. Supersymmetric U(1) theory under gauge fixing and the large N reduction in chiral SU(N) theory are discussed. Regularization based on the stochastic method is studied also.     

Stochastic regularization of quantum field theory

The equivalence between a D-dimensional classical field theory coupled to an external random source having Gaussian correlations and its D−2 dimensional quantum counterpart was established. Utilizing this equivalence, a regularization procedure for scalar theories is developed. The regularization amounts to a compacification of the extra two dimensions. The regularization scheme is interpreted in terms of superpropagator modifications.     

Stochastic processes originating in deterministic microscopic dynamics

We investigate the probability distribution of the scaled trajectory of a test particle moving in an equilibrium fluid according to the laws of classical mechanics, i.e., ifQ(t) is the displacement of the test particle we letQ _A(t) =Q(At)/√A and consider the distribution of the trajectory Q_A(t) in the limit A→∞. The randomness of the motion is due entirely to the randomness of the initial state of the fluid, test particle, or both, and the process is generally non-Markovian. Nevertheless, it can be proven in some cases and we expect it to be true in many more that Q_A (t) looks like Brownian motion in the limit A→∞. Some results for simple model systems are presented.