On the quantum langevin equation

The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.Deceased.     

On the mass spectrum of elementary particles

A simple theory of the elementary particle mass spectrum is proposed. It originates from the Dirac idea of the free electron motion and from the transformed Klein-Gordon equation. The theory is based on an equation that includes the squared mass operator having an infinite sequence of orthogonal eigenfunctions and a discrete spectrum of eigenvalues. A discrete mass formula is derived. It yields values of mass that are in agreement with present-day empiric data for elementary particles.     

Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H₃C) to hydroxymethylene radical (H₂?OH).     

Massive mesons in Weyl–Dirac theory

In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl–Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton–Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.     

Wigner elementary particle in an external homogeneous field

A covariant Hamiltonian is proposed which permits to describe in the Heisenberg picture the motion of a Wigner elementary particle in a homogeneous electromagnetic field. More precisely, at any time, the elementary particle is in a state associated with a given irreducible representation of the Poincaré group. As a remarkable result, the spin motion is shown to be governed by the Thomas-Bargmann-Michel-Telegdi equation. Also the Galilean limit is discussed.     

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined.     

Causal Set Dynamics and Elementary Particles

A causal set is considered a finite, acyclic oriented graph with special restrictions: each vertex has two incident edges directed to this vertex and two incident edges directed from this vertex. This graph is called a causal graph. The vertex with incident edges is called an X-structure. Quantum measurements are discussed. A dynamics of the causal graph is a random sequence of elementary interactions of edges that is described by complex amplitudes. These amplitudes correspond to each pair of interacting edges. The edges are elementary particles. The mass of a particle is a probability of the interaction. An equation of particles is proposed. In a simple case this equation for X-structure is the Dirac's equation. The edges are fermions with the spin 1/2.     

激光点火煤粒着火的模型分析

本文对颗粒煤在激光加热条件下的着火和燃烧进行了数值模拟。采用的是一个简单的煤粒着火与燃烧的一维模型。该模型采用了热解和双平行反应模型,考虑了煤粒表面的多相反应和气相的基元反应以及气相中的传热与传质。从获得的煤粒表面和气相空间的温度随时间的变化规律,可以判断不同煤种的着火方式。     

Decoherence and dynamical entropy generation in quantum field theory

We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simple quantum mechanical model. We show that the entropy following from the perturbative master equation suffers from physically unacceptable secular growth.     

Atomistic and lattice model of a grain boundary defaceting phase transition

Recent calculations have shown that grain boundary (GB) stress is too small to stabilize finite GB facets, suggesting that the existing theory of GB defaceting phase transitions is incomplete. We perform molecular dynamics calculations, which show a reversible phase transition at approximately 400 K with a concerted shuffle of two atoms at the facet junction as the elementary excitation. Based on this excitation we formulate an appropriate lattice model, perform Monte Carlo simulations, and establish an analytical relationship between the elementary excitation energy and the transition temperature.     

An integral equation for radiation transport in an infinite cylinder with Fresnel reflection

We formulate an integral equation for radiation transport in an infinitely long cylinder. Scattering is included and sources arise from incidence on the surface and from an internal volume source. Internal reflection at the surface follows the Fresnel law. For the special case of no scattering and no axial variation of the source, we obtain an exact solution which we have compared numerically with some results of Tian and Chiu [Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces. JQSRT 2006;98:249]. We have also obtained closed form analytical solutions for no scattering with a line source along the cylinder axis and also that for the case of a spatially constant volume source. The general case when there is variation in the axial direction is also presented and the special case of a radially uniform plane source at the origin is explored in some detail. The axial solution is compared with an approximate areal average method introduced by Larsen [A one-dimensional model for three dimensional transport in a pipe. Transp Theory Stat Phys 1984;13:599; Larsen EW, Malvagi F, Pomraning GC. One dimensional models for neutral particle transport in ducts. Nucl Sci Eng 1986;93:13] in another context.     

Dynamic aspect of solid solution cathodes by method of integral transform

A mathematical model is presented for a thin film, spherical and cylindrical particles electrodes under galvanostatic discharge. The model available to simulate the electrochemical behavior is discussed considering not only their electrochemical representation (transport phenomena), but also the mathematical techniques, i.e. Integral transform that have been used for solving the equations. We examine the non-homogeneous material balance equation in the rectangular, spherical and cylindrical coordinate system; determine the elementary solutions, the norms and the eigenvalues of the problems for galvanostatic boundary conditions and systematically tabulate the resulting expressions. Expressions are developed for plane, cylindrical and spherical particles giving the relation between battery load and the amount of cathode material utilized. The particle shape and a single parameter Q is used to describe cathode performance.     

Ab initio yield curve dynamics

We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success of the Nelson–Siegel approach to fitting static yield curves and the empirically observed modal structure of yield curves. A practical numerical implementation of this equation of motion is found by using the Karhunen–Lòeve expansion and Galerkin's method to formulate a reduced-order model of yield curve dynamics.     

Propagators for Scalar Bound States at Finite Temperature in an NJL Model

We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperaturein a chiral Ut(1) x UR(1) NJL model, defined by four-point amputated fimctions subtracted through the gap equation,and prove that they are completely equivalent in the imaginary-time and real-time formalisms by separating carefiullythe imaginary part of the zero-temperature loop integral. It is shown that the same thermal transformation matrix ofthe matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagatorfor an elementary scalar particle and this fact shows the similarity of thermodynamic property between a composite andelementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly fromthe imaginary-time formalism.     

Three-dimensional Laplace’s potentials in a complex representation

A new analytic method for constructing wide classes of three-dimensional Laplace’s potentials that admit a closed representation in terms of elementary functions is developed. These classes are especially useful in designing electron-optics devices on the basis of inverse problems of particle dynamics, in which case there arises an ill-posed Cauchy problem for Laplace’s equation, this problem involving an analytic continuation of the sought potential from a plane to three-dimensional space.     

Liquid-crystal diode generator of low-frequency oscillations

The excitation of rhythmic current oscillations in a diode cell containing a nematic liquid crystal is studied. The external electric field in the interelectrode gap is directed parallel to the surfaces which orient the liquid crystal molecules. The current oscillations are accompanied by the formation of an autosoliton at the cathode, which propagates and disappears at the anode. A hypothetical model is proposed to explain this current instability. Zh. Tekh. Fiz. 68, 125–127 (January 1998)     

Variational Principle for a Schrdinger Equation with Non-Hermitian Hamiltonian and Position-Dependent Mass

A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.     

Investigation an Effective Interaction Potential of Dust Particles in Nonideal Dusty Plasma

Interaction between dusty particles remains to be an interesting issue that still requires deeper theoretical and experimental investigations. In the present paper we formulate a theoretical approach to the calculation of effective interaction potential of dust particles on the basis of Poisson equation and experimentally measured pair correlation functions. By application of our model to the data from the liquid phase of dust formations in stratified dc glow discharge, it is shown that there is an attractive component in the interaction of dust particle (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zitterbewegung in Quantum Mechanics

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.     

Extended Brueckner–Hartree–Fock theory with pionic correlation in finite nuclei

We formulate a nuclear many-body theory with explicit treatment of the strong tensor correlation caused by the pion-exchange interaction. To do this, we have to extend the Hartree–Fock variational model space to include 2-particle 2-hole (2p–2h) states, which are able to handle the tensor correlation and to contain high momentum components originating from its pseudo-scalar nature of the pion. We take the variational principle of the total energy, and obtain equations of motion for the variational parameters as the Hartree–Fock single particle states and 2p–2h states. As for the short range repulsion, we use the unitary correlation operator method (UCOM) to express the short range correlation in the ground state wave function. We then arrive at an extended Hartree–Fock equation with the inclusion of the effect of the pion exchange and short range repulsive interactions. We find this extended Hartree–Fock equation has a structure of the Brueckner theory. Thus, we name the present theoretical framework as an extended Brueckner–Hartree–Fock (EBHF) theory. We compare the EBHF theory with the Feshbach projection method and the Brueckner–Hartree–Fock theory.