Stationary State

Detection of a material particle is accompanied by emission of bremsstrahlung. Thus the dynamics of the energy loss of the particle is determined by radiation reaction force. The description of radiation reaction is a difficult problem still being subject of ongoing debates. There are problems of runaway solutions, preacceleration already in classical description of radiation reaction. Additional complications in quantum mechanical description arise because of the infinite source field energy term in hamiltonian for a point charge. There is still no general consensus on an appropriate quantum mechanical description. Neither the achievements of the radiation theory on the subject nor the problems associated with it are sufficiently taken into account in context with measurement problem. Radiation reaction doesn't effect free particle wave packets, but it favors stationary states of the `wave function of the measured particle" in presence of a potential gradient. We suggest t...

John Stuart Mill is one of the most influential philosophers and political economists within the history of economic thought. Besides being an avant-garde utilitarian, his Principles of Political Economy dominated the political economy domain for more than a quarter of a century. As a utilitarian, he believed that a concept of justice which is grounded in utility is the most

The two-dimensional relativistic configurational $\vec r$-space is proposed and the exactly solvable finite-difference model of the harmonic oscillator in this space is constructed. The wave functions of the stationary states and the corresponding energy spectrum are found for the model under consideration. It is shown that, they have correct non-relativistic limit. Explicit form of the plane momentum operator is determined.

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic \emph{partial} differential equations. The dynamical behavior is shown to be described by a stochastic \emph{ordinary} differential equation on an invariant manifold, under suitable conditions. The change of dynamical structures for the stochastic partial differential equations is thus obtained by investigating the stochastic ordinary differential equation. The random cone invariant property is used in the approach. Moreover, the invariant manifold reduction principle is applied to detect bifurcation phenomena and stationary states in stochastic parabolic and hyperbolic partial differential equations.

The stationary states of the half-line Coulomb potential are described by quantum-mechanical wavefunctions which are controlled by the Laguerre polynomials $L_n^{(1)}(x$). Here we first calculate the $q$th-order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function $F_A^{(2q+1)}(\frac{1}{q},...,\frac{1}{q},1)$ by use

We give a combinatorial derivation and interpretation of the algebra associated with the stationary distribution of the partially asymmetric exclusion process. Our derivation works by constructing a larger Markov chain on a larger set of generalised configurations. A bijection on this new set of configurations allows us to find the stationary distribution of the new chain. We then show that a subset of the generalised configurations is equivalent to the original chain and that the stationary distribution on this subset is simply related to that of the original chain. This derivation allows us to find expressions for the normalisation using both recurrences and path models. These results exhibit classical combinatorial numbers such as n!, 2n and the Catalan numbers.

We study thermal radiation outside equilibrium. The situation considered consists of two bodies emitting photons at two different temperatures. We show that the system evolves to a stationary state characterized by an energy current which satisfies a Stefan-Boltzmann-like law expressing it as the difference of the temperatures to the fourth power of the emitters . The results obtained show how the classical laws governing the thermal radiation at equlibrium can be generalized away from equilibrium situations.

The classical approach in epidemics modelling accounts for the deterministic aspects of the epidemic spread without considering the variability in the transmission of the infectious diseases. Then we propose in this paper, after improving these models by introducing a slow demographic component, to define demographic and epidemic random variables and parameters i n order to take into account fluctuations in

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the ‘linear forcing’, which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary ...

... Lena Ringstad Olsen a , Corresponding Author Contact Information , E-mail The Corresponding Author , Probal Chaudhuri b , E-mail The Corresponding Author and Fred Godtliebsen a , E-mail The Corresponding Author. a Department of Statistics, University of Tromsø, Norway. ...

This paper describes an electronic circuit for periodic interruption of current to a cell with simultaneous observation of closed‐circuit and open‐circuit electrode potentials. The open‐circuit potential may be observed at interruption times ranging from 2.0 μs to 2.0s or longer. The duty cycle of the cell may be adjusted between 40 and 99.93%. Application of the circuit to observe relaxation of polarization is demonstrated with simple electrical test circuits, with commercial dry cells, and with a mass‐transfer controlled rotating disk electrode. The latter example shows that interruption can provide not only resistance measurements but also estimates of mass‐transfer parameters.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the hexapole of alternating phases, as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilit...

We design and study an OLG experimental economy where the government finances a fixed real deficit through seigniorage. The economy has continua of nonstationary rational expectations equilibria and two stationary rational expectations equilibria. We do not observe ...

It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical and high energy physics), the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, the passage to the so-called operators of physical values, etc. Orthodox quantum mechanics was constructed as a physical theory developed in the phase space of the mentioned notions. That is why the formalism of quantum mechanics is aimed only at detailed calculations of the stationary states of the energy of the quantum system studied and is not able to describe a real path running by the system in the real space; instead, the formalism gives an averaged probabilistic prediction. Thus, if we are able to develop quantum mechanics in the real space, an option to clarify all the difficulties associated with the above notions would appear. Such a theory of quantum mechanics developed in the real space in fact has recently been constructed by the author. The theory started from deeper first principles, namely, from the consideration of the notion of a 4D space-time. So, the notion of fundamental particle, the principles of the motion of a particle and other characteristics have been made clear. The theory, rather a submicroscopic one, is characterized by short-range action that automatically means the introduction of a new kind of carriers, i.e. carriers of the quantum mechanical force. The existence of the carriers called "inertons" (because they carry inert properties of matter) has indeed been verified in a number of experiments.

We present an analytical and a numerical study of a coherently driven fiber cavity when working in a low dispersion region. We show that it is necessary to take into account the fourth order dispersion term beta4 to capture the full dynamics of the system. The results are namely, a second frequency of instability is found at the primary threshold and the stationary state can be recovered for high enough pumping intensities.