Phenomenological approach to non-linear Langevin equations

In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together with the macroscopic knowledge of the system is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time-reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models.Comment: LaTex file, 2 figures available upon request, to appear in Phys.Rev.

On Pairs of Difference Operators Satisfying: [P,Q] = Id

Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$ to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of $[P,X]=Id$.Comment: 32 pages, plain Te

NN Interaction JISP16: Current Status and Prospect

We discuss realistic nonlocal NN interactions of a new type - J-matrix Inverse Scattering Potential (JISP). In an ab exitu approach, these interactions are fitted to not only two-nucleon data (NN scattering data and deuteron properties) but also to the properties of light nuclei without referring to three-nucleon forces. We discuss recent progress with the ab initio No-core Shell Model (NCSM) approach and respective progress in developing ab exitu JISP-type NN-interactions together with plans of their forthcoming improvements.Comment: 9 pages, 3 figures, to be published in Proceedings of Few-body 19 conferenc

Simultaneous Brownian Motion of N Particles in a Temperature Gradient

A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system whith internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of non-equilibrium thermodynamics, one then easily obtains the Fokker-Planck equation for simultaneous Brownian motion of N particles in a temperature gradient. This equation accounts for couplings in the motion as a result of hydrodynamic interactions between particles.Comment: 9 pages, RevTe

Charging a Double Kerr Solution in 5D Einstein--Maxwell--Kalb--Ramond Theory

We consider the low-energy effective action of the 5D Einstein-Maxwell-Kalb-Ramond theory. After compactifying this truncated model on a two-torus and switching off the U(1) vector fields of this theory, we recall a formulation of the resulting three-dimensional action as a double Ernst system coupled to gravity. Further, by applying the so-called normalized Harrison transformation on a generic solution of this double Ernst system we recover the U(1) vector field sector of the theory. Afterward, we compute the field content of the generated charged configuration for the special case when the starting Ernst potentials correspond to a pair of interacting Kerr black holes, obtaining in this way an exact field configuration of the 5D Einstein-Maxwell-Kalb-Ramond theory endowed with effective Coulomb and dipole terms with momenta. Some physical properties of this object are analyzed as well as the effect of the normalized Harrison transformation on the double Kerr seed solution.Comment: 15 pages in latex, revised versio