Transport as a consequence of state-dependent diffusion

Overdamped particles subject to a drift in a force field with sinusoidal space dependence and also a sinusoidally modulated space-dependent diffusion, with the same period as the drift, experience a net driving force. The resulting current depends on the amplitude of the modulation of the diffusion and is a periodic function of the phase difference between the sinusoidal drift and the sinusoidal modulation of the diffusion. For small modulation amplitudes a particle subject to state-dependent noise behaves the same way as a particle subject to thermal noise but with a drift which, in addition to the sinusoidal term, contains a net force term [M. Büttiker,Z. Phys. B 68:161 (1987)]. A specific example of this behavior [N. G. van Kampen,IBM J. Res. Dev. 32:107 (1988); R. Landauer,J. Stat. Phys. 53:233 (1988).] is the motion of overdamped particles in a ring subject to a nonuniform temperature field. When the drift and the temperature, which are periodic with a period equal to the ring circumference, are not in phase a noise-induced circulating current results.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Analog simulation of a simple system with state-dependent diffusion

We have constructed an electronic simulator of a simple bistable system driven by noise, whose intensity is determined by the instantaneous value of the coordinate. We observe that the most probable state of the system can be reversed by altering the noise intensity only in the neighborhood of the barrier, an effect pointed out by Landauer many years ago in the context of discussions on entropy-related stability criteria for nonequilibrium systems. We compare detailed measurements on the system with the recent white noise calculations of Landauer and van Kampen. The system also has interesting possibilities for tests of contemporary colored noise theory which we illustrate with an example.     

The nonlinear Fokker-Planck equation with state-dependent diffusion - a nonextensive maximum entropy approach

Nonlinear Fokker-Planck equations (e.g., the diffusion equation for porous medium) are important candidates for describing anomalous diffusion in a variety of systems. In this paper we introduce such nonlinear Fokker-Planck equations with general state-dependent diffusion, thus significantly generalizing the case of constant diffusion which has been discussed previously. An approximate maximum entropy (MaxEnt) approach based on the Tsallis nonextensive entropy is developed for the study of these equations. The MaxEnt solutions are shown to preserve the functional relation between the time derivative of the entropy and the time dependent solution. In some particular important cases of diffusion with power-law multiplicative noise, our MaxEnt scheme provides exact time dependent solutions. We also prove that the stationary solutions of the nonlinear Fokker-Planck equation with diffusion of the (generalized) Stratonovich type exhibit the Tsallis MaxEnt form. Received 26 February 1999     

Intermediate statistics as a consequence of deformed algebra

We present a formulation of deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange symmetry leads to the introduction of the basic number and it is then established that this in turn leads to the deformed algebra of oscillators. We obtain the mean occupation number describing the particles obeying intermediate statistics which thus establishes the interpolating statistics and describe boson-like and fermion-like particles obeying intermediate statistics. We also obtain an expression for the mean occupation number in terms of an infinite continued fraction, thus clarifying successive approximations.     

d-Symmetry superconductivity as a consequence of valence-bond type correlations

It is shown that d _x ²−y ² symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T _c are of the order of 2Δ≃0.1t and 2Δ/kT _c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 350–355 (10 March 1998)     

Thinking Transport as a Twist

The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the ‘energy’ cost of twisting the boundaries) of a quantum-like system. The nature of the coupling to the reservoirs determines the details of the mechanical coupling of the torque at the ends.     

Optical magnus effect as a consequence of Berry phase anisotropy

Presented in this work is a modified geometric optics of smoothly inhomogeneous isotropic medium, which takes into account weak anisotropy introduced by inhomogeneity. Pointed out is the common nature of two fundamental phenomena: Berry’s geometrical phase and the optical Magnus effect, that is, propagation of rays of right and left circular polarization along different trajectories. Shown is that the former phenomenon can be explained by the difference in phase velocity of waves of right-hand and left-hand polarizations, while the latter one is the result of the difference in their group velocity. This work demonstrates that the optical Magnus effect is quite a topological effect that exclusively depends on the geometry of the system’s contour in the momentum space. We predict the effect of the splitting of a ray of mixed polarization into two circularly polarized rays and propose a scheme for the experimental observation of this phenomenon.     

Entropy as a measure of diffusion

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.     

Fractional quantization of Hall resistance as a consequence of mesoscopic feedback

A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model involves the magnetic Schrödinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles (cf. [9, 10]). The model is found to imply exact integer and fractional quantitzation of the Hall conductance. In fact, Hall resistance is found to be R _H = (h/e ²)(M/N) at the filling factor value N/M. The assumed geometry of the Hall plate is rectangular. Special properties of the magnetic Schrödinger equation with the mesoscopic feedback loop allow us to demonstrate quantization of Hall resistance as a direct consequence of charge and flux quantization. I believe results presented here shed light at the overall status of the MeM in quantum physics, confirming its validity.     

Structural asymmetry of Kramers clusters as a consequence of time-reversal symmetry

Asymmetry of Kramers magnetic clusters is shown to be dictated by the structure of magnetic four-color point groups. Factorization of the time-reversal operator is performed for Kramers systems.     

Conservation of spin current as a consequence of a 2D Fermi surface

The possible existence of a previously unseen conservation in the theory of Fermi liquids is proposed for a two-dimensional geometry. If the ground state can be described by a smooth curve in momentum space then one expects spin current to be conserved, as it is not the case in three dimensions. Some immediate consequences that can be checked experimentally are pointed out.     

Transport mechanisms controlling soot production inside a non-buoyant laminar diffusion flame

This study integrates new and existing numerical modeling and experimental observations to provide a consistent explanation to observations pertaining flame length and soot volume fractions for laminar diffusion flames. Integration has been attempted by means of scaling analysis. Emphasis has been given to boundary layer flames. For the experiments, ethylene is injected through a flat porous burner into an oxidizer flowing parallel to the burner surface. The oxidizer is a mixture of oxygen and nitrogen, flowing at various velocities. All experiments were conducted in microgravity to minimize the role of buoyancy in distorting the aerodynamics of the flames. A previous numerical study emphasizing fuel transport was extended to include the oxidizer flow. Fictitious tracer particles were used to establish the conditions in which fuel and oxidizer interact. This allowed establishing regions of soot formation and oxidation as well as relevant characteristic length and time scales. Adequate scaling parameters then allow to establish explanations that are consistent for different burner configurations as well as “open-tip” and “closed-tip” flames.     

Particle creation by a black hole as a consequence of the casimir effect

The accelerated-mirror results are applied to a black hole. As a consequence the hole produces black-body radiation. Its temperature exactly coincides with Hawking's result. An important difference between the energy-momentum tensors of scalar and electromagnetic fields near the horizon is discovered.     

Particle creation by a black hole as a consequence of the Casimir effect

It is shown that the effect of particle creation by a black hole is a consequence of the Casimir effect for a spherical shell. The temperature of black-body radiation coincides with that obtained by Hawking.     

Particle creation by a black hole as a consequence of the Casimir effect

Particle creation by a black hole is investigated in terms of temperature corrections to the Casimir effect. The reduction of the Hawking effect to more familiar effects observed in the laboratory enables us to reveal the mechanism of particle creation. The blackbody nature of the Hawking radiation is due to the interaction of virtual particles with the surface of a cavity formed by the Schwarzschild gravitational field potential barrier. These particles are squeezed out by the contraction of the potential barrier and appear to an observer atJ ⁺ as the real blackbody ones.     

The maximum entropy principle as a consequence of the principle of Laplace

The maximum entropy principle states that the probability distribution which best represents our information is the one which maximizes the entropy with the given evidence as constraints. We prove that this principle is implied from the Laplace principle of equiprobabilities applied to the setS of allN-term sequences of results which are compatible with the given evidence. We generalize to the information gain method of Kullback.     

No-flipping as a consequence of no-signalling and non-increase of entanglement under LOCC

Non-existence of universal flipper for arbitrary quantum states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of qubits that can be flipped by a single machine is a great circle of the Bloch-sphere. In this Letter, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of “non-increase of entanglement under LOCC”. Interestingly, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle.     

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.