de Broglie’s wave hypothesis from Fisher information

Seeking the unknown dynamics obeyed by a particle gives rise to the de Broglie wave representation, without the need for physical assumptions specific to quantum mechanics. The only required physical assumption is conservation of momentum μ. The particle, of mass m, moves through free space from an unknown source-plane position a to an unknown coordinate x in an aperture plane of unknown probability density p_X(x), and then to an output plane of observed position y=a+z. There is no prior knowledge of the probability laws or , with the particle momentum at the source. It is desired to (i) optimally estimate a, in the sense of a maximum likelihood (ML) estimate. The estimate is further optimized, by minimizing its error through (ii) maximizing the Fisher information about a that is received at y. Forming the ML estimate requires (iii) estimation of the likelihood law p_Z(z), which (iv) must obey positivity. The relation p_Z(z)≡|u(z)|²≥0 satisfies this. The same u(z) conveniently defines the Fisher channel capacity, a concept central to the principle of Extreme physical information (EPI). Its output u(z) achieves aims (i)-(iv). The output is parametrized by a free parameter K. For a choice K=0, the result is u(z)=δ(z), indicating classical motion. Or, for a finite, empirical choice K=? (Planck’s constant), u(z) obeys the familiar de Broglie representation as the Fourier transform of the particle’s probability amplitude function P(μ) on momentum μ. For a definite momentum μ,u(z) becomes a sinusoid of wavelength λ=h/μ, the de Broglie result.     

A simple mathematical model for anomalous diffusion via Fisher's information theory

Starting with the relative entropy based on a previously proposed entropy function , we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher information measure with respect to the new function and obtain a differential operator that reduces to a space coordinate second derivative in the q→1 limit. We then propose a simple differential equation for anomalous diffusion and show that its solutions are a generalization of the functions in the Barenblatt-Pattle solution. We find that the mean squared displacement, up to a q-dependent constant, has a time dependence according to 〈x²〉∼K1/qt1/q, where the parameter q takes values (superdiffusion) and (subdiffusion), ∀n?1.     

The partition function zeros of the anisotropic Ising model with multisite interactions on a zigzag ladder

It is shown that the spin- anisotropic Ising model with multisite interactions on a zigzag ladder may be mapped into the one dimensional spin- Axial-Next-Nearest-Neighbor Ising (ANNNI) model with multisite interactions. The partition function zeros of the ANNNI model with multisite interactions are investigated. A comprehensive analysis of the partition function zeros of the ANNNI model with and without three-site interactions on a zigzag ladder is done using the transfer matrix method. Analytical equations for the distribution of the partition function zeros in the complex magnetic field (Yang-Lee zeros) and temperature (Fisher zeros) planes are derived. The Yang-Lee and Fisher zeros distributions are studied numerically for a variety of values of the model parameters. The densities of the Yang-Lee and Fisher zeros are studied and the corresponding edge singularity exponents are calculated. It is shown that the introduction of three-site interaction terms in the ANNNI model leads to a simpler distribution of the partition function zeros. For example, the Yang-Lee zeros tend to a circular distribution when increasing by modulus the three-site interactions term coefficient. It is found that the Yang-Lee and Fisher edge singularity exponents are universal and equal to each other, .     

Isotopically invariant analysis of vibration-rotation transitions of HBr and its isotopologues

The vibration-rotation transition frequencies of HBr and its isotopologues reported in the literature were simultaneously analyzed in a least-squares fit to determine isotopically invariant molecular parameters U_kl and Born-Oppenheimer breakdown parameters Δ_kl. A total of 692 lines was fitted to Watson’s expression involving 25 adjustable parameters to a weighted unitless standard deviation of σ ≈ 0.91. From new data in the far-infrared region and those of improved precision in the mid-infrared and the near-infrared region, the breakdown parameters for the bromine atom were determined; the parameter for the harmonic frequency improved the fit and for the rotational constant enabled us to obtain the information on the adiabatic correction to the Born-Oppenheimer approximation.     

Computation of energy exchanges by combining information theory and a key thermodynamic relation: Physical applications

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation . Using standard axioms from information theory and the fact that the microscopic energy levels depend upon the external parameter A, we show that all usual results of statistical mechanics for reversible processes follow straightforwardly, without invoking the Maximum Entropy principle. For the simple system considered herein, two distinct forms of heat contributions appear naturally in the Clausius definition of entropy, . We give a special attention to the amount of heat , associated with an infinitesimal variation at fixed temperature, for which a “generalized heat capacity”, , may be defined. The usefulness of these results is illustrated by considering some simple thermodynamic cycles.     

Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures and , and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.     

KamLAND and T2K

KamLAND announced the first evidence of disappearance, followed by direct evidence for neutrino oscillation by observing distortion of the reactor energy spectrum, demonstrated almost two cycles of the periodic feature expected neutrino oscillation, and determined a precise value for the neutrino oscillation parameter and stringent constraints on θ₁₂. KamLAND also succeeded in detecting geoneutrinos produced by natural radioactivities in the Earth. This detection allows better estimation of the abundances and distributions of radioactive elements in the Earth and of the Earth’s overall heat generation. In the J-PARC neutrino facility, T2K is ready for operation. T2K is supposed to give critical information, which guides the future direction of the neutrino physics. The current status of T2K is shown.     

Diffuse volume transport in fluids

The diffuse flux of volume in a single-component liquid or gas, the subject of this paper, is a purely molecular quantity defined as the difference between the flux of volume and the convective flux of volume carried by the flowing mass, with the mass flux, the specific volume, and ρ the mass density. Elementary statistical-mechanical arguments are used to derive the linear constitutive equation , valid in near-equilibrium fluids from which body forces are absent. Here, D_S is the fluid’s self-diffusion coefficient. The present derivation is based on Einstein’s mesoscopic Brownian motion arguments, albeit applied here to volume- rather than particle-transport phenomena. In contrast to these mesoscale arguments, all prior derivations were based upon macroscale linear irreversible thermodynamic (LIT) arguments. D_S replaces the thermometric diffusivity α as the phenomenological coefficient appearing in earlier, ad hoc, derivations. The prior scheme based on α, which had been shown to accord with Burnett’s well-known gas-kinetic constitutive data for the heat flux and viscous stress, carries over intact to now show comparable accord of D_S with these same data, since for gases the dimensionless Lewis number Le=α/D_S is essentially unity. On the other hand for most liquids, where Le?1, use of D_S in place of α is shown to agree much better with existing experimental data for liquids. For the case of binary mixtures it is shown for the special case of isothermal, isobaric, force-free, Fick’s law-type molecular diffusion processes that , where D is the binary diffusion coefficient. In contrast with the preceding use in the single-component case of both mesoscopic and LIT models to obtain a constitutive equation for , the corresponding mixture result is derived here without use of any physical model whatsoever. Rather, the derivation effectively requires little more than the respective definitions of the diffuse volume- and Fickian mass-fluxes.     

Spin in the worldline path integral in 2 + 1 dimensions

We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x(τ), the spacetime paths. We then show that the functional integral automatically imposes the constraint , while there is a spin action, which agrees with the one one should expect for a spin- field.     

Relaxor behavior of K0.5La0.5Bi2Ta2O9 ceramics

Potassium lanthanum bismuth tantalate (K_0.5La_0.5Bi₂Ta₂O₉), a new relaxor ferroelectric was synthesized via the solid-state reaction route. X-ray structural studies along with Rietveld refinement confirmed it to be an n=2 member of the Aurivillius family of oxides and the refined lattice parameters are , and . The appearance of 1/2{h00} and 1/2{hk0} type superlattice reflections in the electron diffraction patterns reflected the presence of ordered polar regions. A broad dielectric peak associated with frequency dependent dielectric maximum temperature was observed. The value of the diffuseness parameter γ=1.93, obtained from the fit of a modified Curie-Weiss law established the relaxor nature of the title compound. The dielectric relaxation obeyed the Vogel-Fulcher relation wherein and . The relaxor behavior was attributed to the local polar ordering on A-sites.     

Boltzmann distribution and market temperature

We show that the minute fluctuations of S&P 500 and NASDAQ 100 indices show Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a market temperature for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility σ measured in is related to the temperature T by . Plots over the years 1990-2006 show that the arrival of the 2000 crash was preceded by an increase in market temperature, suggesting that this increase can be used as a warning signal for crashes.