Quantum theory of rotation angles: The problem of angle sum and angle difference

We reconsider the problem of the sum and difference of two angle variables in quantum mechanics. The spectra of the sum and difference operators have widths of , but angles differing by are indistinguishable. This means that the angle sum and difference probability distributions must be cast into a range. We obtain probability distributions for the angle sum and difference and relate this problem to the representation of nonbijective canonical transformations. Received: 6 December 1997 / Revised: 15 April 1998 / Accepted: 7 May 1998     

Spectral action and big desert

The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale Λ=1.1×10¹⁷ GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value obtained from noncommutative geometry for the standard model with three generations only.     

Geometry and Physics Today

“Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “physical theories of a geometrical character.” Thence, “physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “differential” equations, are also being discussed.     

A random walker on a ratchet potential: effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.     

Two-phase heat transfer correlation for multi-component mixtures in the saturated flow-boiling regime

Investigations of two-phase heat transfer in the saturated flow-boiling region for multi-component mixtures has led to a proposed new correlation for the heat transfer coefficient where heat transfer of boiling is simply expressed in terms of the boiling number. This correlation was tested against the existing data on forced convective boiling heat transfer reported in the literature, giving satisfactory results; the correlation should, however, be tested further against wider data on convective heat transfer coefficients in multicomponent systems. The present lack of such data should be remedied.     

Electron scattering from an assembly of point scatterers in the presence of a quantizing magnetic field

Summary We have studied the scattering of electrons by a structured target in the presence of a quantizing static magnetic field, under the assumption that the presence of the field does not affect the behaviour of the massive target nuclei, but it influences only the motion of the incident electrons. In this case, the electron motion in the plane perpendicular to the magnetic field is confined within a typical distance given by the cyclotron radius ρ₀=(cℏ/|e|B)^1/2, that for particular values of the intensity of the magnetic field can be comparable with the distance between two scattering centres. The known field-free interference conditions are modified, depending both on the energy of the incident particle and on the intensity and the direction of the magnetic field. The general case of a three-dimensional scattering array has been derived in detail. Numerical results are given for the case of two scattering centres in perpendicular geometry. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Pairwise Correlations in a Multicomponent Anisotropic Liquid

We investigate a multicomponent anisotropic liquid system. The first spatial moment of the direct correlation function is taken into account to obtain asymptotic expressions for the pairwise correlation functions. In this approximation, we obtain the pairwise correlation functions that describe the system behavior not only in the critical-state neighborhood but also in the noncritical domain. We show that the critical parameters for the anisotropic system differ from those for the isotropic system.     

Thermodynamics and Hydrodynamics (Statistical Foundations): 4. Kinetic Processes in Multicomponent Systems

We use the BBGKY hierarchy and the mass, momentum, and intrinsic energy conservation laws, which are consequences of this hierarchy, to obtain the hydrodynamic equations for multicomponent systems and the diffusion equations. We formulate several restrictions on the thermodynamic equations for irreversible processes.     

Advantage of Quantum Theory over Nonclassical Models of Communication

Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However, a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in “space-like” and/or “time-like” paradigms. In this letter, a communication task involving three spatially separated parties is proposed where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. This task is called authentication with limited communication, the restrictions on communication being: i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several nonclassical theories although they might possess stronger “space-like” and/or “time-like” correlations. Surprisingly, quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other nonclassical strategies.