Interpreting Quantum Interference Using a Berry’s Phase-like Quantity

We show that quantum interference can be interpreted in terms of a phase invariant quantity, not unlike the Berry’s phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides another useful way of assigning meaning to quantum probabilities and quasi-probabilities.     

Comparison between Weber’s electrodynamics and classical electrodynamics

We present the main aspects of Weber’s electrodynamics and of Maxwell’s equations. We discuss Maxwell’s point of view related to Weber’s electrodynamics. We compare Weber’s force with Lorentz’s force. We analyse the relation between Weber’s law and Maxwell’s equations. Finally, we discuss some experiments performed and proposed with which we can distinguish Weber’s force from Lorentz’s one.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

Berry phases in the three-level atoms driven by quantized light fields

A theoretical analysis of Berry’s phases is given for the three-level atoms interacting with external one-mode and two-mode quantized light fields. Three main results are obtained: (i) There is a Berry phase which vanishes in the classical limit or this Berry phase is completely induced by the field quantization; (ii) Berry’s phases for the one-mode field and the two-mode field can be equal so long as the photon numbers of the two-mode field are properly chosen; (iii) In the two-mode case, Berry phases of the atom interacting with one mode is affected by the other mode even if the photon number of the other mode is zero.      

Proof of absence of spooky action at a distance in quantum correlations

I prove that there is no spooky action at a distance and nonlocal state-reduction during measurements on quantum entangled systems. The prediction of quantum theory as well as experimental results are in conflict with the concept of nonlocal state-reduction, as conclusively shown here under very general assumptions. This has far-reaching implications in the interpretation of quantum mechanics in general, and demands a radical change in its present interpretation of measurements on entangled multiparticle systems. Motivated by these results we re-examine Bell’s theorem for correlations of entangled systems and find that the correlation function used by Bell fails to incorporate phase correlations at source. It is the use of such an unphysical correlation function, and not failure of locality, that leads to the Bell’s inequalities.     

Dixon’s extended bodies and weak gravitational waves

General relativity considers Dixon’s theory as the standard theory to deal with the motion of extended bodies in a given gravitational background. We discuss here the features of the “reaction” of an extended body to the passage of a weak gravitational wave. We find that the body acquires a dipolar moment induced by its quadrupole structure. Furthermore, we derive the “world function” for the weak field limit of a gravitational wave background and use it to estimate the deviation between geodesics and the world lines of structured bodies. Measuring such deviations, due to the existence of cumulative effects, should be favorite with respect to measuring the amplitude of the gravitational wave itself.     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.     

Anisotropic Lavine’s Formula and Symmetrised Time Delay in Scattering Theory

We consider, in quantum scattering theory, symmetrised time delay defined in terms of sojourn times in arbitrary spatial regions symmetric with respect to the origin. For potentials decaying more rapidly than |x|^− 4 at infinity, we show the existence of symmetrised time delay, and prove that it satisfies an anisotropic version of Lavine’s formula. The importance of an anisotropic dilations-type operator is revealed in our study.      

Generalized Jarzynski’s Equality of Inhomogeneous Multidimensional Diffusion Processes

Applying the well-known Feynman-Kac formula of inhomogeneous case, an interesting and rigorous mathematical proof of generalized Jarzynski’s equality of inhomogeneous multidimensional diffusion processes is presented, followed by an extension of the second law of thermodynamics. Then, we explain its physical meaning and applications, extending Hummer and Szabo’s work (Proc. Natl. Acad. Sci. USA 98(7):3658–3661, [2001]) and Hatano-Sasa equality of steady state thermodynamics (Phys. Rev. Lett. 86:3463–3466, [2001]) to the general multidimensional case.     

Saha’s ionization equation for highZ elements

Saha’s ionization equation has been solved for highZ elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bohr’s formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha’s equation solutions has been checked by comparing theP _T andE _T computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV.     

Local Causality and Completeness: Bell <Emphasis Type="Italic">vs.</Emphasis> Jarrett

J.S. Bell believed that his famous theorem entailed a deep and troubling conflict between the empirically verified predictions of quantum theory and the notion of local causality that is motivated by relativity theory. Yet many physicists continue to accept, usually on the reports of textbook writers and other commentators, that Bell’s own view was wrong, and that, in fact, the theorem only brings out a conflict with determinism or the hidden-variables program or realism or some other such principle that (unlike local causality), allegedly, nobody should have believed anyway. Moreover, typically such beliefs arise without the person in question even being aware that the view they are accepting differs so radically from Bell’s own. Here we try to shed some light on the situation by focusing on the concept of local causality that is the heart of Bell’s theorem, and, in particular, by contrasting Bell’s own understanding with the analysis of Jon Jarrett which has been the most influential source, in recent decades, for the kinds of claims mentioned previously. We point out a crucial difference between Jarrett’s and Bell’s own understanding of Bell’s formulation of local causality, which turns out to be the basis for the erroneous claim, made by Jarrett and many others, that Bell misunderstood the implications of his own theorem.     

Focusing of an electromagnetic plane wave into a uniaxial crystal by a Wood lens

High frequency fields, refracted by a geometry containing a Wood lens placed at a certain distance from a planar uniaxial interface, are derived by using Maslov’s method. The geometrical optics approximation generally valid for high frequency fields fails in the vicinity of a caustic. Maslov’s method is a systematic procedure for predicting the field in the caustic region, combining the simplicity of the ray and the generality of the transform method. Numerical computations are made for the field pattern around the caustic by using Maslov’s method. The results are found to be in good agreement with those obtained using Kirchhoff’s approximation.      

Schwinger’s action principle,supersymmetry and path integrals

We use Schwinger’s action principle in quantum mechanics to obtain the quantisation from Lagrangian for the fermionic variables, as well as when it contains auxiliary coordinates. We illustrate this with a supersymmetric Lagrangian which naturally includes auxiliary variables. We further show that the action principle also leads to Feynman’s path integral quantisation, which is aesthetically pleasing.     

An Isserlis’ Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density

This work derives a version of Isserlis’ theorem for the specific case of four mixed-Gaussian random variables. The theorem is then used to derive an expression for the auto-bispectral density for quadratically nonlinear systems driven with mixed-Gaussian iid noise. C.C. Olson is a NRC Postdoctoral Research Associate.     

A Wegner-type Estimate for Correlated Potentials

We propose a fairly simple and natural extension of Stollmann’s lemma to correlated random variables. This extension allows to obtain Wegner-type estimates even in various problems of spectral analysis of random operators where the original Wegner’s lemma is inapplicable, e.g., for correlated random potentials with singular marginal distributions and for multi-particle Hamiltonians.      

Violation of Bell’s inequality in neutral kaons system

We show by general considerations that it is not possible to test violation of the existing versions of Bell’s inequality in entangled neutral kaons system using experimentally accessible thin regenerators. We point out the loophole in the recent argument (A Bramon and M Nowakowski, Phys. Rev. Lett. 83, 1 (1999)) that claimed such a test to be possible.     

Brane World Corrections to Newton’s Law

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After giving a brief general exposition, we review in more detail the predicted corrections to Newton’s law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein–Gauss–Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton’s law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.     

Mach’s principle and the notion of time

The role of time coordinate in the realization of March’s principle is highlighted. It is shown that Mach’s principle is linked to the definition of a ‘particle’. These results suggest a deep connection between quantum gravity and Mach’s principle.     

Thermal conduction in a homogeneous two-phase system

Assuming a regular geometry of dispersed phase (λ ₂) an integrated theory for the effective thermal conductivityλ _e of all kind of two-phase materials (including loose materials) is developed. The flux modification is carried out by considering the effective neighbouring interactions in the solution of Poisson’s equation. A comparison of calculatedλ _e values with the reported experimental results over a wide range of two-phase materials shows a good agreement.     

Covariant anomaly and Hawking radiation from the modified black hole in the rainbow gravity theory

Recently, Banerjee and Kulkarni (R. Banerjee, S. Kulkarni, arXiv: 0707. 2449 [hep-th]) suggested that it is conceptually clean and economical to use only the covariant anomaly to derive Hawking radiation from a black hole. Based upon this simplified formalism, we apply the covariant anomaly cancellation method to investigate Hawking radiation from a modified Schwarzschild black hole in the theory of rainbow gravity. Hawking temperature of the gravity’s rainbow black hole is derived from the energy-momentum flux by requiring it to cancel the covariant gravitational anomaly at the horizon. We stress that this temperature is exactly the same as that calculated by the method of cancelling the consistent anomaly.