Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

‘1001’ correlations in random wave fields

Abstract

Correlations in Gaussian speckle patterns are discussed for the intensity and the phase, as well as for the real and imaginary parts of the wavefunction. Application of the sampling theorem to the wave field is described, and five topologically mandated deterministic rules are enumerated that constrain many aspects of the field structure. A brief overview is given of wave-field correlation matrices containing several million coefficients.     

Linearity,non self-interacting spherically symmetric gravitational fields,the “sphereland equivalence principle” and Hamiltonian bubbles

For a large class of spherically symmetric gravitational fields, when matter is dropped in a spherically symmetric way, it is possible to decompose this matter into free-falling shells such that their associated 2+1-dimensional (i.e. surface) energy-momentum tensor is conserved, that is, is not affected by the environment. Further non-interacting features can be found for this class of gravitational fields as can be seen by the fact that Einstein's equations are linear in this case. Matter of a shell falling in one of these fields obeys energy momentum conservation from the point of view of the 2+1-dimensional world-sheet of the shell. This means that in the case of a test particle moving in one of these free falling sheets, the motion follows a 2+1-dimensional geodesic equation, or what is the same, its dynamics is governed by a sphereland equivalence principle. As a result of this, a shell falling in such a gravitational field can be treated as a closed system which can be described by a 2+1-dimensionally defined Hamiltonian.     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

BRS ‘Symmetry’, prehistory and history

Prehistory ?C Starting from ??t Hooft??s (1971) we have a short look at Taylor??s and Slavnov??s works (1971?C72) and at the lectures given by Rouet and Stora in Lausanne (1973) which determine the transition from pre-history to history. History ?C We give a brief account of the main analyses and results of the BRS collaboration concerning the renormalized gauge theories, in particular the method of the regularization-independent, algebraic renormalization, the algebraic proof of S-matrix unitarity and that of gauge choice independence of the renormalized physics. We conclude this report with a suggestion to the crucial question: what could remain of BRS invariance beyond perturbation theory.     

‘‘Extrinsic’’ and ‘‘Intrinsic’’ Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures

We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a meaningful (intrinsic) and a not meaningful (extrinsic) part. We are able to give an asymptotically tight separation of this form, with the intrinsic data quantified by the Holevo mutual information of a certain state ensemble associated to the POVM and the source, in a model that can be viewed as the asymptotic version of the convex decomposition of POVMs into extremal ones. This result is applied to a similar separation therorem for quantum instruments and quantum operations, in their Kraus form. Finally we comment on links to related subjects: we stress the difference between data and information (in particular by pointing out that information typically is strictly less than data), derive the Holevo bound from our main result, and look at its classical case: we show that this includes the solution to the problem of extrinsic/intrinsic data separation with a known source, then compare with the well–known notion of sufficient statistics. The result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics. An appendix collects several estimates for mixed state fidelity and trace norm distance, that seem to be new, in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity.     

Spectral anomalies of polychromatic, spatially coherent light diffracted by an annular aperture in the far field

In recent years, a great deal of attention has been paid to the structure of wave fields in the neighborhood of points where the field amplitude has zero value[1-3]. At such points the phase of fields is singular. It has been known that in the neighborhood of the singular points, the wave fields exhibit a rather complex structure, for example, dislocations and optical vortices. Studies of phenomena associated with phase singularities have gradually devel- oped into a new branch of physical opt…     

Contextuality and Nonlocality in ‘No Signaling’ Theories

We define a family of ‘no signaling’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no signaling’ polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in ‘no signaling’ theories.     

Mixing and its rate in ‘soft’ and ‘hard’ billiards motivated by the Lorentz process

Billiards corresponding to planar periodic Lorentz processes are considered in the usual (hard) sense and in the case when the hard core potential of the scatterers is replaced by some other circularly symmetric potential. A review on certain important aspects of the history of the subject is given and some new results on exponential decay of correlations are formulated. Both the results from the literature and those of our own mentioned are mathematically rigorous, nevertheless, proofs are only briefly sketched. For further details, see the preprint [Correlation decay in certain soft billiards, Commun. Math. Phys., in press].     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

Simulating Suppression Effects in Pulsed ENDOR, and the ‘Hole in the Middle’ of Mims and Davies ENDOR Spectra

All pulsed electron-nuclear double resonance (ENDOR) techniques, and in particular the Mims and Davies sequences, suffer from detectability biases (‘blindspots’) that are directly correlated to the size of the hyperfine interactions of coupled nuclei. Our efforts at ENDOR ‘crystallography’ and ‘mechanism determination’ with these techniques have led our group to refine our simulations of pulsed ENDOR spectra to take into account these biases, and we here describe the process and illustrate it with several examples. We first focus on an issue whose major significance is not widely appreciated, the ‘hole in the middle’ of pulsed ENDOR spectra caused by the n = 0 suppression hole in Mims ENDOR and by the analogous A → 0 suppression in Davies ENDOR for I = ½ and for ²H (I = 1). We then discuss the general treatment of suppression effects for I = 1, illustrating it with a treatment of Mims suppression for ¹⁴N.     

Proton spin relaxation and self-diffusion in some ‘isotropic’ nematogens

Angular distributions of reactive scattering arising from a long-lived collision complex dissociating via a transition state that approximates to a linear rotator are predicted for H atom displacement occurring over a distribution of bending angles β with respect to the rotator axis. A conical angular distribution may be generated when only a narrow range of bending angles contributes to the reactive scattering. However, the angular distribution may take on quite different character as the distribution of bending angles becomes broader. Thus, an isotropic angular distribution is generated by a bending angle distribution which follows the spherical polar weighting P(β) ∝ sin β. Forward and backward scattering is generated by bending angle distributions favouring less strongly bent displacement, while sideways scattering is generated by a bending angle distribution favouring more strongly bent displacement. The experimental angular distribution for OH + CO reactive scattering which shows mild forward and backward peaking, corresponds to a range of bending angles for H atom displacement from the H-OCO transition state which is broadened about the nominal preferred direction β = 45° but avoids strongly bent directions with β ≈ 90°.     

Soft mode dispersion and ‘waterfall’ phenomenon in relaxors revisited

Results of recent inelastic neutron scattering studies of lead-based relaxor ferroelectrics by Gvasaliya et al. [J. Phys.: Condens. Matter 17, 4343 (2005); J. Phys.: Condens. Matter 19, 016219 (2007)] have put in question the existence of the “waterfall” anomaly–an apparent vertical dispersion segment joining the TA and TO branches–observed earlier in low-energy [ξ00] phonon dispersion curves of these materials. In the present article, we review the results of earlier experiments and model calculations together with the outcome of our recent measurements on PMN using the same instrumental set-up as Gvasaliya et al. to conclude that the “waterfall” feature is not an experimental artefact. We also give some hints on a possible explanation of the results of Gvasaliya et al., by exploring the fact that the reported dispersion of the underdamped transverse optic branch follows the longitudinal acoustic (LA) branch dispersion surprisingly closely.     

Recurrence spectra of non—hydrogen Rydberg atoms in paralled electric and magnetic fields

We present a new method for computing the recurrence spectra of n≈40, m=0 lithium Rydberg atoms in strong parallel external electric and magnetic fields. This method is based on an extended closed-orbit theory allowing the computation of the scattering of the electron by the ionic core. We pay particular attention to the scaling properties, which are extremely important for understanding the correspondence between classical and quantum mechanics. The spectra with a constant scaled electric field \tilde F=0.01 and a scaled energy ε=-0.03 are recorded and compared with those of hydrogen obtained by the standard closed-orbit theory. The result shows that the additional strong resonance structures can be interpreted in terms of the core-scattered classical closed orbits.     

Resolving Fermi, PAMELA and ATIC anomalies in split supersymmetry without R-parity

A long-lived decaying dark matter as a resolution to Fermi, PAMELA and ATIC anomalies is investigated in the framework of split supersymmetry (SUSY) without R-parity, where the neutralino is regarded as the dark matter and the extreme fine-tuned couplings for the long-lived neutralino are naturally evaded in the usual approach. The energy spectra of electron and positron are from not only the direct neutralino decays denoted by χ→e ⁺ e ^? ν, but also the decaying chains such as $\chi\to e^{+}\nu\mu(\to \nu_{\mu}e\bar{\nu}_{e})$ . We find that with a proper lifetime of the neutralino, slepton-mediated effects could explain the ATIC and PAMELA data well, but an inconsistence occurs to the Fermi and PAMELA data without considering the ATIC one. However, by a suitable combination of χ→e ⁺ e ^? ν and $\chi\to e^{+}\nu \mu(\to\nu_{\mu}e\bar{\nu}_{e})$ , the sneutrino-mediated effects could simultaneously account for the Fermi and PAMELA data.