Duality in Off-Shell Electromagnetism

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with Stueckelberg-Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five dimensional theory prevents a natural generalization of the Dirac monopole, since the theory is not symmetric under duality transformations. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles.Comment: 18 page

A numerical study of two-photon ionization of helium using the Pyprop framework

Few-photon induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold (54.4 eV), versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process, caused by the bandwidth of the applied field.Comment: 7 pages, 3 figure

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Discrete Symmetries of Off-Shell Electromagnetism

We discuss the discrete symmetries of the Stueckelberg-Schrodinger relativistic quantum theory and its associated 5D local gauge theory, a dynamical description of particle/antiparticle interactions, with monotonically increasing Poincare-invariant parameter. In this framework, worldlines are traced out through the parameterized evolution of spacetime events, advancing or retreating with respect to the laboratory clock, with negative energy trajectories appearing as antiparticles when the observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections, unlike the standard Maxwell fields, and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories -- charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock.Comment: 26 page

Analysis of chronic rejection and obliterative arteriopathy: Possible contributions of donor antigen-presenting cells and lymphatic disruption

Sequential analysis of changes that lead to chronic rejection was undertaken in an animal model of chronic rejection and obliterative arteriopathy. Brown Norway rats are pretreated with a Lewis bone marrow infusion or a Lewis orthotopic liver allograft and a short course of immunosuppression. They are challenged 100 days later with a Lewis heterotopic heart graft without immunosuppression. The heart grafts in both groups undergo a transient acute rejection, but all rats are operationally tolerant; the heart grafts are accepted and remain beating for more than 100 days. Early arterial remodeling, marked by arterial bromodeoxyuridine incorporation, occurred in both groups between 5 and 30 days during the transient acute rejection. It coincided with the presence of interstitial (but not arterial intimal) inflammation and lymphatic disruption and resulted in mild intimal thickening. Significant arterial narrowing occurred only in the bone-marrow-pretreated rats between 60 and 100 days. It was associated with T lymphocyte and macrophage inflammation of the heart graft that accumulated in the endocardium and arterial intima and adventitia near draining lymphatics. There also was loss of passenger leukocytes from the heart graft, up-regulation of cytokine mRNA and major histocompatibility class II on the endothelium, and focal disruption of lymphatics. In contrast, long-surviving heart grafts from the Lewis orthotopic liver allograft pretreated group are near normal and freedom from chronic rejection in this group was associated with persistence of donor major histocompatibility class-II-positive hematolymphoid cells, including OX62+ donor dendritic cells. This study offers insights into two different aspects of chronic rejection: 1) possible mechanisms underlying the persistent immunological injury and 2) the association between immunological injury and the development of obliterative arteriopathy. Based on the findings, it is not unreasonable to raise the testable hypothesis that direct presentation of alloantigen by donor antigen-presenting cells is required for long-term, chronic-rejection-free allograft acceptance. In addition, chronic intermittent lymphatic disruption is implicated as a possible mechanism for the association between chronic interstitial allograft inflammation and the development of obliterative arteriopathy

Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes

We obtain phase diagrams of regular and irregular finite connectivity spin-glasses. Contact is firstly established between properties of the phase diagram and the performances of low density parity check codes (LDPC) within the Replica Symmetric (RS) ansatz. We then study the location of the dynamical and critical transition of these systems within the one step Replica Symmetry Breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that, away from the Nishimori line, in the low temperature region, the location of the dynamical transition line does change within the RSB theory, in comparison with the (RS) case. For LDPC decoding over the binary erasure channel we find, at zero temperature and rate R=1/4 an RS critical transition point located at p_c = 0.67 while the critical RSB transition point is located at p_c = 0.7450, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel (BSC) we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes within the RSB theory; the location of the dynamical transition point occurring at higher values of the channel noise. Possible practical implications to improve the performances of the state-of-the-art error correcting codes are discussed.Comment: 21 pages, 15 figure

Typical Performance of Gallager-type Error-Correcting Codes

The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.Comment: 6 pages, latex, 1 figur

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric channels is provided, based on which Gallager and MacKay-Neal codes are studied as examples of LDPC codes. It has been shown that the basic properties of these codes known for particular channels, including the property to potentially saturate Shannon's limit, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.Comment: 10 pages, 4 figures, RevTeX4; an error in reference correcte