The Solution of the Relativistic Schrodinger Equation for the δ′\delta'-Function Potential in 1-dimension Using Cutoff Regularization

We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultra-violet divergent, and the resultant expression cannot be renormalized in the usual sense. Therefore a general procedure has been developed to derive different physical properties of the system. The procedure is used first on the non-relativistic case for the purpose of clarification and comparisons. The results from the relativistic case show that this system behaves exactly like the delta function potential, which means it also shares the same features with quantum field theories, like being asymptotically free, and in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point.Comment: 32 pages, 5 figure

Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the δ\delta-Function Potential in 1-dimensional Relativistic Quantum Mechanics

We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics

Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity

The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius $R$ with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter $\gamma$, in general the accidental $SO(4)$ symmetry is lifted. However, for $R = (l+1)(l+2) a$ (where $a$ is the Bohr radius and $l$ is the orbital angular momentum) some degeneracy remains when $\gamma = \infty$ or $\gamma = \frac{2}{R}$. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of $R$ and $\gamma$.Comment: 27 pages, 7 figure

Majorana Fermions in a Box

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schr\"odinger equation that does not suffer from these problems.Comment: 23 pages, 2 figure

Reducing Interconnect Cost in NoC through Serialized Asynchronous Links

This work investigates the application of serialization as a means of reducing the number of wires in NoC combined with asynchronous links in order to simplify the clocking of the link. Throughput is reduced but savings in routing area and reduction in power could make this attractiv

Exploiting Aging Benefits for the Design of Reliable Drowsy Cache Memories

In this paper, we show how beneficial effects of aging on static power consumption can be exploited to design reliable drowsy cache memories adopting dynamic voltage scaling(DVS) to reduce static power. First, we develop an analytical model allowing designers to evaluate the long-term threshold voltage degradation induced by bias temperature instability (BTI)in a drowsy cache memory. Through HSPICE simulations, we demonstrate that, as drowsy memories age, static power reduction techniques based on DVS become more effective because of reduction in sub-threshold current due to BTI aging. We develop a simulation framework to evaluate trade-offs between static power and reliability, and a methodology to properly select the “drowsy” data retention voltage. We then propose different architectures of a drowsy cache memory allowing designers to meet different power and reliability constraints. The performed HSPICE simulations show a soft error rate and static noise margin improvement up to 20.8% and 22.7%, respectively, compared to standard aging unaware drowsy technique. This is achieved with a limited static power increase during the very early lifetime, and with static energy saving of up to 37% in 10 years of operation, at no or very limited hardware overhead

Determination of the Optimal Sterilization Regime of Canned Quail Meat with Hydrocoloids Application

The use of hydrocolloids in the modern meat industry is the one of prospective directions for improving functional and technological characteristics of meat and meat products, including poultry at long storage terms. A series of concrete requirements to functional-technological, physical-chemical and organoleptic parameters is offered for canned poultry in correspondence with minimal specifications for the quality of products of an animal origin.There is presented the study of the optimization of the process of meat products sterilization using meat of chicken-broilers, quails and hydrocolloids depending on physical-chemical and organoleptic properties. The parameters of quail meat use in recipes of canned poultry meat with hydrocolloids were considered. The influence of the sterilization process on characteristics of chicken-broiler and quail meat was established.There was revealed the essential difference in the influence on functional and technological parameters of canned quail meat using hydrocolloid mixtures comparing with canned chicken-broiler meat, manifested in changes of MKC (moisture keeping capacity), plasticity and salt content in jelly. At changing sterilization regimes, there takes place the change of physical and chemical characteristics of gels that correlates with organoleptic characteristics. For providing high quality parameters of canned poultry meat and industrial sterility, sterilization regimes for canned chicken-broiler meat must be realized for containers with the volume 500 with sterilization time no more than 90 minutes. For canned quail meat the sterilization process duration must be increased to 120 min at the temperature 115 ° С

Evaluation of home-mode ELISA system for thedetection of antibodies against Escherichia coli O157:H7 using purified lipopolysaccharide

An enzyme linked immunosorbent assay (ELISA) for the detection and quantitation of human immunoglobulin G (IgG) antibodies against vero- cytotoxine (VT) producing Escherichia coli serogroup O157:H7 was produced. E. coli O157: H7 lipopolysaccharide was extracted from locally isolated strains by using hot phenol- water method, followed by partial purification using gel filtration chromatography by sepharose- 4B. The purity of the lipopolysaccharide was checked by measuring the protein and nucleic acid content and then used as antigen. Four isolates of vero- cytotoxin producing E. coli serogroup O157:H7 was obtained by culturing 350 stool samples from children suffering from bloody diarrhea. These isolates were identified on bacteriological, serological and biochemical basis. Toxin production was confirmed on laboratory animals as well as by cytopathic effect on tissue culture. The possibility of using E. coli O157:H7 lipopolysaccharide in an enzyme- linked immunosorbent assay for the routine diagnostic testing of serum from patients for evidence of O157:H7 infection is discussed