Reaching the continuum limit in lattice gauge theory - without a computer

The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with respect to a one-plaquette mean field state the results demonstrate clear scaling of M at and beyond the transition from strong to weak coupling. The scaling parameters determined agree well with the range of numerical determinations available.Comment: 4 pages, 2 figure

Adiabatic & non-adiabatic perturbation theory for coherence vector description of neutrino oscillations

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and non-adiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g. matter) potentials. Neglecting effects of ensemble decoherence for now we study the evolution of a neutrino ensemble governed by the associated Quantum Kinetic Equations, which apply to systems with finite temperature. The Quantum Kinetic Equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g. the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g. an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.Comment: 14 page

Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

Neutrino-antineutrino oscillations as a possible solution for the LSND and MiniBooNE anomalies?

We investigate resonance structures in CPT and Lorentz symmetry violating neutrino-antineutrino oscillations in a two generation framework. We work with four non-zero CPT-violating parameters that allow for resonant enhancements in neutrino-antineutrino oscillation phenomena in vacuo which are suitably described in terms of charge conjugation eigenstates of the system. We study the relation between the flavor, charge conjugation and mass eigenbasis of neutrino-antineutrino oscillations and examine the interplay between the available CPT-violating parameter space and possible resonance structures. Eventually we remark on the consequences of such scenarios for neutrino oscillation experiments, namely possible solutions for the LSND and MiniBooNE anomalies.Comment: 14 pages, 3 figure

Explaining LSND and MiniBooNE using altered neutrino dispersion relations

We investigate the possibility to explain the MiniBooNE anomaly by CPT and Lorentz symmetry violating neutrino-antineutrino oscillations in a two generation framework. We work with four non-zero CPT-violating parameters that allow for resonant enhancements in neutrino-antineutrino oscillation phenomena in vacuo which are suitably described in terms of charge conjugation eigenstates of the system. We study the relation between the flavor, charge conjugation and mass eigenbasis of neutrino-antineutrino oscillations and examine the interplay between the available CPT-violating parameter space and possible resonance structures.Comment: 3 pages, 1 figure, Proceedings for Erice 2009 Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physic

Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu