Search results for "Degenerate energy levels"

Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

2007

We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking…

A-superharmonic functions and supersolutions of degenerate elliptic equations

1988

Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data

2008

Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.

New descent rules for solving the linear semi-infinite programming problem

1994

The algorithm described in this paper approaches the optimal solution of a continuous semi-infinite linear programming problem through a sequence of basic feasible solutions. The descent rules that we present for the improvement step are quite different when one deals with non-degenerate or degenerate extreme points. For the non-degenerate case we use a simplex-type approach, and for the other case a search direction scheme is applied. Some numerical examples illustrating the method are given.

Hölder Continuity up to the Boundary of Minimizers for Some Integral Functionals with Degenerate Integrands

2007

We study qualitative properties of minimizers for a class of integral functionals, defined in a weighted space. In particular we obtain Hölder regularity up to the boundary for the minimizers of an integral functional of high order by using an interior local regularity result and a modified Moser method with special test function.

Modular Structures on Trace Class Operators and Applications to Landau Levels

2009

The energy levels, generally known as the Landau levels, which characterize the motion of an electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator, with each level being infinitely degenerate. We show in this paper how the associated von Neumann algebra of observables displays a modular structure in the sense of the Tomita–Takesaki theory, with the algebra and its commutant referring to the two orientations of the magnetic field. A Kubo–Martin–Schwinger state can be built which, in fact, is the Gibbs state for an ensemble of harmonic oscillators. Mathematically, the modular structure is shown to arise as the natural modular structure associated with the…

Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model

2016

We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…

Doubling the success of quantum walk search using internal-state measurements

2015

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve a…

Quantum Walk Search on Johnson Graphs

2016

The Johnson graph $J(n,k)$ is defined by $n$ symbols, where vertices are $k$-element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, $J(n,1)$ is the complete graph $K_n$, and $J(n,2)$ is the strongly regular triangular graph $T_n$, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that $J(n,3)$, which is the $n$-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs $J(n,k)$ with fixed $k$.

Four solutions for fractional p-Laplacian equations with asymmetric reactions

2020

We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.