15,669 research outputs found
Brownian Motion on a Sphere: Distribution of Solid Angles
We study the diffusion of Brownian particles on the surface of a sphere and
compute the distribution of solid angles enclosed by the diffusing particles.
This function describes the distribution of geometric phases in two state
quantum systems (or polarised light) undergoing random evolution. Our results
are also relevant to recent experiments which observe the Brownian motion of
molecules on curved surfaces like micelles and biological membranes. Our
theoretical analysis agrees well with the results of computer experiments.Comment: 11 pages, two figures, Fig2 in Colour,references update
Weak Phase gamma Using Isospin Analysis and Time Dependent Asymmetry in B_d -> K_s pi^+ pi^-
We present a method for measuring the weak phase gamma using isospin analysis
of three body B decays into K pi pi channels. Differential decay widths and
time dependent asymmetry in B_d -> K_s pi^+pi^- mode needs to be measured into
even isospin pi pi states. The method can be used to extract gamma, as well as,
the size of the electroweak penguin contributions. The technique is free from
assumptions like SU(3) or neglect of any contributions to the decay amplitudes.
By studying different regions of the Dalitz plot, it is possible to reduce the
ambiguity in the value of gamma.Comment: 11 pages, 1 figur
Scattering states of a particle, with position-dependent mass, in a symmetric heterojunction
The study of a particle with position-dependent effective mass (pdem), within
a double heterojunction is extended into the complex domain --- when the region
within the heterojunctions is described by a non Hermitian
symmetric potential. After obtaining the exact analytical solutions, the
reflection and transmission coefficients are calculated, and plotted as a
function of the energy. It is observed that at least two of the characteristic
features of non Hermitian symmetric systems --- viz., left / right
asymmetry and anomalous behaviour at spectral singularity, are preserved even
in the presence of pdem. The possibility of charge conservation is also
discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor.
(2012
New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
We examine in detail the possibilty of applying Darboux transformation to non
Hermitian hamiltonians. In particular we propose a simple method of
constructing exactly solvable PT symmetric potentials by applying Darboux
transformation to higher states of an exactly solvable PT symmetric potential.
It is shown that the resulting hamiltonian and the original one are pseudo
supersymmetric partners. We also discuss application of Darboux transformation
to hamiltonians with spontaneously broken PT symmetry.Comment: 11 pages, 2 figures, To be published in Journal of Physics A (2004
The Quantum Effective Mass Hamilton-Jacobi Problem
In this article, the quantum Hamilton- Jacobi theory based on the position
dependent mass model is studied. Two effective mass functions having different
singularity structures are used to examine the Morse and Poschl- Teller
potentials. The residue method is used to obtain the solutions of the quantum
effective mass- Hamilton Jacobi equation. Further, it is shown that the
eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and
Poschl-Teller potentials can be obtained by using the Riccati equation without
solving a differential equation
Neutrino oscillation probabilities: Sensitivity to parameters
We study in detail the sensitivity of neutrino oscillation probabilities to
the fundamental neutrino parameters and their possible determination through
experiments. The first part of the paper is devoted to the broad theme of
isolating regions in the neutrino (and anti-neutrino) energy and propagation
length that are sensitive to the oscillation parameters. Such a study is
relevant to neutrinos both from the Earth's atmosphere or from a neutrino
factory. For completeness we discuss the sensitivity, however small, to the
parameters involved in a three-generation framework, and to the Earth matter
density profile. We then study processes relevant to atmospheric neutrinos
which are sensitive to and allow precision measurements of the mixing angle
theta_23 and mass-squared difference delta_32 apart from the mixing angle
theta_13. Crucial to this analysis is charge identification; detectors having
this capability can isolate these matter effects. In particular, we address the
issue of using matter effects to determine whether the mixing angle theta_23 is
maximal, and, if not, to explore how well its octant can be determined. When
realistic detector resolutions are included, we find that deviations of about
15% (20%) from a maximal value of sin^2 theta_23=1/2 can be measured at 95%
(99%) CL provided theta_13 is non-zero, sin^2 theta_13 >= 0.015, and the
neutrino mass ordering is normal, with fairly large exposures of 1000
kton-years.Comment: 37 pages Latex file, 30 eps figure files; minor typos fixe
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