scholarly journals ON THE PSEUDO-HERMITICITY OF A CLASS OF PT-SYMMETRIC HAMILTONIANS IN ONE DIMENSION

2002 ◽  
Vol 17 (30) ◽  
pp. 1973-1977 ◽  
Author(s):  
ALI MOSTAFAZADEH
Keyword(s):  
Explicit Form ◽  
Vector Potential ◽  
Scalar Potential ◽  
Invertible Operator ◽  
Degree Of Freedom ◽  
One Dimension ◽  
Complex Scalar ◽  
Arbitrary Complex ◽  
Antilinear Operator

For a given standard Hamiltonian H = [p - A(x)]2/(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, we construct an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H† = τHτ-1. We use this result to give the explicit form of a linear hermitian invertible operator with respect to which any standard PT-symmetric Hamiltonian with a real degree of freedom is pseudo-hermitian. Our results do not make use of the assumption that H is diagonalizable or that its spectrum is discrete.

Mass transport under partially reflected waves in a rectangular channel

1994 ◽  
Vol 266 ◽  
pp. 121-145 ◽  
Author(s):  
Jiangang Wen ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Vector Potential ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Scalar Potential ◽  
Second Order ◽  
Nonlinear Transport ◽  
Reflected Waves ◽  
Transport Velocity ◽  
Mass Transport Velocity

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals SOME ASPECTS OF SPHERICAL SYMMETRIC EXTREMAL DYONIC BLACK HOLES IN 4D N = 1 SUPERGRAVITY

2013 ◽  
Vol 28 (18) ◽  
pp. 1350084 ◽  
Author(s):  
BOBBY E. GUNARA ◽  
FREDDY P. ZEN ◽  
FIKI T. AKBAR ◽  
AGUS SUROSO ◽  
ARIANTO
Keyword(s):  
Black Hole ◽  
Scalar Potential ◽  
Local Existence ◽  
Scalar Fields ◽  
Asymptotic Region ◽  
De Sitter ◽  
Complex Scalar ◽  
Symmetric Black Hole ◽  
Scalar Potentials ◽  
Nonzero Scalar

In this paper, we study several aspects of extremal spherical symmetric black hole solutions of four-dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region, the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and nonzero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincide. In addition, we prove the local existence of nontrivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ℂn-models with both linear superpotential and gauge couplings.

scholarly journals Dirac equation with complex potentials

2014 ◽  
Vol 29 (40) ◽  
pp. 1450210 ◽  
Author(s):  
C.-L. Ho ◽  
P. Roy
Keyword(s):  
Dirac Equation ◽  
Scalar Potential ◽  
Complex Potentials ◽  
Zero Energy ◽  
Complex Scalar ◽  
Exact Analytical Solutions ◽  
Exactly Solvable ◽  
Lorentz Scalar ◽  
Scalar Potentials ◽  
Energy Dependent

We study (2+1)-dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy-dependent Schrödinger equations.

Investigating the Difficulty of One Degree of Freedom Positioning: Associating Movement Phases with Regions

2009 ◽  
Vol 53 (15) ◽  
pp. 965-969 ◽  
Author(s):  
Robert Pastel
Keyword(s):  
Movement Time ◽  
Touch Screen ◽  
Degree Of Freedom ◽  
One Dimension ◽  
Mouse Button ◽  
Total Movement ◽  
Remaining Time ◽  
Total Movement Time

Positioning an object within specified bounds is a common daily computer task, for example making selections using a touch screen or positioning icons relative to each other. This experiment measured times for participants ( n = 145) to position rectangular cursors with various widths, p, within rectangular targets with various tolerances, t, in one dimension. The analysis divides the total movement time into three parts, the time for the cursor to touch the target, the time to enter the target after touching, and the centering time, the remaining time for participants to indicate that the cursor is completely within the target by clicking on the mouse button. The time to touch the target was modeled well by the initial cursor-target separation, r2/sup> = 0.95. The entering time was modeled well by log2( p/t + 1), r2/sup> = 0.99, and the centering time was modeled well by r2/sup> = 0.94

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