DYON–DYON BOUND STATES IN NON-RELATIVISTIC AND RELATIVISTIC FRAMEWORKS

1998 ◽  
Vol 13 (30) ◽  
pp. 5245-5256 ◽  
Author(s):  
B. S. RAJPUT ◽  
V. P. PANDEY
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
Dirac Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
The Other ◽  
System A ◽  
Relativistic Framework

Investigating dyon–dyon bound states in non-relativistic as well as in relativistic frameworks, it has been shown that in this system a dyon moves on a cone with its apex at the other dyon and axis along its angular momentum. Dyon–dyon bound states have been investigated in a non-relativistic framework to obtain energy eigenvalue and energy eigenfunction. It has also been shown that the exact solution of Dirac equation for this system is not possible due to the presence of a term vanishing more rapidly than r-1 in the potential of the system.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

Effective-range parameters and vertex constants for Λ-nuclear systems

2017 ◽  
Vol 26 (04) ◽  
pp. 1750014
Author(s):  
S. A. Rakityansky ◽  
I. M. Gopane
Keyword(s):  
Angular Momentum ◽  
Bound States ◽  
The Other ◽  
Effective Range ◽  
Asymptotic Normalization ◽  
The Core ◽  
Wide Range ◽  
Nuclear Systems ◽  
Text Model ◽  
Scattering Lengths

For a wide range of the core-nuclei ([Formula: see text]), the scattering lengths, effective radii, and the other effective-range parameters (up to the order [Formula: see text]) for the angular momentum [Formula: see text] are calculated within a two-body [Formula: see text]-model. For the same hypernuclear systems, the [Formula: see text]-matrix residues as well as the corresponding Nuclear-Vertex and Asymptotic-Normalization constants (NVC’s and ANC’s) for the bound states are also found.

ALGEBRAIC APPROACH TO SPIN SYMMETRY FOR THE DIRAC EQUATION WITH THE TRIGONOMETRIC SCARF POTENTIAL

2010 ◽  
Vol 25 (08) ◽  
pp. 1649-1659 ◽  
Author(s):  
GAO-FENG WEI ◽  
XIAO-YONG DUAN ◽  
XU-YANG LIU
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Algebraic Approach ◽  
Spin Symmetry ◽  
Positive Energy ◽  
Scarf Potential ◽  
Vector Case ◽  
Energy Bound ◽  
Spinor Wave

By a simple algebraic approach we study the exact solution to the Dirac equation with scalar and vector trigonometric Scarf potentials in the case of spin symmetry. The transcendental energy equation and spinor wave functions are presented. It is found that there exist only positive energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter α goes to zero. The equally scalar and vector case is studied briefly.

Experimentalism as a Tool of Economic Innovation in Germany

2001 ◽  
Vol 19 (3) ◽  
pp. 1-33 ◽  
Author(s):  
Wade Jacoby ◽  
Martin Behrens
Keyword(s):  
Industrial Relations ◽  
Information Gathering ◽  
Wage Bargaining ◽  
The Other ◽  
Social Partner ◽  
Social Actor ◽  
Comparative Political Economy ◽  
System A ◽  
German Model ◽  
Economic Innovation

Our purpose in this article is to analyze changes in the German wagebargaining system, a system that has attracted enormous attentionfrom scholars of comparative political economy and comparativeindustrial relations. We argue that the wage bargaining portion ofthe German model is neither frozen in place, headed for deregulation,nor merely “muddling through.” Rather, we see the institutionalcapacities of the key actors—especially the unions and employerassociations—making possible a process we term “experimentalism.”In briefest form, experimentalism allows organizations that combinedecentralized information-gathering abilities with centralized decision-making capacity to probe for new possibilities, which, oncefound, can be quickly diffused throughout the organization. We willshow that the capacity for such experimentalism varies across actorsand sectors. And, to make things even tougher, neither major Germansocial actor can sustain innovation in the longer term withoutbringing along the other “social partner.”

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

Hedley Bull, states systems and international societies

1987 ◽  
Vol 13 (2) ◽  
pp. 147-153 ◽  
Author(s):  
Adam Watson
Keyword(s):  
International Relations ◽  
International Society ◽  
The Other ◽  
Common Values ◽  
System A ◽  
Common Interests ◽  
Hedley Bull ◽  
Regular Contact

Hedley Bull's contribution to the theory of international relations is considerable; and nowhere more acute than in the distinction which he made between the concept of a system of states and that of an international society. His definitive formulation is set out in Chapter I of The Anarchical Society. ‘Where states are in regular contact with one another, and where in addition there is interaction between them sufficient to make the behaviour of each a necessary element in the calculations of the other, then we may speak of their forming a system.’ ‘A society of states (or international society) exists when a group of states, conscious of certain common interests and common values, form a society in the sense that they conceive themselves to be bound by a common set of rules in their relations with one another, and share in the working of common institutions.’

Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

2004 ◽  
Vol 17 (1-2) ◽  
pp. 165-197 ◽  
Author(s):  
Erhard Scholz
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
A Priori ◽  
Group Extension ◽  
Central Idea ◽  
German Word ◽  
General Relativistic ◽  
Empirical Turn ◽  
Relativistic Framework ◽  
Internal Symmetries

Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.

Study of Oscillating Flow of Viscoelastic Fluid With the Fractional Maxwell Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jiu-hong Jia ◽  
Hong-xing Hua
Keyword(s):  
Exact Solution ◽  
Petroleum Chemistry ◽  
Viscoelastic Fluid ◽  
Maxwell Model ◽  
The Other ◽  
Oscillating Flow ◽  
Model Parameters ◽  
Series Approximation ◽  
Phase Lags ◽  
Annular Effect

The oscillating flow of the viscoelastic fluid in cylindrical pipes has been applied in many fields, such as industries of petroleum, chemistry, and bioengineering. It is studied using the fractional derivative Maxwell model in this paper. The exact solution is obtained utilizing a simpler and more reasonable technique. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From analysis, it is found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Moreover, two series approximations for the velocity are obtained and analyzed for different model parameters. In one series approximation, the velocity is parabolic in profile, while in the other series approximation, the velocity presents three characteristics: (1) it is independent of radius and at the centerline is smaller than that of steady Poiseuille flow, (2) the phase lags about 90deg with respect to the imposed pressure gradient, and (3) the Richardson annular effect is found near the wall.

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