Energy levels of charged particles confined in a multiply connected structure in a magnetic field

1993 ◽  
Vol 73 (5) ◽  
pp. 2364-2375 ◽  
Author(s):  
A. Ishibashi ◽  
D. G. Ravenhall ◽  
R. L. Schult ◽  
H. W. Wyld
Keyword(s):  
Magnetic Field ◽  
Energy Levels ◽  
Charged Particles ◽  
Multiply Connected ◽  
Connected Structure

TOPOLOGICAL MANIFESTATIONS IN CLASSICAL MECHANICS: DISCRETE ALLOWED AND FORBIDDEN STATES OF MOTION

1994 ◽  
Vol 09 (39) ◽  
pp. 3653-3661 ◽  
Author(s):  
RAM K. VARMA
Keyword(s):  
Magnetic Field ◽  
Dynamical System ◽  
Classical Mechanics ◽  
Charged Particles ◽  
Coherent System ◽  
Forbidden States ◽  
Multiply Connected ◽  
Action Integral ◽  
Relationship Of ◽  
The Relationship

Consequences of the topology of the configuration space of a Hamiltonian dynamical system are considered for a coherent system of trajectories. It is shown that when the space is multiply-connected and therefore the action integral is multivalued, the allowed states of motion (labeled by the initial data) are constrained to a discrete set by the requirement that the action be single-valued. One thus obtains a quantum-like discretization of allowed states of motion even in classical mechanics. Such discrete “allowed” and “forbidden” states have indeed been observed in the classical mechanical system of charged particles in a magnetic field. The relationship of this formalism with a Schrödinger-like formalism for the latter problem given earlier is discussed.

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

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