scholarly journals DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

1999 ◽  
Vol 14 (30) ◽  
pp. 4749-4761 ◽  
Author(s):  
C. G. BENEVENTANO ◽  
M. DE FRANCIA ◽  
E. M. SANTANGELO
Keyword(s):  
Magnetic Flux ◽  
Boundary Conditions ◽  
Index Theorem ◽  
Casimir Energy ◽  
The Self ◽  
Dirac Field ◽  
Finite Region ◽  
Finite Radius ◽  
Dirac Fields ◽  
Aharonov Bohm

We study the problem of a Dirac field in the background of an Aharonov–Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behavior of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

BOUND FERMION STATES IN A VECTOR 1/r AND AHARONOV–BOHM POTENTIAL IN (2+1) DIMENSIONS

2011 ◽  
Vol 26 (12) ◽  
pp. 865-883 ◽  
Author(s):  
V. R. KHALILOV ◽  
K. E. LEE
Keyword(s):  
Magnetic Flux ◽  
Boundary Conditions ◽  
Effective Charge ◽  
The Self ◽  
Critical Charge ◽  
Spin Particle ◽  
Bohm Potential ◽  
Aharonov Bohm

We construct systematically all the self-adjoint Dirac Hamiltonians with a vector 1/r and Aharonov–Bohm potential in (2+1) dimensions with taking into account the fermion spin. Then we find spectra of these self-adjoint Dirac Hamiltonians. There are one-parameter families of the self-adjoint Dirac Hamiltonians selected by physically acceptable boundary conditions. Equations determining spectra of the self-adjoint radial Dirac Hamiltonians are derived for various values of parameters. We show that the lowest fermion state in the considered potential becomes unstable when the effective charge is greater than the so-called critical charge, and that the effective charge is influenced by the magnetic flux and spin particle.

scholarly journals CASIMIR ENERGY AND FORCE INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

2013 ◽  
Vol 28 (31) ◽  
pp. 1350161 ◽  
Author(s):  
VOLODYMYR M. GORKAVENKO ◽  
YURII A. SITENKO ◽  
OLEXANDER B. STEPANOV
Keyword(s):  
Magnetic Flux ◽  
Vacuum Polarization ◽  
Dirichlet Boundary ◽  
Topological Defect ◽  
Casimir Energy ◽  
Matter Field ◽  
Tube Radius ◽  
Finite Radius ◽  
Polarization Effects ◽  
Scalar Matter

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

scholarly journals Vacuum Energy for a Scalar Field with Self-Interaction in (1 + 1) Dimensions

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 55
Author(s):  
Michael Bordag
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Strong Coupling ◽  
Vacuum Energy ◽  
Dirichlet Boundary ◽  
Casimir Energy ◽  
The Self ◽  
Dirichlet Boundary Conditions ◽  
Massless Fields

We calculate the vacuum (Casimir) energy for a scalar field with ϕ4 self-interaction in (1 + 1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with Dirichlet boundary conditions and on the whole axis as well. For strong coupling, the vacuum energy is negative indicating some instability.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux parameter

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Yuri Gorodetski ◽  
Sergey Nechayev ◽  
Vladimir Kleiner ◽  
Erez Hasman
Keyword(s):  
Magnetic Flux ◽  
Flux Parameter ◽  
Bohm Effect ◽  
Aharonov Bohm

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

Semibounded Extensions of Singular Ordinary Differential Operators

1988 ◽  
Vol 31 (4) ◽  
pp. 432-438
Author(s):  
Allan M. Krall
Keyword(s):  
Differential Operator ◽  
Lower Bound ◽  
Boundary Conditions ◽  
Differential Operators ◽  
The Self ◽  
Limit Circle ◽  
Singular Differential Operator ◽  
Ordinary Differential Operators

AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

Linearized theory of inhomogeneous multiple ‘water-bag’ plasmas

1973 ◽  
Vol 9 (2) ◽  
pp. 235-247 ◽  
Author(s):  
H. W. Bloomberg ◽  
H. L. Berk
Keyword(s):  
Boundary Conditions ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Special Boundary ◽  
Finite Region ◽  
Trapped Particles ◽  
Linearized Theory ◽  
Beam Approximation ◽  
The Stability

The problem of the stability of inhomogeneous, electrostatic, multiple water-bag plasmas is considered. Equations are derived for general stationary water-bag equilibria, as well as for the corresponding perturbations. Particular attention is directed to systems with trapped particles in periodic equilibria, and special boundary conditions for the perturbation equations at the trapped-particle turning points are introduced. A normal-mode analysis is carried out for a configuration involving trapped particles occupying a finite region in the vicinity of the trough of an equilibrium wave (BGK mode). The results confirm the validity of the bunched-beam approximation.

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