CASIMIR ENERGY, FERMION FRACTIONALIZATION AND STABILITY OF A FERMI FIELD IN AN ELECTRIC POTENTIAL IN (1+1) DIMENSIONS

2012 ◽  
Vol 27 (18) ◽  
pp. 1250093 ◽  
Author(s):  
Z. DEHGHAN ◽  
S. S. GOUSHEH
Keyword(s):  
Total Energy ◽  
Electric Potential ◽  
Bound States ◽  
Vacuum Polarization ◽  
Direct Calculation ◽  
Phase Shifts ◽  
Casimir Energy ◽  
Dirac Field ◽  
Local Maxima ◽  
Densities Of States

In this paper we compute and study the Casimir energy, vacuum polarization and the resulting fermion fractionalization, the phase shifts and the stability of the bound states of a Dirac field, all due to its interaction with an electric potential in (1+1) dimension. We also explore the inter-relation between these effects. All of these effects are different manifestations of one single source, which is the distortion of the fermionic spectrum and appears as spectral deficiencies in the continua and bound states. We compute and display the spatial densities of these deficiencies and those of the bound states, along with their associated energy densities. We find that in both cases the total spatial densities of states with E > 0 and E < 0 are exact mirror images of each other. Therefore these densities for the complete spectrum are unchanged as compared to the free case, and in particular they remain uniform. The densities of states with E < 0 are precisely the vacuum polarization density and the Casimir energy density, respectively. We find that the vacuum polarization is in general noninteger. We then compute and display the energy densities of the spectral deficiencies in the momentum space, and show that levels exiting or entering the continua leave their distinctive marks on these energy densities. We also use the phase shifts to calculate the Casimir energy and obtain the same result as in the direct calculation. In this problem the Casimir energy is always positive and is on the average an increasing function of the depth and width of the potential. It has a cusp whenever an energy level crosses E = 0. These cusps are local maxima in the extreme relativistic limits. Finally we show that the taking the Casimir energy into account, the total energy will be stable under small fluctuations in the parameters of the potential. However only the first two bound states are absolutely stable in the sense that their total energy is smaller than the mass.

Vacuum polarization and particle creation in the presence of a potential step

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641031 ◽  
Author(s):  
S. P. Gavrilov ◽  
D. M. Gitman
Keyword(s):  
Electric Potential ◽  
Canonical Quantization ◽  
Particle Creation ◽  
Pair Creation ◽  
Dirac Field ◽  
Potential Step ◽  
Electron Positron ◽  
Physical Impact ◽  
Particle Interpretation ◽  
Electron Positron Pair

We consider QED with strong external backgrounds that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can create particles from the vacuum, the Klein paradox being closely related to this process. We describe a canonical quantization of the Dirac field with x-electric potential step in terms of adequate in- and out-creation and annihilation operators that allow one to have consistent particle interpretation of the physical system under consideration and develop a nonperturbative (in the external field) technics to calculate scattering, reflection, and electron-positron pair creation. We resume the physical impact of this development.

High resolution spectrum of NO2 loosely bound states: densities of states and long range forces

2001 ◽  
Vol 3 (12) ◽  
pp. 2268-2274 ◽  
Author(s):  
Sylvain Heilliette ◽  
Antoine Delon ◽  
Patrick Dupre´ ◽  
Re´my Jost
Keyword(s):  
High Resolution ◽  
Long Range ◽  
Bound States ◽  
High Resolution Spectrum ◽  
Densities Of States

scholarly journals NEUTRON STARS AND THE FERMIONIC CASIMIR EFFECT

2002 ◽  
Vol 17 (06n07) ◽  
pp. 1059-1064 ◽  
Author(s):  
PIOTR MAGIERSKI ◽  
AUREL BULGAC ◽  
PAUL-HENRI HEENEN
Keyword(s):  
Total Energy ◽  
Neutron Stars ◽  
Crystal Lattice ◽  
Coulomb Interaction ◽  
Quantum Correction ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Large Influence

The inner crust of neutron stars consists of nuclei of various shapes immersed in a neutron gas and stabilized by the Coulomb interaction in the form of a crystal lattice. The scattering of neutrons on nuclear inhomegeneities leads to the quantum correction to the total energy of the system. This correction resemble the Casimir energy and turn out to have a large influence on the structure of the crust.

The nucleon–nucleon interaction. I. Scalar mesons

1976 ◽  
Vol 54 (3) ◽  
pp. 322-332
Author(s):  
A. Z. Capri ◽  
D. Menon ◽  
R. Teshima
Keyword(s):  
Bound States ◽  
Bound State ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
Variational Calculation ◽  
Coupling Constant ◽  
Nucleon Interaction ◽  
Scalar Mesons ◽  
T Matrix ◽  
Nucleon Nucleon Interaction

The two-nucleon interaction, via the exchange of scalar mesons, is examined in a nonperturbative manner. 'Schrödinger' equations are derived, and nonlocal potentials arise naturally. Both scattering and bound states are examined. A half-off-shell T matrix is obtained, and corresponding phase shifts are evaluated. In the bound state, a variational calculation is employed to determine the coupling constant.

scholarly journals The spectrum of the Schrödinger–Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions

2018 ◽  
Vol 15 (08) ◽  
pp. 1850135 ◽  
Author(s):  
Fassari Silvestro ◽  
Rinaldi Fabio ◽  
Viaggiu Stefano
Keyword(s):  
Quantum Dot ◽  
Harmonic Oscillator ◽  
Total Energy ◽  
Spectral Properties ◽  
Bound States ◽  
Three Dimensional ◽  
Point Interactions ◽  
One Dimensional ◽  
The One ◽  
Math Phys

In this paper, we exploit the technique used in [Albeverio and Nizhnik, On the number of negative eigenvalues of one-dimensional Schrödinger operator with point interactions, Lett. Math. Phys. 65 (2003) 27; Albeverio, Gesztesy, Hoegh-Krohn and Holden, Solvable Models in Quantum Mechanics (second edition with an appendix by P. Exner, AMS Chelsea Series 2004); Albeverio and Kurasov, Singular Perturbations of Differential Operators: Solvable Type Operators (Cambridge University Press, 2000); Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian with a particular configuration of three one-dimensional point interactions, Rep. Math. Phys. 3 (2009) 367; Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions, Rep. Math. Phys. 3 (2012) 353; Albeverio, Fassari and Rinaldi, The Hamiltonian of the harmonic oscillator with an attractive-interaction centered at the origin as approximated by the one with a triple of attractive-interactions, J. Phys. A: Math. Theor. 49 (2016) 025302; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin II, Nanosyst. Phys. Chem. Math. 7(5) (2016) 803; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin, Nanosyst. Phys. Chem. Math. 7(2) (2016) 268] to deal with delta interactions in a rigorous way in a curved spacetime represented by a cosmic string along the [Formula: see text] axis. This mathematical machinery is applied in order to study the discrete spectrum of a point-mass particle confined in an infinitely long cylinder with a conical defect on the [Formula: see text] axis and perturbed by two identical attractive delta interactions symmetrically situated around the origin. We derive a suitable approximate formula for the total energy. As a consequence, we found the existence of a mixing of states with positive or zero energy with the ones with negative energy (bound states). This mixture depends on the radius [Formula: see text] of the trapping cylinder. The number of quantum bound states is an increasing function of the radius [Formula: see text]. It is also interesting to note the presence of states with zero total energy (quasi free states). Apart from the gravitational background, the model presented in this paper is of interest in the context of nanophysics and graphene modeling. In particular, the graphene with double layer in this framework, with the double layer given by the aforementioned delta interactions and the string on the [Formula: see text]-axis modeling topological defects connecting the two layers. As a consequence of these setups, we obtain the usual mixture of positive and negative bound states present in the graphene literature.

Calculations of SiH3 Diffusion and Growth Processes on a-Si:H Surfaces

2003 ◽  
Vol 762 ◽  
Author(s):  
P Vigneron ◽  
P W Peacock ◽  
K Xiong ◽  
J Robertson
Keyword(s):  
Total Energy ◽  
Amorphous Silicon ◽  
Surface Diffusion ◽  
Bound States ◽  
Smooth Surface ◽  
Hydrogenated Amorphous Silicon ◽  
Weakly Bound ◽  
Growth Site ◽  
Pseudopotential Calculations ◽  
Hydrogenated Amorphous

AbstractSurface diffusion of a growth species is needed to give the observed smooth surface of hydrogenated amorphous silicon (a-Si:H). But what diffuses, the weakly bound SiH3 radical on the hydrogenated surface, or the bound SiH3 at a growth site. Diffusion is complicated by the change in the surface termination of a-Si:H as temperature rises. We use total energy pseudopotential calculations on a variety of periodic Si:H surface configurations to show that it is the weakly bound SiH3 that diffuses. We provide an overall energy scheme of the bound states and transport levels of SiH3 on a-Si:H surfaces.

XV.—Quantum Mechanics of Fields. III. Electromagnetic Field and Electron Field in Interaction

1946 ◽  
Vol 62 (2) ◽  
pp. 127-137
Author(s):  
Max Born ◽  
H. W. Peng
Keyword(s):  
Electromagnetic Field ◽  
Quantum Mechanics ◽  
Total Energy ◽  
Dirac Field ◽  
Single Particles ◽  
System Of Particles ◽  
Electron Field ◽  
Energy And Momentum ◽  
Ordinary Quantum

Studying the interaction of different pure fields, we have been led to some essential modifications of the ideas on which our quantum mechanics of fields is based. We shall explain these here for the example of the interaction of the Maxwell and the Dirac field.In Part I we showed that a pure field in a given volume Ω can be described by considering the potentials and field components as matrices, not attached to single points in Ω (as the theory of Heisenberg and Pauli), but to the whole volume. Further, we assumed the total energy and momentum to be the product of Ω and the corresponding densities. In Part † we showed that this conception has to be modified; the eigenvalues of the energy and momentum as defined in Part I represent neither the states of single particles nor of a system of particles, but of something intermediate which corresponds to the simple oscillators of Heisenberg-Pauli and which we have called apeirons. The total energy and momentum of the system is a sum over the contributions of an assembly of apeirons. Mathematically the differences of the quantum mechanics of a field from that of a set of mass points (as treated in ordinary quantum mechanics) is the fact that the matrices representing a field are reducible (while those representing co-ordinates of mass points are irreducible); each irreducible submatrix corresponds to an apeiron.

Direct calculation of nuclear structure from the two-nucleon phase shifts

1967 ◽  
Vol 24 (8) ◽  
pp. 358-360 ◽  
Author(s):  
J.P. Elliot ◽  
H.A. Mavromatis ◽  
E.A. Sanderson
Keyword(s):  
Nuclear Structure ◽  
Direct Calculation ◽  
Phase Shifts

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.

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