scholarly journals Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 210
Author(s):  
Vladimir Ch. Zhukovsky
Keyword(s):  
Domain Walls ◽  
Analytic Solutions ◽  
Space Time ◽  
Monolayer Graphene ◽  
Dirac Fermion ◽  
Induced Current ◽  
Bohm Potential ◽  
Exact Analytic Solutions ◽  
Compact Dimension ◽  
Aharonov Bohm

We consider fermion models in 3D- and 5D-space-time with an Aharonov–Bohm potential and a domain wall. Induced current is calculated, which is due to vacuum effects in the topologically nontrivial space-time. Violation of chiral symmetry and appearance of induced current is demonstrated in a simple example of quantum mechanical violation of symmetry in a model of a massless Dirac fermion moving in a background vector field and domain walls as barriers for the electron propagation. The effective Dirac equation for massless electrons modeling monolayer graphene is used. One of the solutions to the problem of describing domain walls in planar systems is reduced to finding exact analytic solutions. In this paper, we consider appearance of induced current in two-fermion model with a compact dimension as a result of vacuum polarization in the field of the external gauge field in the 4 + 1 and the 2 + 1 dimensional models with one type of fermions and with two types of fermions living in the brane and in the bulk. Two different approaches (Kaluza–Klein and Aharonov–Bohm) to the problem of induced current are used. Production of an induced current in a planar model with a thin solenoid is also studied.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

DIRAC ELECTRON IN AHARONOV–BOHM AND PLANAR COULOMB POTENTIALS

2004 ◽  
Vol 19 (28) ◽  
pp. 2121-2127 ◽  
Author(s):  
V. R. KHALILOV
Keyword(s):  
Dirac Equation ◽  
Analytic Solutions ◽  
Electron States ◽  
Exact Analytic Solutions ◽  
Dirac Electron ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Bound Electron ◽  
Coulomb Potentials

Exact analytic solutions are found to the Dirac equation in (2+1) dimensions for a combination of Aharonov–Bohm and Lorentz 3-vector Coulomb potentials. By means of solutions obtained the relativistic Aharonov–Bohm effect is studied for free and bound electron states.

scholarly journals An Archimedes' Screw for Light

2021 ◽  
Author(s):  
Emanuele Galiffi ◽  
Paloma Huidobro ◽  
John Pendry
Keyword(s):  
Analytic Solutions ◽  
Space Time ◽  
Time Varying ◽  
Pump Probe ◽  
Circularly Polarized ◽  
Polarized Beams ◽  
Exact Analytic Solutions ◽  
Potential Applications ◽  
Chiral Systems ◽  
Wide Family

Abstract An Archimedes' Screw captures water, feeding energy into it by lifting it to a higher level. We introduce the first instance of an optical Archimedes' Screw, and demonstrate how this system is capable of capturing light, dragging it and amplifying it. We unveil new exact analytic solutions to Maxwell's Equations for a wide family of chiral space-time media, and show their potential to achieve chirally selective amplification within widely tunable parity-time-broken phases. Our work, which may be readily implemented via pump-probe experiments with circularly polarized beams, opens a new direction in the physics of time-varying media by merging the rising field of space-time metamaterials and that of chiral systems, and offers a new playground for topological and non-Hermitian photonics, with potential applications to chiral spectroscopy and sensing.

scholarly journals Evolution of a domain wall in expanding universe: inflation and after it

2018 ◽  
Vol 191 ◽  
pp. 08004
Author(s):  
A.D. Dolgov ◽  
S.I. Godunov ◽  
A.S. Rudenko
Keyword(s):  
Domain Wall ◽  
Hubble Parameter ◽  
Domain Walls ◽  
Flat Space ◽  
Space Time ◽  
Time Dependent ◽  
Expanding Universe ◽  
Large Size ◽  
Dependent Parameter ◽  
Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

scholarly journals Exact analytical solutions of continuously graded models of flat lenses based on transformation optics

2017 ◽  
Vol 30 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Mariana Dalarsson ◽  
Raj Mittra
Keyword(s):  
Magnetic Fields ◽  
Longitudinal Direction ◽  
Middle Layer ◽  
Analytic Solutions ◽  
Transformation Optics ◽  
Confluent Hypergeometric Functions ◽  
Graded Index ◽  
Exact Analytic Solutions ◽  
Electric And Magnetic Fields ◽  
Physical Insight

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantum-mechanical radial Schr?dinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

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