14 research outputs found
Induced vacuum condensates in the background of a singular magnetic vortex in 2+1-dimensional space-time
We show that the vacuum of the quantized massless spinor field in
2+1-dimensional space-time is polarized in the presence of a singular magnetic
vortex. Depending on the choice of the boundary condition at the location of
the vortex, either chiral symmetry or parity is broken; the formation of the
appropriate vacuum condensates is comprehensively studied. In addition, we find
that current, energy and other quantum numbers are induced in the vacuum.Comment: LaTeX2e, 27 page
Electronic properties of graphene with a topological defect
Various types of topological defects in graphene are considered in the
framework of the continuum model for long-wavelength electronic excitations,
which is based on the Dirac--Weyl equation. The condition for the electronic
wave function is specified, and we show that a topological defect can be
presented as a pseudomagnetic vortex at the apex of a graphitic nanocone; the
flux of the vortex is related to the deficit angle of the cone. The cases of
all possible types of pentagonal defects, as well as several types of
heptagonal defects (with the numbers of heptagons up to three, and six), are
analyzed. The density of states and the ground state charge are determined.Comment: 25 pages, 3 figures, 1 table,minor correction
Self-Adjointness of the Dirac Hamiltonian and Fermion Number Fractionization in the Background of a Singular Magnetic Vortex
The method of self-adjoint extensions is employed to determine the vacuum
quantum numbers induced by a singular static magnetic vortex in
-dimensional spinor electrodynamics. The results obtained are
gauge-invariant and, for certain values of the extension parameter, both
periodic in the value of the vortex flux and possessing definite parity with
respect to the charge conjugation.Comment: LaTe
Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time
Charged scalar field is quantized in the background of a static d-2 - brane
which is a core of the magnetic flux lines in flat d+1 - dimensional
space-time. We find that vector potential of the magnetic core induces the
energy-momentum tensor in the vacuum. The tensor components are periodic
functions of the brane flux and holomorphic functions of space dimension. The
dependence on the distance from the brane and on the coupling to the space-time
curvature scalar is comprehensively analysed.Comment: 32 pages, 3 figures, journal version, some references adde
Fractionalization of angular momentum at finite temperature around a magnetic vortex
Ambiguities in the definition of angular momentum of a quantum-mechanical
particle in the presence of a magnetic vortex are reviewed. We show that the
long-standing problem of the adequate definition is resolved in the framework
of the second-quantized theory at nonzero temperature. Planar relativistic
Fermi gas in the background of a point-like magnetic vortex with arbitrary flux
is considered, and we find thermal averages, quadratic fluctuations, and
correlations of all observables, including angular momentum, in this system.
The kinetic definition of angular momentum is picked out unambiguously by the
requirement of plausible behaviour for the angular momentum fluctuation and its
correlation with fermion number.Comment: 32 pages, submitted to Annals of Physic
Aharonov-Bohm effect in scattering of high-energy particles
Quantum-mechanical scattering of coherent high-energy charged particles by a magnetic vortex is considered. The vortex core is assumed to be impermeable to scattered particles, and effects of its transverse size are taken into account. The limit of high energies of scattered particles corresponds to the quasiclassical limit, and we show that in the scattering the Aharonov-Bohm effect persists in this limit owing to the Fraunhofer diffraction in the forward direction. The issue of the experimental detection of the Fraunhofer diffraction peak and the Aharonov-Bohm effect in the quasiclassical limit is discussed.Рассматривается квантово-механическое рассеяние высокоэнергетических заряженных частиц магнитным вихрем. Ядро вихря предполагается непроницаемым для рассеиваемых частиц, и учитываются эффекты его поперечных размеров. Предел высоких энергий рассеиваемых частиц соответствует квазиклассическому пределу, и мы показываем, что эффект Ааронова-Бома в рассеянии в этом пределе выживает благодаря дифракции Фраунгофера в направлении вперед. Обсуждаются вопросы экспериментального детектирования пика Фраунгоферовой дифракции и эффекта Ааронова-Бома в квазиклассическом пределе.Розглядається квантово-механічне розсіяння високоенергетичних заряджених частинок магнітним вихором. Припускається, що ядро вихора є непроникним для розсіюваних частинок, та враховуються ефекти його поперечних розмірів. Границя високих енергій розсіюваних частинок відповідає квазікласичній границі, і ми показуємо, що ефект Ааронова-Бома в розсіянні в цій границі виживає завдяки дифракції Фраунгофера в напрямку вперед. Обговорюються питання експериментального детектування піка Фраунгоферової дифракції та ефекта Ааронова-Бома в квазікласичній границі
Vacuum polarization in graphene with a topological defect
The influence of a topological defect in graphene on the ground state of electronic quasiparticle
excitations is studied in the framework of the long-wavelength continuum model originating in the tightbinding
approximation for the nearest neighbour interaction in the graphitic lattice. Atopological defect that
rolls up a graphitic sheet into a nanocone is represented by a pointlike pseudomagnetic vortex with a flux
which is related to the deficit angle of the cone. The method of self-adjoint extensions is employed to define
the set of physically acceptable boundary conditions at the apex of the nanocone. The electronic system on a
graphitic nanocone is found to acquire the ground state condensate and current of special type, and we
determine the dependence of these quantities on the deficit angle of the nanocone, continuous parameter of
the boundary condition at the apex, and the distance from the apex
Induced Vacuum Polarization of Scalar Field by Impenetrable Magnetic Tube
We investigate the influence of an external magnetic field in a tube on the vacuum of a massive charged scalar field for arbitrary space-time dimensions. The tube is considered impenetrable for the scalar field and obeys the Dirichlet boundary condition on the bounding surface. It was shown that, for a particular case of the 2 + 1-dimensional space-time, the induced vacuum energy of the scalar field outside the tube can be numerically calculated without regularization procedure. The dependences of the induced vacuum energy upon the distance from the tube at its various transversal radii are obtained.У роботi дослiджено узагальнену на випадок простору-часу довiльної розмiрностi задачу про вплив на вакуум зарядженого масивного скалярного поля зовнiшнього магнiтного поля, розташованого в трубцi скiнченого радiуса. Трубка є непроникливою для бозонного поля та має на поверхнi граничнi умови типу Дiрiхле. Показано, що для часткового випадку просторучасу розмiрнiстю 2+1 iндукована густина енергiї вакууму ззовнi трубки може бути знайдена чисельними методами без застосування процедури регуляризацiї. Отримано залежностi iндукованої густини енергiї вакууму вiд вiдстанi до трубки при рiзних значеннях її поперечного радiуса
Point interactions in one dimension and holonomic quantum fields
We introduce and study a family of quantum fields, associated to
delta-interactions in one dimension. These fields are analogous to holonomic
quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators
belong to an infinite-dimensional representation of the group SL(2,\Rb) in
the Fock space of ordinary harmonic oscillator. We compute form factors of such
fields and their correlation functions, which are related to the determinants
of Schroedinger operators with a finite number of point interactions. It is
also shown that these determinants coincide with tau functions, obtained
through the trivialization of the -bundle over a Grassmannian
associated to a family of Schroedinger operators.Comment: 17 page
Quark zero modes in intersecting center vortex gauge fields
The zero modes of the Dirac operator in the background of center vortex gauge
field configurations in and are examined. If the net flux in D=2
is larger than 1 we obtain normalizable zero modes which are mainly localized
at the vortices. In D=4 quasi-normalizable zero modes exist for intersecting
flat vortex sheets with the Pontryagin index equal to 2. These zero modes are
mainly localized at the vortex intersection points, which carry a topological
charge of . To circumvent the problem of normalizability the
space-time manifold is chosen to be the (compact) torus \T^2 and \T^4,
respectively. According to the index theorem there are normalizable zero modes
on \T^2 if the net flux is non-zero. These zero modes are localized at the
vortices. On \T^4 zero modes exist for a non-vanishing Pontryagin index. As
in these zero modes are localized at the vortex intersection points.Comment: 20 pages, 4 figures, LaTeX2e, references added, treatment of ideal
vortices on the torus shortene