Induced quantum numbers of a magnetic vortex at nonzero temperature

The phenomenon of the finite-temperature induced quantum numbers in fermionic systems with topological defects is analyzed. We consider an ideal gas of twodimensional relativistic massive electrons in the background of a defect in the form of a pointlike magnetic vortex with arbitrary flux. This system is found to acquire, in addition to fermion number, also orbital angular momentum, spin, and induced magnetic flux, and we determine the functional dependence of the appropriate thermal averages and correlations on the temperature, the vortex flux, and the continuous parameter of the boundary condition at the location of the defect. We find that nonnegativeness of thermal quadratic fluctuations imposes a restriction on the admissible range of values of the boundary parameter. The long-standing problem of the adequate definition of total angular momentum for the system considered is resolved.Comment: 40 pages, 7 figures, journal version, minor correction

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

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

Fractional electric charge of a magnetic vortex at nonzero temperature

An ideal gas of twodimensional Dirac fermions in the background of a pointlike magnetic vortex with arbitrary flux is considered. We find that this system acquires fractional electric charge at finite temperatures and determine the functional dependence of the thermal average and quadratic fluctuation of the charge on the temperature, the vortex flux, and the continuous parameter of the boundary condition at the location of the vortex.Comment: 25 pages, 5 figures, journal version, minor changes, Eqs.(3.2)-(3.5) correcte

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 $2+1$-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

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin 0 and 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.Comment: 14 pages, constants $\hbar$ and $c$ are recovered in formula (40). arXiv admin note: text overlap with arXiv:1411.246

Induced quantum numbers of a magnetic monopole at finite temperature

A Dirac electron field is quantized in the background of a Dirac magnetic monopole, and the phenomenon of induced quantum numbers in this system is analyzed. We show that, in addition to electric charge, also squares of orbital angular momentum, spin, and total angular momentum are induced. The functional dependence of these quantities on the temperature and the CP-violating vacuum angle is determined. Thermal quadratic fluctuations of charge and squared total angular momentum, as well as the correlation between them and their correlations with squared orbital angular momentum and squared spin, are examined. We find the conditions when charge and squared total angular momentum at zero temperature are sharp quantum observables rather than mere quantum averages.Comment: 24 pages, minor grammatical changes, journal versio