Electrical Resistivity of a Thin Metallic Film

The electrical resistivity of a pure sample of a thin metallic film is found to depend on the boundary conditions. This conclusion is supported by a free-electron model calculation and confirmed by an ab initio relativistic Korringa-Kohn-Rostoker computation. The low-temperature resistivity is found to be zero for a free-standing film (reflecting boundary conditions) but nonzero when the film is sandwiched between two semi-infinite samples of the same material (outgoing boundary conditions). In the latter case, this resistivity scales inversely with the number of monolayers and is due to the background diffusive scattering by a finite lattice.Comment: 20 pages. To be published in Physical Review B, December 15, 199

Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates

The path-integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat spacetime geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.Comment: 16 page

Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics; 1, General Theory

This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Transmuting potentials are completely characterized and their general properties are derived. A strategy for dimensional renormalization of these systems is presented, both for the bound-state and scattering sectors. Finally, the emergence of an energy scale from the renormalization procedure is explicitly illustrated for the two-dimensional delta-function potential

Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic outcome.Comment: 23 pages, 1 figure. v2 & v3: expanded explanations and proofs, references added, typos corrected; v3: published versio

Origin of the anomalies: the modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe

Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange

Atom capture by nanotube and scaling anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of bound state. Binding of the polarizable atoms in the coupling constant interval \eta^2\in[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in literature.Comment: Accepted in Int.J.Theor.Phy