79 research outputs found
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
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
Effective Field Theory Program for Conformal Quantum Anomalies
The emergence of conformal states is established for any problem involving a
domain of scales where the long-range, SO(2,1) conformally invariant
interaction is applicable. Whenever a clear-cut separation of ultraviolet and
infrared cutoffs is in place, this renormalization mechanism produces binding
in the strong-coupling regime. A realization of this phenomenon, in the form of
dipole-bound anions, is discussed.Comment: 15 pages. Expanded, with additional calculational details. To be
published in Phys. Rev.
- …