139 research outputs found
Anomalous Commutator Algebra for Conformal Quantum Mechanics
The structure of the commutator algebra for conformal quantum mechanics is
considered. Specifically, it is shown that the emergence of a dimensional scale
by renormalization implies the existence of an anomaly or quantum-mechanical
symmetry breaking, which is explicitly displayed at the level of the generators
of the SO(2,1) conformal group. Correspondingly, the associated breakdown of
the conservation of the dilation and special conformal charges is derived.Comment: 23 pages. A few typos corrected in the final version (which agrees
with the published Phys. Rev. D article
SO(2,1) conformal anomaly: Beyond contact interactions
The existence of anomalous symmetry-breaking solutions of the SO(2,1)
commutator algebra is explicitly extended beyond the case of scale-invariant
contact interactions. In particular, the failure of the conservation laws of
the dilation and special conformal charges is displayed for the two-dimensional
inverse square potential. As a consequence, this anomaly appears to be a
generic feature of conformal quantum mechanics and not merely an artifact of
contact interactions. Moreover, a renormalization procedure traces the
emergence of this conformal anomaly to the ultraviolet sector of the theory,
within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final 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
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
Singular Potentials and Limit Cycles
We show that a central singular potential (with ) is
renormalized by a one-parameter square-well counterterm; low-energy observables
are made independent of the square-well width by adjusting the square-well
strength. We find a closed form expression for the renormalization-group
evolution of the square-well counterterm.Comment: 15 pages LaTex, 5 eps figures, error in figures and text correcte
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
Analytic structure of the S-matrix for singular quantum mechanics
The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.Fil: Camblong, Horacio E.. University of San Francisco; Estados UnidosFil: Epele, Luis Nicolas. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de FĂsica. Laboratorio de FĂsica TeĂłrica; ArgentinaFil: Fanchiotti, Huner. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de FĂsica. Laboratorio de FĂsica TeĂłrica; ArgentinaFil: GarcĂa Canal, Carlos Alberto. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de FĂsica. Laboratorio de FĂsica TeĂłrica; Argentin
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
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.
Electrical transport properties of bulk NiFe alloys and related spin-valve systems
Within the Kubo-Greenwood formalism we use the fully relativistic,
spin-polarized, screened Korringa-Kohn-Rostoker method together with the
coherent-potential approximation for layered systems to calculate the
resistivity for the permalloy series NiFe. We are able to
reproduce the variation of the resistivity across the entire series; notably
the discontinuous behavior in the vicinity of the structural phase transition
from bcc to fcc. The absolute values for the resistivity are within a factor of
two of the experimental data. Also the giant magnetoresistance of a series of
permalloy-based spin-valve structures is estimated; we are able to reproduce
the trends and values observed on prototypical spin-valve structures.Comment: 6 pages, ReVTeX + 4 figures (Encapsulated Postscript), submitted to
PR
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