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 $1/r^n$ singular potential (with $n\geq 2$) 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 Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; ArgentinaFil: Fanchiotti, Huner. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; ArgentinaFil: García Canal, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; 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 Nic_{c}Fe1−c_{1-c} 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 Ni$_{c}$Fe$_{1-c}$. 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