Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes

An improved method is given for the computation of the stress-energy tensor of a quantized scalar field using adiabatic regularization. The method works for fields with arbitrary mass and curvature coupling in Robertson-Walker spacetimes and is particularly useful for spacetimes with compact spatial sections. For massless fields it yields an analytic approximation for the stress-energy tensor that is similar in nature to those obtained previously for massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure

Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric

Continuing our investigation of the regularization of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001 (2001)] we adopt the modified point separation scheme for the class of optical spacetimes using the Gaussian approximation for the Green functions a la Bekenstein-Parker-Page. In the first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical Schwarzschild spacetime we obtain a finite expression for the noise kernel at the horizon and recover the hot flat space result at infinity. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation backreaction. We show that the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel there. We identify the failure as occurring at the fourth covariant derivative order.Comment: 21 pages, RevTeX

Tunneling ``zero-bias'' anomaly in the quasi-ballistic regime

For the first time, we study the tunneling density of states (DOS) of the interacting electron gas beyond the diffusive limit. A strong correction to the DOS persists even at electron energies exceeding the inverse transport relaxation time, which could not be expected from the well-known Altshuler-Aronov-Lee (AAL) theory. This correction originates from the interference between the electron waves scattered by an impurity and by the Friedel oscillation this impurity creates. Account for such processes also revises the AAL formula for the DOS in the diffusive limit.Comment: 4 pages, 2 .eps figures, submitted to Phys. Rev. Let

Quantum interference effects in p-Si1−xGex quantum wells

Quantum interference effects, such as weak localization and electronelectron interaction (EEI), have been investigated in magnetic fields up to 11 T for hole gases in a set of Si1−xGex quantum wells with 0.13 < x < 0.95. The temperature dependence of the hole phase relaxation time has been extracted from the magneto-resistance between 35 mK and 10 K. The spin-orbit effects that can be described within the Rashba model were observed in low magnetic fields. A quadratic negative magneto-resistance was observed in strong magnetic fields, due to the EEI effect. The hole-phonon scattering time was determined from hole overheating in a strong magnetic field

Van Hove Singularity and D-Wave Pairing in Disordered Superconductors

We apply the coherent potential approximation (CPA) to a simple model for disordered superconductors with d-wave pairing. We demonstrate that whilst the effectiveness of an electronic Van Hove singularity to enhance the transition temperature T$_c$ is reduced by disorder it is not eliminated. In fact we give a qualitative account of changes in the T$_c$ vs. doping curve with increasing disorder and compare our results with experiments on the Y_{0.8}Ca_{0.2}Ba_2(Cu_{1-c}Zn_c)_{3}O_{7-\delta} alloys.Comment: 4 pages of text and 7 postscript file

Weak Chaos in a Quantum Kepler Problem

Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=\lambda |r|^{-\sigma}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has marginal singularity. We study the critical line sigma=1 by means of a renormalization group technique, and describe universality classes of this new transition. An RG equation is written in the basis of states localized in momentum space. The RG flow evolves the distribution of coupling parameters to a universal stationary distribution. Analytic properties of the RG equation are similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma=1 are used to derive scaling laws for transport and to calculate critical exponents.Comment: 28 pages, ReVTeX, 4 EPS figures, to appear in the I. M. Lifshitz memorial volume of Physics Report

Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief discussion of their relevance included. To appear in the proceedings of the 10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th birthda

Renormalization Group and Decoupling in Curved Space: II. The Standard Model and Beyond

We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The QCD sector at low-energies is described in terms of the composite effective fields. For fermions and scalars the massless limit shows perfect correspondence with the conformal anomaly, but similar limit in a massive vector case requires an extra compensating scalar. In all three cases the decoupling goes smoothly and monotonic. A particularly interesting case is the renormalization group flow in the theory with broken supersymmetry, where the sign of one of the beta-functions changes on the way from the UV to IR.Comment: 27 pages, 8 figure

Electron Dephasing in Mesoscopic Metal Wires

The low-temperature behavior of the electron phase coherence time, $\tau_{\phi}$, in mesoscopic metal wires has been a subject of controversy recently. Whereas theory predicts that $\tau_{\phi}(T)$ in narrow wires should increase as $T^{-2/3}$ as the temperature $T$ is lowered, many samples exhibit a saturation of $\tau_{\phi}$ below about 1 K. We review here the experiments we have performed recently to address this issue. In particular we emphasize that in sufficiently pure Ag and Au samples we observe no saturation of $\tau_{\phi}$ down to our base temperature of 40 mK. In addition, the measured magnitude of $\tau_{\phi}$ is in excellent quantitative agreement with the prediction of the perturbative theory of Altshuler, Aronov and Khmelnitskii. We discuss possible explanations why saturation of $\tau_{\phi}$ is observed in many other samples measured in our laboratory and elsewhere, and answer the criticisms raised recently by Mohanty and Webb regarding our work.Comment: 14 pages, 3 figures; to appear in proceedings of conference "Fundamental Problems of Mesoscopic Physics", Granada, Spain, 6-11 September, 200