Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analogue of such a magnetoelectric effect in the thermal (or gravitational) and the magnetic dipole responses in all symmetry classes which admit topologically non-trivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry which lack SU(2) spin rotation symmetry (e.g. due to spin-orbit interactions), such as the B phase of $^3$He, the thermal response is the only probe which can detect the non-trivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover we find, for a significant part of the 'ten-fold' list of topological insulators found in previous work in the absence of interactions, that in general dimensions the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting or not, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure

Statistics and Quantum Chaos

We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.Comment: 12 pages, LateX, no figures, restructured versio

Metastability in the BCS model

We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t. another equilibrium state. The intermediate states are explicitly constructed and their stability properties are derived. The notion of metastability in this genuine quantum system, is expressed by means of energy-entropy balance inequalities and canonical coordinates of observables

Celestial mechanics in Kerr spacetime

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by solving the Hamilton-Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with the radial, polar and azimuthal components of orbital motion. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this article, it is shown that the fundamental frequencies are geometric invariants and explicit formulas in terms of quadratures are derived. The numerical evaluation of these formulas in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or the inclination parameter $\theta_{-}$ are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra

Low-energy limits and renormalization in meson theory

A technique is developed for deriving rigorous expressions for zero-energy mesonic processes. Making use of the ambiguity of mesonic charge renormalization, the coupling constant is defined by zero-energy pion-nucleon scattering. The threshold photomeson production amplitude is also calculated. The experimental value of the coupling constant defined by scattering is at least an order of magnitude less than that of the coupling constant deduced from the photoproduction data. It is shown that pair suppression effects are absent in both cases. The possibility that the results obtained imply disagreement of pseudoscalar theory with experiment is discussed

Comment on "On Mach's critique of Newton and Copernicus"

Hartman and Nissim-Sabat have argued that Mach's idea of the relativity of rotational motion suffers from internal inconsistencies and leads to a contradiction that there cannot be a stationary bucket in a rotating universe. They also claimed that non-inertial electromagnetic and stellar aberration observations can distinguish between a rotating and a stationary universe, whereas according to Mach there cannot be any observable way to distinguish these two cases. We contest these objections.Comment: Six pages, to appear in AJ

Use of Causality Conditions in Quantum Theory

The limitations on scattering amplitudes imposed by causality requirements are deduced from the demand that the commutator of field operators vanish if the operators are taken at points with space-like separations. The problems of the scattering of spin-zero particles by a force center and the scattering of photons by a quantized matter field are discussed. The causality requirements lead in a natural way to the well-known dispersion relation of Kramers and Kronig. A new sum rule for the nuclear photoeffect is derived and the scattering of photons by nucleons is discussed

Cosmological gravitomagnetism and Mach's principle

The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state for cosmological matter, are: 1) The dragging of a gyroscope axis by rotational perturbations of matter beyond the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot is the derivative with respect to cosmic time. 2) If the perturbation of matter is a homogeneous rotation inside some radius around a gyroscope, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For the most general linear cosmological perturbations the time-evolution of all gyroscope spin axes exactly follow a weighted average of the energy currents of cosmological matter. The weight function is the same as in Ampere's law except that the inverse square law is replaced by the Yukawa force with the Hubble-dot cutoff. Our results demonstrate (in first order perturbation theory for FRW cosmologies with k = 0) the validity of Mach's hypothesis that axes of local non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde

Information-Disturbance Theorem for Mutually Unbiased Observables

We derive a novel version of information-disturbance theorems for mutually unbiased observables. We show that the information gain by Eve inevitably makes the outcomes by Bob in the conjugate basis not only erroneous but random

Proof that the Hydrogen-antihydrogen Molecule is Unstable

In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges $(m_{1}^+, m_{2}^-, m_{3}^+, m_{4}^-)$, where all masses are assumed finite, to form the stable system. The obtained stability condition is physical and is expressed through the required minimal ratio of Jacobi masses. In particular this provides the rigorous proof that the hydrogen-antihydrogen molecule is unstable. This is the first result of this sort for four particles.Comment: Submitted to Phys.Rev.Let