Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe

A trick for passing degenerate points in Ashtekar formulation

We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite, we conclude that an essential trick for such a continuous evolution is in complexifying variables. In order to restrict the complex region locally, we propose some `reality recovering' conditions on spacetime. Using a degenerate solution derived by pull-back technique, and integrating the dynamical equations numerically, we show that this idea works in an actual dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style file are include

Spectra of phase point operators in odd prime dimensions and the extended Clifford group

We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields. To do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field. Auxiliary results include a derivation of the conjugacy classes of ${\rm ESL}(2, \mathbb{F}_N)$.Comment: Latex, 19page

Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states

A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a cyclotomic field. By including Galois unitaries we are able to remove a mismatch between the finite projective group acting on the bases on the one hand, and the set of those permutations of the bases that can be implemented as transformations in Hilbert space on the other hand. In particular we show that there exist transformations that cycle through all the bases in every dimension which is an odd power of an odd prime. (For even primes unitary MUB-cyclers exist.) These transformations have eigenvectors, which are MUB-balanced states (i.e. rotationally symmetric states in the original terminology of Wootters and Sussman) if and only if d = 3 modulo 4. We conjecture that this construction yields all such states in odd prime power dimension.Comment: 32 pages, 2 figures, AMS Latex. Version 2: minor improvements plus a few additional reference

The monomial representations of the Clifford group

We show that the Clifford group - the normaliser of the Weyl-Heisenberg group - can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.Comment: Additional author and exact solutions to the SIC problem in dimension 16 adde

Low energy dynamics of spinor condensates

We present a derivation of the low energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate, for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet, for which the low energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas

Analysis of complete positivity conditions for quantum qutrit channels

We present an analysis of complete positivity (CP) constraints on qutrit quantum channels that have a form of affine transformations of generalized Bloch vector. For diagonal (damping) channels we derive conditions analogous to the ones that in qubit case produce tetrahedron structure in the channel parameter space.Comment: 12 pages, 8 figures (.eps), minor changes in the text and formula

Disentanglement of two harmonic oscillators in relativistic motion

We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time ("sudden death"). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.Comment: 16 pages, 8 figures; typos added, minor changes in Secs. I and

Particle alignments and shape change in 66^{66}Ge and 68^{68}Ge

The structure of the $N \approx Z$ nuclei $^{66}$Ge and $^{68}$Ge is studied by the shell model on a spherical basis. The calculations with an extended $P+QQ$ Hamiltonian in the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$, $1g_{9/2}$) succeed in reproducing experimental energy levels, moments of inertia and $Q$ moments in Ge isotopes. Using the reliable wave functions, this paper investigates particle alignments and nuclear shapes in $^{66}$Ge and $^{68}$Ge. It is shown that structural changes in the four sequences of the positive- and negative-parity yrast states with even $J$ and odd $J$ are caused by various types of particle alignments in the $g_{9/2}$ orbit. The nuclear shape is investigated by calculating spectroscopic $Q$ moments of the first and second $2^+$ states, and moreover the triaxiality is examined by the constrained Hatree-Fock method. The changes of the first band crossing and the nuclear deformation depending on the neutron number are discussed.Comment: 18 pages, 21 figures; submitted to Phys. Rev.

Period multiplication in a parametrically driven superconducting resonator

We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength resonator, with frequencies $n\omega$ close to multiples, $n=2,\,3,\,4,\,5$, of the resonator fundamental mode and observe intense output radiation at $\omega$. The output field manifests $n$-fold degeneracy with respect to the phase, the $n$ states are phase shifted by $2\pi/n$ with respect to each other. Our demonstration verifies the theoretical prediction by Guo et al. in PRL 111, 205303 (2013), and paves the way for engineering complex macroscopic quantum cat states with microwave photons