Phase Transition in Lattice Surface Systems with Gonihedric Action

We prove the existence of an ordered low temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The statistical weight of each surface configuration depends only on the mean extrinsic curvature and on an interaction term arising when two surfaces touch each other along some contour. The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version of the gonihedric string, which is an action for triangulated random surfaces.Comment: 17 pages, Postscript figures include

Colliding Plane Waves in String Theory

We construct colliding plane wave solutions in higher dimensional gravity theory with dilaton and higher form flux, which appears naturally in the low energy theory of string theory. Especially, the role of the junction condition in constructing the solutions is emphasized. Our results not only include the previously known CPW solutions, but also provide a wide class of new solutions that is not known in the literature before. We find that late time curvature singularity is always developed for the solutions we obtained in this paper. This supports the generalized version of Tipler's theorem in higher dimensional supergravity.Comment: latex, 25 pages, 1 figur

Many worlds in one

A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as \O-regions. We argue that the number of possible histories which may take place inside of an \O-region, from the time of recombination up to the present time, is finite. Hence, there are an infinite number of \O-regions with identical histories up to the present, but which need not be identical in the future. Moreover, all histories which are not forbidden by conservation laws will occur in a finite fraction of all \O-regions. The ensemble of \O-regions is reminiscent of the ensemble of universes in the many-world picture of quantum mechanics. An important difference, however, is that other \O-regions are unquestionably real.Comment: 9 pages, 2 figures, comments and references adde

Low temperature expansion of the gonihedric Ising model

We investigate a model of closed $(d-1)$-dimensional soft-self-avoiding random surfaces on a $d$-dimensional cubic lattice. The energy of a surface configuration is given by $E=J(n_{2}+4k n_{4})$, where $n_{2}$ is the number of edges, where two plaquettes meet at a right angle and $n_{4}$ is the number of edges, where 4 plaquettes meet. This model can be represented as a $\Z_{2}$-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic next-nearest-neighbour- and plaquette-interaction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaption of Peierls argument, we prove the existence of infinitely many ordered low temperature phases for the case $k=0$. A low temperature expansion of the free energy in 3 dimensions up to order $x^{38}$ ($x={e}^{-\beta J}$) shows, that for $k>0$ only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order $x^{44}$ for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results.Comment: 27 pages, Postscript figures include

Correlation inequalities for classical and quantum XY models

We review correlation inequalities of truncated functions for the classical and quantum XY models. A consequence is that the critical temperature of the XY model is necessarily smaller than that of the Ising model, in both the classical and quantum cases. We also discuss an explicit lower bound on the critical temperature of the quantum XY model.Comment: 13 pages. Submitted to the volume "Advances in Quantum Mechanics: contemporary trends and open problems" of the INdAM-Springer series, proceedings of the INdAM meeting "Contemporary Trends in the Mathematics of Quantum Mechanics" (4-8 July 2016) organised by G. Dell'Antonio and A. Michelangel

Sensitive Radio-Frequency Measurements of a Quantum Dot by Tuning to Perfect Impedance Matching

Electrical readout of spin qubits requires fast and sensitive measurements, which are hindered by poor impedance matching to the device. We demonstrate perfect impedance matching in a radio-frequency readout circuit, using voltage-tunable varactors to cancel out parasitic capacitances. An optimized capacitance sensitivity of 1.6   aF / √ Hz is achieved at a maximum source-drain bias of 170 − μ V root-mean-square and with a bandwidth of 18 MHz. Coulomb blockade in a quantum-dot is measured in both conductance and capacitance, and the two contributions are found to be proportional as expected from a quasistatic tunneling model. We benchmark our results against the requirements for single-shot qubit readout using quantum capacitance, a goal that has so far been elusive

Methane Mitigation:Methods to Reduce Emissions, on the Path to the Paris Agreement

The atmospheric methane burden is increasing rapidly, contrary to pathways compatible with the goals of the 2015 United Nations Framework Convention on Climate Change Paris Agreement. Urgent action is required to bring methane back to a pathway more in line with the Paris goals. Emission reduction from “tractable” (easier to mitigate) anthropogenic sources such as the fossil fuel industries and landfills is being much facilitated by technical advances in the past decade, which have radically improved our ability to locate, identify, quantify, and reduce emissions. Measures to reduce emissions from “intractable” (harder to mitigate) anthropogenic sources such as agriculture and biomass burning have received less attention and are also becoming more feasible, including removal from elevated-methane ambient air near to sources. The wider effort to use microbiological and dietary intervention to reduce emissions from cattle (and humans) is not addressed in detail in this essentially geophysical review. Though they cannot replace the need to reach “net-zero” emissions of CO2, significant reductions in the methane burden will ease the timescales needed to reach required CO2 reduction targets for any particular future temperature limit. There is no single magic bullet, but implementation of a wide array of mitigation and emission reduction strategies could substantially cut the global methane burden, at a cost that is relatively low compared to the parallel and necessary measures to reduce CO2, and thereby reduce the atmospheric methane burden back toward pathways consistent with the goals of the Paris Agreement

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ` Thomas Fermi' (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone

Coulomb gauge approach to (qqg)over-bar hybrid mesons

An effective Coulomb gauge Hamiltonian, H-eff, is used to calculate the light ( u (u) over barg), strange ( s (s) over barg) and charmed (c (c) over barg) hybrid meson spectra. For the same two parameter H-eff providing glueball masses consistent with lattice results and a good description of the observed u, d, s and c quark mesons, a large-scale variational treatment predicts that the lightest hybrid has J(PC) = 0(++) and mass 2.1 GeV. The lightest exotic 1(-+) state is just above 2.2 GeV, near the upper limit of lattice and flux tube predictions. These theoretical formulations all indicate that the observed 1(-+) pi(1)(1600) and, more clearly, pi(1)(1400) are not hybrid states. The Coulomb gauge approach further predicts that in the strange and charmed sectors, respectively, the ground state hybrids have 1(+-) with masses 2.1 and 3.8 GeV, while the. rst exotic 1( +) states are at 2.4 and 4.0 GeV. Finally, using our hybrid wavefunctions and the Franck-Condon principle, a novel experimental signature is presented to assist heavy hybrid meson searches