Geodesic measures of the landscape

We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic time-like geodesics have undesirable dependence on initial conditions. In contrast, the predictions extracted from ``eternal'' geodesics, which never enter terminal vacua, do not suffer from this problem. We derive measure equations for ensembles of geodesics and discuss possible interpretations of initial conditions in eternal inflation.Comment: 7 pages, 4 figure

On the concurrence of superpositions of many states

In this paper we use the \textit{concurrence vector}, as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by \textit{I-concurrence}, so that our results can be compared to those given in [Phys. Rev. A {\bf 76}, 042328 (2007)]. We obtain a tighter lower bound in the case that two superposed states are orthogonal. We also show that when the two superposed states are not necessarily orthogonal, both lower and bounds are, in general, tighter than the bounds given in terms of the I-concurrence. An extension of the results to the case with more than two states in the superpositions is also given.Comment: 1 figure, 8 page

Quantitative ultraviolet measurements on wetted thin-layer chromatography plates using a charge-coupled device camera

This paper presents the first study of the UV imaging of spots on thin-layer chromatographic plates whilst still wet with solvent. Imaging of spots of benzophenone during and after development was carried out using a charge-coupled device camera. Limits of detection were found to be 5 ng on a wetted plate and 3 ng for a dry plate and the relationship between peak area and sample loading was found to be linear in the low nanograrn range over an order of magnitude for both wet and dry modes with r(2) values > 0.99. It was found that UV measurements on wet glass-backed plates suffer from low sensitivity; however, the use of aluminium-backed plates gave increased sensitivity. The apparent absorption coefficient (epsilon(app)) of 10AU m(2) g(-1) at 254 nm is consistent with reflection of the light from the aluminium surface with a double pass through the sorbent layer, and suggests that use of aluminium-backed plates should enable monitoring of separations by UV absorbance during TLC development. (c) 2008 Elsevier B.V. All rights reserved

Antiferromagnetic ordering of energy levels for spin ladder with four-spin cyclic exchange: Generalization of the Lieb-Mattis theorem

The Lieb-Mattis theorem is generalized to an antiferromagnetic spin-ladder model with four-spin cyclic exchange interaction. We prove that for J>2K, the antiferromagnetic ordering of energy levels takes place separately in two sectors, which remain symmetric and antisymmetric under the reflection with respect to the longitudinal axis of the ladder. We prove also that at the self-dual point J=2K, the Lieb-Mattis rule holds in the sectors with fixed number of rung singlets. In both cases, it agrees with the similar rule for Haldane chain with appropriate spin number.Comment: 4 pages, some references updated and added, typos corrected, to appear in Phys. Rev.

Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice

We calculate rigorous lower bounds for the ground state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-$q$ series expansions for the sq and sc lattices and also present numerical comparisons.Comment: 7 pages, late

Energy-level ordering and ground-state quantum numbers for frustrated two-leg spin-1/2 ladder model

The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels on bipartite lattices is generalized to finite-size two-leg spin-1/2 ladder model frustrated by diagonal interactions. For reflection-symmetric model with site-dependent interactions we prove exactly that the lowest energies in sectors with fixed total spin and reflection quantum numbers are monotone increasing functions of total spin. The nondegeneracy of most levels is proved also. We also establish the uniqueness and obtain the spin value of the lowest-level multiplet in the whole sector formed by reflection-symmetric (antisymmetric) states. For a wide range of coupling constants, we prove that the ground state is a unique spin singlet. For other values of couplings, it may be also a unique spin triplet or may consist of both multiplets. Similar results have been obtained for the ladder with arbitrary boundary impurity spin. Some partial results have also been obtained in the case of periodical boundary conditions.Comment: 17 page

The effect of exercise on resilience, its mediators and moderators, in a general population during the UK COVID-19 pandemic in 2020: a cross-sectional online study.

BackgroundResilience is central to positive mental health and well-being especially when faced with adverse events. Factors such as exercise, location, sleep, mental health, and personality are moderators and mediators of resilience. However, the impact of these factors on resilience during severe adverse events are unknown. The present study examined how the COVID-19 pandemic affected resilience and its moderators and mediators by investigating whether there was a difference in resilience and quality of life between people with varying levels of exercise, including those who changed their exercise levels pre and during a COVID-19-related lockdown, and whether location affected the relationship between levels of exercise and resilience and quality of life.MethodsFollowing ethical approval, a cross-sectional online survey capturing data on self-reported key moderators and mediators of resilience before and during the COVID-19 lockdown imposed on the 23rd March 2020 in the UK was distributed via social media and completed over a three week time period during July 2020 via a self-selecting sample of the general population (N = 85). The key moderators and mediators of resilience the survey assessed were exercise, location, life-orientation, mental health, and sleep quality. All data were self-reported.ResultsParticipants' exercise intensity level increased as resilience increased (F(2,82) = 4.22, p = .003: Wilks' lambda = .82, partial n2 = 0.09). The relationship between exercise, and resilience and quality of life was independent of sleep and mental health status pre-lockdown (p = .013, p = .027 respectively). In the face of the COVID-19 pandemic, this relationship was dependent on mental health but not sleep quality (p = ConclusionExercise is strongly correlated to resilience and during a pandemic such as COVID-19 it becomes a mechanism in which to moderate resilience. The relationship between exercise and resilience is supported by this study. The influence that a pandemic had on mental health is mediated by its effect on quality of life

Slow synaptic transmission in frog sympathetic ganglia

Bullfrog ganglia contain two classes of neurone, B and C cells, which receive different inputs and exhibit different slow synaptic potentials. B cells, to which most effort has been directed, possess slow and late slow EPSPs. The sEPSP reflects a muscarinic action of acetylcholine released from boutons on B cells, whereas the late sEPSP is caused by a peptide (similar to teleost LHRH) released from boutons on C cells. During either sEPSP there is a selective reduction in two slow potassium conductances, designated 'M' and 'AHP'. The M conductance is voltage dependent and the AHP conductance is calcium dependent. Normally they act synergistically to prevent repetitive firing of action potentials during maintained stimuli. Computer stimulation of the interactions of these conductances with the other five voltage-dependent conductances present in the membrane allows a complete reconstruction of the effects of slow synaptic transmission on electrical behaviour

Quantal interferometry with dissipative internal motion

In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds of external influences on quantal interference. The concept of mixed-state phase and concomitant gauge invariance is extended to dissipative internal motion. The resulting complex-valued mixed-state interference effects lead to well-known results in the unitary limit and in the case of dissipative motion of pure quantal states. Dissipative interferometry is applied to fault-tolerant geometric quantum computation.Comment: Slight revision, journal reference adde