Higher level twisted Zhu algebras

The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper we consider the general set-up of a vertex algebra $V$, graded by \G/\Z for some subgroup \G of $\R$ containing $\Z$, and with a Hamiltonian operator $H$ having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level $p$ Zhu algebras \zhu_{p, \G}(V), and we prove the following theorems: For each $p$ there is a bijection between the irreducible \zhu_{p, \G}(V)-modules and the irreducible \G-twisted positive energy $V$-modules, and $V$ is (\G, H)-rational if and only if all its Zhu algebras \zhu_{p, \G}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for $H$. We provide an explicit description of the level $p$ Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra \vir^c and the universal affine Kac-Moody vertex algebra V^k(\g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.Comment: 47 pages, no figure

Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters

We investigate the influence of random errors in external control parameters on the stability of holonomic quantum computation in the case of arbitrary loops and adiabatic connections. A simple expression is obtained for the case of small random uncorrelated errors. Due to universality of mathematical description our results are valid for any physical system which can be described in terms of holonomies. Theoretical results are confirmed by numerical simulations.Comment: 7 pages, 3 figure

Significant Scales in Community Structure

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of "significance" of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine "good" resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.Comment: To appear in Scientific Report

Arrest of flow and emergence of activated processes at the glass transition of a suspension of particles with hard sphere-like interactions

By combining aspects of the coherent and self intermediate scattering functions, measured by dynamical light scattering on a suspension of hard sphere-like particles, we show that the arrest of particle number density fluctuations spreads from the position of the main structure factor peak. Taking the velocity auto-correlation function into account we propose that as density fluctuations are arrested the system's ability to respond to diffusing momentum currents is impaired and, accordingly, the viscosity increases. From the stretching of the coherent intermediate scattering function we read a quantitative manifestation of the undissipated thermal energy, the source of those, ergodicity restoring, processes that short-circuit the sharp transition to a perfect glass.Comment: 9 pages, 4 figure

Generalized Richardson-Gaudin Nuclear Models

The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie algebra. As an example, the $so(5)\sim sp(4)$ model of T=1 pairing is discussed and illustrated for the case of $^{64}$Ge with non-degenerate single-particle energies

The wave equation as a port-Hamiltonian system and a finite-dimensional approximation

The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws

Low-carbohydrate diets affect energy balance and fuel homeostasis differentially in lean and obese rats

In parallel with increased prevalence of overweight people in affluent societies are individuals trying to lose weight, often using low-carbohydrate diets. Nevertheless, long-term metabolic consequences of those diets, usually high in (saturated) fat, remain unclear. Therefore, we investigated long-term effects of high-fat diets with different carbohydrate/protein ratios on energy balance and fuel homeostasis in obese (fa/fa) Zucker and lean Wistar rats. Animals were fed high-carbohydrate (HC), high-fat (HsF), or low-carbohydrate, high-fat, high-protein (LC-HsF-HP) diets for 60 days. Both lines fed the LC-HsF-HP diet displayed reduced energy intake compared with those fed the HsF diet (Zucker, -3.7%) or the HC diet (Wistar rats, -12.4%). This was not associated with lower weight gain relative to HC fed rats, because of increased food efficiencies in each line fed HsF and particularly LC-HsF-HP food. Zucker rats were less glucose tolerant than Wistar rats. Lowest glucose tolerances were found in HsF and particularly in LC-HsF-HP-fed animals irrespective of line, but this paralleled reduced plasma adiponectin levels, elevated plasma resistin levels, higher retroperitoneal fat masses, and reduced insulin sensitivity (indexed by insulin-induced hypoglycemia) only in Wistar rats. In Zucker rats, however, improved insulin responses during glucose tolerance testing and tendency toward increased insulin sensitivities were observed with HsF or LC-HsF-HP feeding relative to HC feeding. Thus, despite adverse consequences of LC-HsF diets on blood glucose homeostasis, principal differences exist in the underlying hormonal regulatory mechanisms, which could have benefits for B-cell functioning and insulin action in the obese state but not in the lean state.

On a Possibility to Measure Thermoelectric Power in SNS Structures

Two dissimilar Josephson junctions, which are connected to a heater can act as precise batteries. Because of the difference in thermoelectric power of these batteries, circuit with two dissimilar batteries, under heat flow $\Delta T\sim 10^{-5}K$ would have a net EMF $10^{-11} V$ around the zero-resistance loop leading to a loop's magnetic flux oscillating in time. It is shown its theoretical value is proportional to both the temperature difference as well as the disparity in the thermoelectric powers of the two junctions.Comment: 5 page

Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum