Refined limit multiplicity for varying conductor

Recent results by Abert, Bergeron, Biringer et al., Finis, Lapid and Mueller, and Shin and Templier have extended the limit multiplicity property to quite general classes of groups and sequences of level subgroups. Automorphic representations in the limit multiplicity problem are traditionally counted with multiplicity according to the number of fixed vectors of a level subgroup; our goal is to perform a slightly more refined analysis and count only automorphic representations with a given conductor with multiplicity 1.Comment: 13 page

Quantacell: Powerful charging of quantum batteries

We study the problem of charging a quantum battery in finite time. We demonstrate an analytical optimal protocol for the case of a single qubit. Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted. The exemplary analytic argument for this quantum advantage in the charging power is backed up by numerical analysis using optimal control techniques. It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable.Comment: 11 pages, 3 figures, comments welcom

Absorption Bands of Hydrogen Cyanide Gas in the Near Infrared

The absorption spectrum of gaseous hydrogen cyanide has been investigated by photographic methods in the region λ7000-9200. Two weak bands of very simple structure were found, having P and R branches but no Q branches. The band at λ7912 is apparently a harmonic of a fundamental band at 3.04μ, and the very weak band at λ8563 is a combination band. The hydrogen cyanide molecule is linear in the normal state, and has a moment of inertia I=18.79×10^-40 g·cm^2. The distance of separation of the carbon and nitrogen atoms is estimated to be 1.15×10^-8 cm. Hydrogen cyanide is discussed in regard to its three fundamental oscillations which have frequencies 3290, 2090, and 710, respectively, and in regard to its dissociation energy and dissociation products. The evidence requires a molecular structure represented by the formula HCN, and shows that the normal molecule is built from a normal hydrogen atom and a normal CN radical. The absorption of cyanogen gas has also been investigated in the photographic infrared, but no absorption bands could be detected

Phase transition of a one-dimensional Ising model with distance-dependent connections

The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta(l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising model on networks with different $m$ values, this paper discusses the impact of the global correlation, which decays with the increase of $m$, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter $[]$, it is observed that in the whole range of $0<m<2$, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.Comment: 5 pages,8 figure

Enhancing the charging power of quantum batteries

Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when $N$ batteries are charged collectively. We first derive analytic upper bounds for the collective \emph{quantum advantage} in charging power for two choices of constraints on the charging Hamiltonian. We then highlight the importance of entanglement by proving that the quantum advantage vanishes when the collective state of the batteries is restricted to be in the separable ball. Finally, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted, i.e., at most $k$ batteries are interacting. Our result is a fundamental limit on the advantage offered by quantum technologies over their classical counterparts as far as energy deposition is concerned.Comment: In this new updated version Theorem 1 has been changed with Proposition 1. The paper has been published on PRL, and DOI included accordingl

Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model

We apply the recently developed critical minimum energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via the Wang-Landau and broad histogram methods in a unified implementation by employing the N-fold version of the Wang-Landau scheme. The random-fields are obtained from a bimodal distribution ($h_{i}=\pm2$), and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from $L=4$ to $L=32$. Observing the finite-size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat. The lack of self-averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above.Comment: 8 pages, 7 figures, extended version with two new figures, version as accepted for publication to Physical Review

Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1