Proof of the generalized Lieb-Wehrl conjecture for integer indices larger than one

Gnutzmann and Zyczkowski have proposed the Renyi-Wehrl entropy as a generalization of the Wehrl entropy, and conjectured that its minimum is obtained for coherent states. We prove this conjecture for the Renyi index q=2,3,... in the cases of compact semisimple Lie groups. A general formula for the minimum value is given.Comment: 8 pages, typos fixed, published versio

Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas

By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.Comment: 5 pages, 3 figure

Using Pilot Systems to Execute Many Task Workloads on Supercomputers

High performance computing systems have historically been designed to support applications comprised of mostly monolithic, single-job workloads. Pilot systems decouple workload specification, resource selection, and task execution via job placeholders and late-binding. Pilot systems help to satisfy the resource requirements of workloads comprised of multiple tasks. RADICAL-Pilot (RP) is a modular and extensible Python-based pilot system. In this paper we describe RP's design, architecture and implementation, and characterize its performance. RP is capable of spawning more than 100 tasks/second and supports the steady-state execution of up to 16K concurrent tasks. RP can be used stand-alone, as well as integrated with other application-level tools as a runtime system

Moments of generalized Husimi distributions and complexity of many-body quantum states

We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to the systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution.Comment: published version, 33 pages, 7 figre

Second moment of the Husimi distribution as a measure of complexity of quantum states

We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.Comment: 25 pages, 10 figures. to appear in PR

Foundation of Statistical Mechanics under experimentally realistic conditions

We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared to the resolution limit. Both properties are fulfilled under many, if not all, experimentally realistic conditions. At equilibrium, the predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let

Prediction of melt depth in selected architectural materials during high power diode laser treatment

The development of an accurate analysis procedure for many laser applications, including the surface treatment of architectural materials, is extremely complicated due to the multitude of process parameters and materials characteristics involved. A one-dimensional analytical model based on Fourier’s law, with quasi-stationary situations in an isotropic and inhomogeneous workpiece with a parabolic meltpool geometry being assumed, was successfully developed. This model, with the inclusion of an empirically determined correction factor, predicted high power diode laser (HPDL) induced melt depths in clay quarry tiles, ceramic tiles and ordinary Portland cement (OPC) that were in close agreement with those obtained experimentally. It was observed, however, that as the incident laser line energy increased (>15 W mm-1 s-1/2), the calculated and the experimental melt depths began to diverge at an increasing rate. It is believed that this observed increasing discrepancy can be attributed to the fact the model developed neglects sideways conduction which, although it can be reasonably neglected at low energy densities, becomes significant at higher energy densities since one-dimensional heat transfer no longer holds true

Simulated Tempering and Magnetizing: An Application of Two-Dimensional Simulated Tempering to Two-Dimensional Ising Model and Its Crossover

We performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional ST's applicability to dealing with phase transitions and to study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus, this simulation can be referred to as "Simulated Tempering and Magnetizing (STM)." We also performed the "Simulated Magnetizing" (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. As has been discussed by previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Flipping of the entire magnetization did not occur in the SM simulations under $T_\mathrm{c}$ in large lattice-size simulations. However, the phase changed through the high temperature region in the STM simulations. Thus, the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study wide area of the phase space. We then discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior was clearly observed in the simulations in agreement with the theoretical implications.Comment: 15 pages, (Revtex4-1), 23 figures, 1 video (link