Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions

Several authors have considered the possibility of a generalized Bose-Einstein condensation (BEC) in which a band of low states is occupied so that the total occupation number is macroscopic, even if the occupation number of each state is not extensive. The Hohenberg theorem (HT) states that there is no BEC into a single state in 2D; we consider its validity for the case of a generalized condensation and find that, under certain conditions, the HT does not forbid a BEC in 2D. We discuss whether this situation actually occurs in any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys., Quantum Fluids and Solids Conference QFS200

Pension systems in East Asia and the Pacific : challenges and opportunities

With the recovery from the recent crisis, countries of the East Asia and Pacific region are rethinking their financial, and social policy, including old-age protection. Population aging, in combination with ongoing urbanization, and economic transformation, will place increasing pressure on traditional family care arrangements. Coverage under formal pension systems is generally low, and the absence of social safety nets for the needy elderly, poses risks in the face of breaks in the economic growth path. In addition to common systemic challenges, formal old-age income support systems confront issues specific to their design type: 1) The national provident fund, and social security systems with reserve funds, have demonstrated problems with investment policy, and performance, governance and management. 2) In the established market economies, social security systems are fiscally unsustainable in the long run, and often have a weak benefit-contribution link. 3) These types of systems encounter additional problems in transition economies, including low contribution collection from previously socialized enterprises. Options addressed by the paper involve the adoption of an integrated view on retirement income provision, averting fiscal un-sustainability, and, integrating public, and private sector pensions. Additionally, moving toward a multi-pillar structure with prudent coverage extension, and, fostering financial markets, to allow decentralized pension funds management, are also suggested.Health Economics&Finance,Public Sector Economics,Pensions&Retirement Systems,Environmental Economics&Policies,Banks&Banking Reform

Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas

We present Quantum Monte Carlo calculations with up to N=576000 interacting bosons in a quasi two-dimensional trap geometry closely related to recent experiments with atomic gases. The density profile of the gas and the non-classical moment of inertia yield intrinsic signatures for the Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body density matrix, we compute the condensate fraction, which is quite large for small systems. It decreases slowly with increasing system sizes, vanishing in the thermodynamic limit. We interpret our data in the framework of the local-density approximation, and point out the relevance of our results for the analysis of experiments.Comment: 4 pages, 4 figure

D-optimal matrices of orders 118, 138, 150, 154 and 174

We construct supplementary difference sets (SDS) with parameters $(59;28,22;21)$, $(69;31,27;24)$, $(75;36,29;28)$, $(77;34,31;27)$ and $(87;38,36;31)$. These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs of orders 138,154 and 174 were known. While a DO-design (not of two-circulant type) of order 150 was constructed previously by Holzmann and Kharaghani, no such design of two-circulant type was known. The smallest undecided order for DO-designs is now 198. We use a novel property of the compression map to speed up some computations.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1409.596

Optimal Scheduling Using Branch and Bound with SPIN 4.0

The use of model checkers to solve discrete optimisation problems is appealing. A model checker can first be used to verify that the model of the problem is correct. Subsequently, the same model can be used to find an optimal solution for the problem. This paper describes how to apply the new PROMELA primitives of SPIN 4.0 to search effectively for the optimal solution. We show how Branch-and-Bound techniques can be added to the LTL property that is used to find the solution. The LTL property is dynamically changed during the verification. We also show how the syntactical reordering of statements and/or processes in the PROMELA model can improve the search even further. The techniques are illustrated using two running examples: the Travelling Salesman Problem and a job-shop scheduling problem

PHENIX and the Reaction Plane: Recent Results

During the past several years, experiments at RHIC have established that a dense partonic medium is produced in Au+Au collisions at sqrt(s)=200 GeV. Subsequently, a primary goal of analysis has been to understand and characterize the dynamics underlying this new form of matter. Among the many probes available, the measurements with respect to the reaction plane has proven to be crucial to our understanding of a wide range of topics, from the hydrodynamics of the initial expansion of the collision region to high-pt jet quenching phenomena. Few tools have the ability to shed light on such a wide variety of observables as the reacion plane. In this article, we discuss recent PHENIX measurements with respect to the reaction plane, and the implications for understanding the underlying physics of RHIC collisions.Comment: 9 pages, 13 figures, Submitted for proceedings to the Winter Workshop on Nuclear Dynamics 2010, Ocho Rios, Jamaic

Directed Explicit Model Checking with HSF-SPIN

We present the explicit state model checker HSF-SPIN which is based on the model checker SPIN and its Promela modeling language. HSF-SPIN incorporates directed search algorithms for checking safety and a large class of LTL-specified liveness properties. We start off from the A* algorithm and define heuristics to accelerate the search into the direction of a specified failure situation. Next we propose an improved nested depth-first search algorithm that exploits the structure of Promela Never-Claims. As a result of both improvements, counterexamples will be shorter and the explored part of the state space will be smaller than with classical approaches, allowing to analyze larger state spaces. We evaluate the impact of the new heuristics and algorithms on a set of protocol models, some of which are real-world industrial protocols

Instability in a Two-Dimensional Dilute Interacting Bose System

The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition temperature, as a function of the scattering length, that are in good agreement with those of Green’s function and quantum Monte Carlo methods. We have applied the same equations to a uniform two-dimensional system and find that, as we alter the chemical potential, an instability develops so that the self-consistent equations no longer have a solution. This instability, which seems to indicate that interactions restore a transition, occurs at a non-zero value of an effective chemical potential. The non-linear equations are limited to temperatures greater than or equal to Tc, so that they do not indicate the nature of the new stable state, but we speculate concerning whether it is a Kosterlitz-Thouless state or a “smeared” BEC, which might avoid any violation of the Hohenberg theorem, as described in an accompanying paper

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur