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

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure

A multi-paradigm language for reactive synthesis

This paper proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms, extended with past LTL. The implementation translates Promela to input for the Slugs synthesizer and is written in Python. The AMBA AHB bus case study is revisited and synthesized efficiently, identifying the need to reorder binary decision diagrams during strategy construction, in order to prevent the exponential blowup observed in previous work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078

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

Bounded LTL Model Checking with Stable Models

In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin

Shaping an ultracold atomic soliton in a travelling wave laser beam

An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton.This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a time dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping can be obtained in the force-free case by chirping the laser frequency thus representing a way of coherent control of the soliton form. The experimental consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let

Support for Systematic Code Reviews with the SCRUB Tool

SCRUB is a code review tool that supports both large, team-based software development efforts (e.g., for mission software) as well as individual tasks. The tool was developed at JPL to support a new, streamlined code review process that combines human-generated review reports with program-generated review reports from a customizable range of state-of-the-art source code analyzers. The leading commercial tools include Codesonar, Coverity, and Klocwork, each of which can achieve a reasonably low rate of false-positives in the warnings that they generate. The time required to analyze code with these tools can vary greatly. In each case, however, the tools produce results that would be difficult to realize with human code inspections alone. There is little overlap in the results produced by the different analyzers, and each analyzer used generally increases the effectiveness of the overall effort. The SCRUB tool allows all reports to be accessed through a single, uniform interface (see figure) that facilitates brows ing code and reports. Improvements over existing software include significant simplification, and leveraging of a range of commercial, static source code analyzers in a single, uniform framework. The tool runs as a small stand-alone application, avoiding the security problems related to tools based on Web browsers. A developer or reviewer, for instance, must have already obtained access rights to a code base before that code can be browsed and reviewed with the SCRUB tool. The tool cannot open any files or folders to which the user does not already have access. This means that the tool does not need to enforce or administer any additional security policies. The analysis results presented through the SCRUB tool s user interface are always computed off-line, given that, especially for larger projects, this computation can take longer than appropriate for interactive tool use. The recommended code review process that is supported by the SCRUB tool consists of three phases: Code Review, Developer Response, and Closeout Resolution. In the Code Review phase, all tool-based analysis reports are generated, and specific comments from expert code reviewers are entered into the SCRUB tool. In the second phase, Developer Response, the developer is asked to respond to each comment and tool-report that was produced, either agreeing or disagreeing to provide a fix that addresses the issue that was raised. In the third phase, Closeout Resolution, all disagreements are discussed in a meeting of all parties involved, and a resolution is made for all disagreements. The first two phases generally take one week each, and the third phase is concluded in a single closeout meeting

A low-offset low-voltage CMOS Op Amp with rail-to-rail input and output ranges

A low voltage CMOS op amp is presented. The circuit uses complementary input pairs to achieve a rail-to-rail common mode input voltage range. Special attention has been given to the reduction of the op amp's systematic offset voltage. Gain boost amplifiers are connected in a special way to provide not only an increase of the low-frequency open-loop gain but also a significant reduction of the systematic offset voltag

Concept of Formation Length in Radiation Theory

The features of electromagnetic processes are considered which connected with finite size of space region in which final particles (photon, electron-positron pair) are formed. The longitudinal dimension of the region is known as the formation length. If some external agent is acting on an electron while traveling this distance the emission process can be disrupted. There are different agents: multiple scattering of projectile, polarization of a medium, action of external fields, etc. The theory of radiation under influence of the multiple scattering, the Landau-Pomeranchuk-Migdal (LPM) effect, is presented. The probability of radiation is calculated with an accuracy up to "next to leading logarithm" and with the Coulomb corrections taken into account. The integral characteristics of bremsstrahlung are given, it is shown that the effective radiation length increases due to the LPM effect at high energy. The LPM effect for pair creation is also presented. The multiple scattering influences also on radiative corrections in a medium (and an external field too) including the anomalous magnetic moment of an electron and the polarization tensor as well as coherent scattering of a photon in a Coulomb field. The polarization of a medium alters the radiation probability in soft part of spectrum. Specific features of radiation from a target of finite thickness include: the boundary photon emission, interference effects for thin target, multi-photon radiation. The experimental study of LPM effect is described. For electron-positron colliding beams following items are discussed: the separation of coherent and incoherent mechanisms of radiation, the beam-size effect in bremsstrahlung, coherent radiation and mechanisms of electron-positron creation.Comment: Revised review paper, 96 pages, 28 figures. Description of SLAC E-146 experiment removed, discussion of CERN SPS experiment adde