Generalized Random Phase Approximation and Gauge Theories

Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach to the Random Phase Approximation (RPA) well-known from nuclear physics and recently also employed in pion physics to general bosonic theories with a standard kinetic term. We focus especially on conservation laws, and how they are translated from the full to the approximated theories, demonstrate that the operator approach has the same spectrum as the RPA derived from the time-dependent variational principle, and give - for Yang-Mills theory - a discussion of the moment of inertia connected to the energy contribution of the zero modes to the RPA ground state energy. We also indicate a line of thought that might be useful to improve the results of the Random Phase Approximation.Comment: 66 pages, REVTeX4, uses amsfonts and package longtabl

Reachability of Communicating Timed Processes

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata.Comment: Extended versio

A Decidable Extension of Data Automata

Data automata on data words is a decidable model proposed by Boja\'nczyk et al. in 2006. Class automata, introduced recently by Boja\'nczyk and Lasota, is an extension of data automata which unifies different automata models on data words. The nonemptiness of class automata is undecidable, since class automata can simulate two-counter machines. In this paper, a decidable model called class automata with priority class condition, which restricts class automata but strictly extends data automata, is proposed. The decidability of this model is obtained by establishing a correspondence with priority multicounter automata. This correspondence also completes the picture of the links between various class conditions of class automata and various models of counter machines. Moreover, this model is applied to extend a decidability result of Alur, Cern\'y and Weinstein on the algorithmic analysis of array-accessing programs.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Quantum metastability in a class of moving potentials

In this paper we consider quantum metastability in a class of moving potentials introduced by Berry and Klein. Potential in this class has its height and width scaled in a specific way so that it can be transformed into a stationary one. In deriving the non-decay probability of the system, we argue that the appropriate technique to use is the less known method of scattering states. This method is illustrated through two examples, namely, a moving delta-potential and a moving barrier potential. For expanding potentials, one finds that a small but finite non-decay probability persists at large times. Generalization to scaling potentials of arbitrary shape is briefly indicated.Comment: 10 pages, 1 figure

Quark droplets stability induced by external magnetic field

The influence of a constant homogeneous external magnetic field $H$ on the formation and stability of quark droplets is investigated within a simple Nambu -- Jona-Lasinio model by using a thermodynamic approach. For a vanishing magnetic field stable quark droplets, which are schematically the bags of massless quarks, are allowed to exist only at $G>G_{bag}$, where $G$ is the quark coupling constant, $G_{bag}=1.37G_{crit}$, and $G_{crit}$ is the value of the coupling constant above which chiral symmetry is spontaneously broken down. On the other hand, a nonvanishing external magnetic field can induce the stability of quark droplets so that they may exist even at $G<G_{bag}$. In this case, depending on the value of $H$, quark droplets are composed either of massive or massless quarks.Comment: 16 pages, 9 figures, REVTEX4; new references added; minor changes of the tex

Nonlinear atom optics and bright gap soliton generation in finite optical lattices

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture for the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due the atom-atom interaction are discussed in detail, such as atom optical limiting and atom optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A new scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded in a controlled way starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties

Non-perturbative Euler-Heisenberg Lagrangian and Paraelectricity in Magnetized Massless QED

In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta much smaller than $\sqrt{eH}$, the magnetic field introduces a dynamical ultraviolet cutoff in the theory that also enters in the non-perturbative Euler-Heisenberg action. Using this action, we show that the system exhibits a significant paraelectricity in the direction parallel to the magnetic field. The nonperturbative nature of this effect is reflected in the non-analytic dependence of the obtained electric susceptibility on the fine-structure constant. The strong paraelectricity in the field direction is linked to the orientation of the electric dipole moments of the pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.Comment: 18 pages, to be published in NP

The logic of the floral transition: reverse-engineering the switch controlling the identity of lateral organs

Much laboratory work has been carried out to determine the gene regulatory network (GRN) that results in plant cells becoming flowers instead of leaves. However, this also involves the spatial distribution of different cell types, and poses the question of whether alternative networks could produce the same set of observed results. This issue has been addressed here through a survey of the published intercellular distribution of expressed regulatory genes and techniques both developed and applied to Boolean network models. This has uncovered a large number of models which are compatible with the currently available data. An exhaustive exploration had some success but proved to be unfeasible due to the massive number of alternative models, so genetic programming algorithms have also been employed. This approach allows exploration on the basis of both data-fitting criteria and parsimony of the regulatory processes, ruling out biologically unrealistic mechanisms. One of the conclusions is that, despite the multiplicity of acceptable models, an overall structure dominates, with differences mostly in alternative fine-grained regulatory interactions. The overall structure confirms the known interactions, including some that were not present in the training set, showing that current data are sufficient to determine the overall structure of the GRN. The model stresses the importance of relative spatial location, through explicit references to this aspect. This approach also provides a quantitative indication of how likely some regulatory interactions might be, and can be applied to the study of other developmental transitions

Newt-omics: a comprehensive repository for omics data from the newt Notophthalmus viridescens

Notophthalmus viridescens, a member of the salamander family is an excellent model organism to study regenerative processes due to its unique ability to replace lost appendages and to repair internal organs. Molecular insights into regenerative events have been severely hampered by the lack of genomic, transcriptomic and proteomic data, as well as an appropriate database to store such novel information. Here, we describe ‘Newt-omics’ (http://newt-omics.mpi-bn.mpg.de), a database, which enables researchers to locate, retrieve and store data sets dedicated to the molecular characterization of newts. Newt-omics is a transcript-centred database, based on an Expressed Sequence Tag (EST) data set from the newt, covering ∼50 000 Sanger sequenced transcripts and a set of high-density microarray data, generated from regenerating hearts. Newt-omics also contains a large set of peptides identified by mass spectrometry, which was used to validate 13 810 ESTs as true protein coding. Newt-omics is open to implement additional high-throughput data sets without changing the database structure. Via a user-friendly interface Newt-omics allows access to a huge set of molecular data without the need for prior bioinformatical expertise