Phase Transitions from Saddles of the Potential Energy Landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated.Comment: 5 pages, no figure

Phases of a fermionic model with chiral condensates and Cooper pairs in 1+1 dimensions

We study the phase structure of a 4-fermi model with three bare coupling constants, which potentially has three types of bound states. This model is a generalization of the model discussed previously by A. Chodos et al. [Phys. Rev. D 61, 045011 (2000)], which contained both chiral condensates and Cooper pairs. For this generalization we find that there are two independent renormalized coupling constants which determine the phase structure at finite density and temperature. We find that the vacuum can be in one of three distinct phases depending on the value of these two renormalized coupling constants

Nonanalyticities of the entropy induced by saddle points of the potential energy landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived for the generic case of potentials having the Morse property. With increasing system size the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Nonetheless, a distribution of an unboundedly growing number of saddle points may cause a phase transition in the thermodynamic limit. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, conditions on the distribution of saddle points and their curvatures are derived which are necessary for a phase transition to occur. With these results, the puzzling absence of topological signatures in the spherical model is elucidated. As further applications, the phase transitions of the mean-field XY model and the mean-field k-trigonometric model are shown to be induced by saddle points of vanishing curvature.Comment: 24 pages, 2 figure

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the results in Mathematica forma

Fate of the H-NS–Repressed bgl Operon in Evolution of Escherichia coli

In the enterobacterial species Escherichia coli and Salmonella enterica, expression of horizontally acquired genes with a higher than average AT content is repressed by the nucleoid-associated protein H-NS. A classical example of an H-NS–repressed locus is the bgl (aryl-β,D-glucoside) operon of E. coli. This locus is “cryptic,” as no laboratory growth conditions are known to relieve repression of bgl by H-NS in E. coli K12. However, repression can be relieved by spontaneous mutations. Here, we investigated the phylogeny of the bgl operon. Typing of bgl in a representative collection of E. coli demonstrated that it evolved clonally and that it is present in strains of the phylogenetic groups A, B1, and B2, while it is presumably replaced by a cluster of ORFans in the phylogenetic group D. Interestingly, the bgl operon is mutated in 20% of the strains of phylogenetic groups A and B1, suggesting erosion of bgl in these groups. However, bgl is functional in almost all B2 isolates and, in approximately 50% of them, it is weakly expressed at laboratory growth conditions. Homologs of bgl genes exist in Klebsiella, Enterobacter, and Erwinia species and also in low GC-content Gram-positive bacteria, while absent in E. albertii and Salmonella sp. This suggests horizontal transfer of bgl genes to an ancestral Enterobacterium. Conservation and weak expression of bgl in isolates of phylogenetic group B2 may indicate a functional role of bgl in extraintestinal pathogenic E. coli

A Novel Mechanism of Transposon-Mediated Gene Activation

Transposable Insertion Sequences (IS elements) have been shown to provide various benefits to their hosts via gene activation or inactivation under stress conditions by appropriately inserting into specific chromosomal sites. Activation is usually due to derepression or introduction of a complete or partial promoter located within the element. Here we define a novel mechanism of gene activation by the transposon IS5 in Escherichia coli. The glycerol utilization operon, glpFK, that is silent in the absence of the cAMP-Crp complex, is activated by IS5 when inserted upstream of its promoter. High-level expression is nearly constitutive, only mildly dependent on glycerol, glucose, GlpR, and Crp, and allows growth at a rate similar to or more rapid than that of wild-type cells. Expression is from the glpFK promoter and dependent on (1) the DNA phase, (2) integration host factor (IHF), and (3) a short region at the 3′ end of IS5 harboring a permanent bend and an IHF binding site. The lacZYA operon is also subject to such activation in the absence of Crp. Thus, we have defined a novel mechanism of gene activation involving transposon insertion that may be generally applicable to many organisms

From DNA sequence to application: possibilities and complications

The development of sophisticated genetic tools during the past 15 years have facilitated a tremendous increase of fundamental and application-oriented knowledge of lactic acid bacteria (LAB) and their bacteriophages. This knowledge relates both to the assignments of open reading frames (ORF’s) and the function of non-coding DNA sequences. Comparison of the complete nucleotide sequences of several LAB bacteriophages has revealed that their chromosomes have a fixed, modular structure, each module having a set of genes involved in a specific phase of the bacteriophage life cycle. LAB bacteriophage genes and DNA sequences have been used for the construction of temperature-inducible gene expression systems, gene-integration systems, and bacteriophage defence systems. The function of several LAB open reading frames and transcriptional units have been identified and characterized in detail. Many of these could find practical applications, such as induced lysis of LAB to enhance cheese ripening and re-routing of carbon fluxes for the production of a specific amino acid enantiomer. More knowledge has also become available concerning the function and structure of non-coding DNA positioned at or in the vicinity of promoters. In several cases the mRNA produced from this DNA contains a transcriptional terminator-antiterminator pair, in which the antiterminator can be stabilized either by uncharged tRNA or by interaction with a regulatory protein, thus preventing formation of the terminator so that mRNA elongation can proceed. Evidence has accumulated showing that also in LAB carbon catabolite repression in LAB is mediated by specific DNA elements in the vicinity of promoters governing the transcription of catabolic operons. Although some biological barriers have yet to be solved, the vast body of scientific information presently available allows the construction of tailor-made genetically modified LAB. Today, it appears that societal constraints rather than biological hurdles impede the use of genetically modified LAB.

Chiral Modulations in Curved Space II: Conifold Geometries

In this paper, we extend our previous analysis concerning the formation of inhomogeneous condensates in strongly-coupled fermion effective field theories on curved spaces and include the case of conifold geometries that represent the simplest tractable case of manifolds with curvature singularities. In the set-up considered here, by keeping the genuine thermodynamical temperature constant, we may single out the role that curvature effects play on the breaking/restoration of chiral symmetry and on the appearance of inhomogeneous phases. The first goal of this paper is to construct a general expression of the finite temperature effective action for inhomogeneous condensates in the case of four-fermion effective field theories on conifold geometries with generic Riemannian smooth base (generalised cones). The other goal is to implement numerically the above formal results and construct self-consistent solutions for the condensate. We explicitly show that the condensate assumes a kink-like profile, vanishing at the singularity that is surrounded by a bubble of restored chiral symmetry phase.Comment: 14 pages; 4 figure