Quantum Fields on Star Graphs with Bound States at the Vertex

We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires. The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix. The general case of off-critical scattering matrix with bound and/or antibound states is considered. We demonstrate that the contribution of these states to the scalar field is fixed by causality (local commutativity), which is the key point of our investigation. Two different regimes of the theory emerge at this stage. If bound sates are absent, the energy is conserved and the theory admits unitary time evolution. The behavior changes if bound states are present, because each such state generates a kind of damped harmonic oscillator in the spectrum of the field. These oscillators lead to the breakdown of time translation invariance. We study in both regimes the electromagnetic conductance of the Luttinger liquid on the quantum wire junction. We derive an explicit expression for the conductance in terms of the scattering matrix and show that antibound and bound states have a different impact, giving raise to oscillations with exponentially damped and growing amplitudes respectively.Comment: LaTex 1+29 pages, 2 figures: Expanded version with new title and abstract; clarifying comments, fig.2 and references added; final version to appear in J. Math. Phy

Bosonization and Vertex Algebras with Defects

The method of bosonization is extended to the case when a dissipationless point-like defect is present in space-time. Introducing the chiral components of a massless scalar field, interacting with the defect in two dimensions, we construct the associated vertex operators. The main features of the corresponding vertex algebra are established. As an application of this framework we solve the massless Thirring model with defect. We also construct the vertex representation of the sl(2) Kac-Moody algebra, describing the complex interplay between the left and right sectors due to the interaction with the defect. The Sugawara form of the energy-momentum tensor is also explored.Comment: 23 pages, 1 figur

Luttinger Liquid in Non-equilibrium Steady State

We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix S, which describes the splitting of the electric current among the leads. The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials. The associated non-equilibrium steady state depends on S and is explicitly constructed. In this context we develop a non-equilibrium bosonization procedure and compute some basic correlation functions. Luttinger liquids with general anyon statistics are considered. The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures. Both the charge and heat transport are studied. The exact current-current correlation function is derived and the zero-frequency noise power is determined.Comment: LaTex, 1+28 pages, 7 figure

A Minimum Principle in Codon-Anticodon Interaction

Imposing a minimum principle in the framework of the so called crystal basis model of the genetic code, we determine the structure of the minimum set of anticodons which allows the translational-transcription for animal mitochondrial code. The results are in very good agreement with the observed anticodons.Comment: 13 pages, 6 Tables, to appear in Biosystem

Symmetry and Minimum Principle at the Basis of the Genetic Code

The importance of the notion of symmetry in physics is well established: could it also be the case for the genetic code? In this spirit, a model for the Genetic Code based on continuous symmetries and entitled the "Crystal Basis Model" has been proposed a few years ago. The present paper is a review of the model, of some of its first applications as well as of its recent developments. Indeed, after a motivated presentation of our mathematical model, we illustrate its pertinence by applying it for the elaboration and verification of sum rules for codon usage probabilities, as well as for establishing relations and some predictions between physical-chemical properties of amino-acids. Then, defining in this context a "bio-spin" structure for the nucleotides and codons, the interaction between a couple of codon-anticodon can simply be represented by a (bio) spin-spin potential. This approach will constitute the second part of the paper where, imposing the minimum energy principle, an analysis of the evolution of the genetic code can be performed with good agreement with the generally accepted scheme. A more precise study of this interaction model provides informations on codon bias, consistent with data.Comment: To appear in BIOMAT 2016, 326 - 362, 201

Yangian realisations from finite W algebras

We construct an algebra homomorphism between the Yangian Y(sl(n)) and the finite W-algebras W(sl(np),n.sl(p)) for any p. We show how this result can be applied to determine properties of the finite dimensional representations of such W-algebras.Comment: 26 pages, Latex2

Missing Stellar Mass in SED Fitting: Spatially Unresolved Photometry can Underestimate Galaxy Masses

We fit model spectral energy distributions to each pixel in 67 nearby (=0.0057) galaxies using broadband photometry from the Sloan Digital Sky Survey and GALEX. For each galaxy, we compare the stellar mass derived by summing the mass of each pixel to that found from fitting the entire galaxy treated as an unresolved point source. We find that, while the pixel-by-pixel and unresolved masses of galaxies with low specific star formation rates (such as ellipticals and lenticulars) are in rough agreement, the unresolved mass estimate for star-forming galaxies is systematically lower then the measurement from spatially-resolved photometry. The discrepancy is strongly correlated with sSFR, with the highest sSFRs in our sample having masses underestimated by 25% (0.12 dex) when treated as point sources. We found a simple relation to statistically correct mass estimates derived from unresolved broad-band SED fitting to the resolved mass estimates: m_{resolved} = m_{unresolved}/(-0.057log(sSFR) + 0.34) where sSFR is in units of yr^{-1}. We study the effect of varying spatial resolution by degrading the image resolution of the largest images and find a sharp decrease in the pixel-by-pixel mass estimate at a physical scale of approximately 3 kpc, which is comparable to spiral arm widths. The effects we observe are consistent with the "outshining" idea which posits that the youngest stellar populations mask more massive, older -- and thus fainter -- stellar populations. Although the presence of strong dust lanes can also lead to a drastic difference between resolved and unresolved mass estimates (up to 45% or 0.3 dex) for any individual galaxy, we found that resolving dust does not affect mass estimates on average. The strong correlation between mass discrepancy and sSFR is thus most likely due to the outshining systematic bias.Comment: 13 pages, 8 figures, accepted for publication in MNRA