Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space.Comment: 17 pages, no figur

Fourier transform of the 2kF Luttinger liquid density correlation function with different spin and charge velocities

We obtain a closed-form analytical expression for the zero-temperature Fourier transform of the 2kF component of the density-density correlation function in a Luttinger liquid with different spin and charge velocities. For frequencies near the spin and charge singularities, approximate analytical forms are given and compared with the exact result. We find power-law-like singularities leading to either divergence or cusps, depending on the values of the Luttinger parameters, and compute the corresponding exponents. Exact integral expressions and numerical results are given for the finite-temperature case as well. We show, in particular, how the temperature rounds the singularities in the correlation function

Non-equilibrium relaxation of an elastic string in random media

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \sim L^\theta$.Comment: 2 pages, 1 figure, Proceedings of ECRYS-2005 International Workshop on Electronic Crysta

Competition for Listings

We develop a model in which two profit maximizing exchanges compete for IPO listings. They choose the listing fees paid by firms wishing to go public and control the trading costs incurred by investors. All firms prefer lower costs, however firms differ in how they value a decrease in trading costs. Hence, in equilibrium, the exchanges obtain positive expected profits by charging different trading fees and different listing fees. As a result, firms that list on different exchanges have different characteristics. The model has testable implications for the cross-sectional characteristics of IPOs' on different quality exchanges and the relationship between the level of trading costs and listing fees. We also find that competition does not guarantee that exchanges choose welfare maximizing trading rules. In some cases, welfare is larger with a monopolist exchange than with oligopolist exchanges.market microstructure; listings; competition; exchanges; regulation

"Bargaining and Fixed Price Offers: How Online Intermediaries are Changing New Car Transactions"

The Internet has introduced a variety of online buying services that expand the reach of sellers and reduce search costs for buyers. In markets in which traditional outlets establish prices through bargaining, these online intermediaries have also altered the price setting process. Perhaps the most well known example is Autobytel.com which provides referral services in the automobile market. By using Autobytel, a buyer can obtain a non-negotiable price offer as an alternative to bargaining with a car dealership. To understand the effect of online referral systems on the price setting process, we construct a theoretical model of oligopolistic price competition in which one dealership has an exclusive contract with a referral intermediary. We derive market conditions under which the fixed price offered through the referral system will or will not be lower than offline (bargained) prices. Our model provides theoretical insights relevant to results in the empirical literature addressing the role that Autobytel and other infomediaries play in online markets.online markets, E-commerce, intermediary, autobytel, pricing

Screening and conductance relaxations in insulating granular aluminium thin films

We have recently found in insulating granular Al thin film a new experimental feature (Delahaye et al., Phys. Rev. Lett. 106, 186602, 2011), namely the existence of a conductance relaxation that is not sensitive to gate voltage changes. This conductance relaxation is related to the existence of a metallic-like screening in the film and can be used to estimate its characteristic length scale. In the present paper, we give some experimental details on how this feature was measured and present our first results on the screening length temperature dependence.Comment: 14th Transport in interacting disordered systems (TIDS14) conference, September 5-8 2011, Acre (Israel

Mode coupling induced dissipative and thermal effects at long times after a quantum quench

An interaction quench in a Luttinger liquid can drive it into an athermal steady state. We analyze the effects on such an out of equilibrium state of a mode coupling term due to a periodic potential. Employing a perturbative renormalization group approach we show that even when the periodic potential is an irrelevant perturbation in equilibrium, it has important consequences on the athermal steady state as it generates a temperature as well as a dissipation and hence a finite life-time for the bosonic modes.Comment: 4+ pages and 2 figure

Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states

We have developed a Green's function formalism based on the use of an overcomplete semicoherent basis of vortex states, specially devoted to the study of the Hamiltonian quantum dynamics of electrons at high magnetic fields and in an arbitrary potential landscape smooth on the scale of the magnetic length. This formalism is used here to derive the exact Green's function for an arbitrary quadratic potential in the special limit where Landau level mixing becomes negligible. This solution remarkably embraces under a unified form the cases of confining and unconfining quadratic potentials. This property results from the fact that the overcomplete vortex representation provides a more general type of spectral decomposition of the Hamiltonian operator than usually considered. Whereas confining potentials are naturally characterized by quantization effects, lifetime effects emerge instead in the case of saddle-point potentials. Our derivation proves that the appearance of lifetimes has for origin the instability of the dynamics due to quantum tunneling at saddle points of the potential landscape. In fact, the overcompleteness of the vortex representation reveals an intrinsic microscopic irreversibility of the states synonymous with a spontaneous breaking of the time symmetry exhibited by the Hamiltonian dynamics.Comment: 19 pages, 4 figures ; a few typos corrected + some passages in Sec. V rewritte

Luttinger liquid of trimers in Fermi gases with unequal masses

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states - "trimers" - exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities $n_\uparrow=n_\downarrow/2$ an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid ordering. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.Comment: 4 pages, 4 figures. Final accepted versio

Observation of thermally activated glassiness and memory dip in a-NbSi insulating thin films

We present electrical conductance measurements on amorphous NbSi insulating thin films. These films display out-of equilibrium electronic features that are markedly different from what has been reported so far in disordered insulators. Like in the most studied systems (indium oxide and granular Al films), a slow relaxation of the conductance is observed after a quench to liquid helium temperature which gives rise to the growth of a memory dip in MOSFET devices. But unlike in these systems, this memory dip and the related conductance relaxations are still visible up to room temperature, with clear signatures of a temperature dependent dynamics