Universal scaling behavior of the single electron box in the strong tunneling limit

We perform a numerical analysis of recently proposed scaling functions for the single electron box. Specifically, we study the ``magnetic'' susceptibility as a function of tunneling conductance and gate charge, and the effective charging energy at zero gate charge as a function of tunneling conductance in the strong tunneling limit. Our Monte Carlo results confirm the accuracy of the theoretical predictions.Comment: Published versio

Transport of interacting electrons through a potential barrier: nonperturbative RG approach

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) \beta-function are identified. A universal part of the \beta-function is given by a ladder series and summed to all orders in g_2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature dependent conductance is solved analytically. Our result agrees with known limiting cases.Comment: 6 pages, 5 figure

`Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the ''composite particles'' in terms of creation operators attached to the Young tableaux. Using the technique of bosonisation, we obtain a position space representation of the ''composite particles'' in terms of products of vertex operators. In the special case where the ''composite particles'' are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series $\nu =p/(2np\pm 1)$ of the fractional quantum Hall effect.Comment: latex calcomp2.tex, 5 files, 30 pages [SPhT-T99/080], submitted to J. Math. Phy

Correlation amplitude for the XXZ spin chain in the disordered regime

We proposed an analytical expression for the amplitude defining the long distance asymptotic of the correlation function .Comment: 5 pages, harvmac.tex, one epsf figur

High-Energy Approach for Heavy-Ion Scattering with Excitations of Nuclear Collective States

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach analytical expressions for elastic and inelastic scattering amplitudes are obtained where all the orders in the deformation parameters are included. The multistep effect of the 2$^+$ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the $^{17}$O ions scattered on different nuclei at about hundred Mev/nucleon are compared with experimental data, and important role of the Coulomb excitation is established.Comment: 9 pages; 3 figures. Submitted to the Physics of Atomic Nucle

Asymptotic Freedom of Elastic Strings and Barriers

We study the problem of a quantized elastic string in the presence of an impenetrable wall. This is a two-dimensional field theory of an N-component real scalar field $\phi$ which becomes interacting through the restriction that the magnitude of $\phi$ is less than $\phi_{\rm max}$, for a spherical wall of radius $\phi_{\rm max}$. The N=1 case is a string vibrating in a plane between two straight walls. We review a simple nonperturbative argument that there is a gap in the spectrum, with asymptotically-free behavior in the coupling (which is the reciprocal of $\phi_{\rm max}$) for N greater than or equal to one. This scaling behavior of the mass gap has been disputed in some of the recent literature. We find, however, that perturbation theory and the 1/N expansion each confirms that these theories are asymptotically free. The large N limit coincides with that of the O(N) nonlinear sigma model. A theta parameter exists for the N=2 model, which describes a string confined to the interior of a cylinder of radius $\phi_{\rm max}$.Comment: Text slightly improved, bibilography corrected, more typos corrected, still Latex 7 page

Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile

We complement a recent exact study by L. Samaj on the properties of a guest charge $Q$ immersed in a two-dimensional electrolyte with charges $+1/-1$. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Samaj's previous work, exact results for arbitrary coulombic coupling $\beta$ were obtained for a system where all the charges are points, provided $\beta Q<2$ and $\beta < 2$. Here, we first focus on the mean field situation which we believe describes correctly the limit $\beta\to 0$ but $\beta Q$ large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value $\beta Q>2$. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Samaj for the renormalized charge are not valid for $\beta Q>2$, contrary to a hypothesis put forward by Samaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough ($\beta Q\geq 2-\beta$). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning--Oosawa threshold $\beta Q=2$