Related papers: Finite Size Corrections for the Pairing Hamiltonia…
The paper is devoted to the effects of superconducting pairing in small metallic grains. It turns out that at strong superconducting coupling and in the limit of large Thouless conductance one can explicitly determine the low energy…
The Richardson exact solution for the reduced BCS Hamiltonian is applied to examine how sensitive are the pairing characteristics (condensation energy, spectroscopic gap, parity gap) to a specific configuration of single-electron energy…
Studies of pairing correlations in ultrasmall metallic grains have commonly been based on a simple reduced BCS-model describing the scattering of pairs of electrons between discrete energy levels that come in time-reversed pairs. This model…
We review recent experimental and theoretical work on superconductivity in ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an…
For assemblies of superconductor nanograins, the magnetic response is analyzed as a function of both temperature and magnetic field. In order to describe the interaction energy of electron pairs for a huge number of many-particle states,…
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant…
The Richardson Hamiltonian describes superconducting correlations in a metallic nanograin. We do a perturbative analysis of this and related Hamiltonians, around the strong pairing limit, without having to invoke Bethe Ansatz solvability.…
Motivated by recent advances in the creation of few-body atomic Fermi gases with attractive interactions, we study theoretically the few-to-many-particle crossover of pair excitations, which for large particle numbers evolve into a mode…
We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are…
We develop a theory of superconductivity in ultrasmall (nm-scale) metallic grains having a discrete electronic eigenspectrum with a mean level spacing of order of the bulk gap. The theory is based on calculating the eigenspectrum using a…
We use two truly canonical approaches to describe superconductivity in ultrasmall metallic grains: (a) a variational fixed-N projected BCS-like theory and (b) an exact solution of the model Hamiltonian developed by Richardson in context…
The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a…
We identify the leading finite-size (Luscher-type) correction to the energy of open strings ending on maximal giant gravitons. In particular we obtain the leading finite size correction at weak 't Hooft coupling and in the planar limit to…
By means of the Lanczos method we analyze superconducting correlations in ultrasmall grains at fixed particle number. We compute the ground state properties and the excitation gap of the pairing Hamiltonian as a function of the level…
We study the superconductivity in small grains in the regime when the quantum level spacing $\delta\varepsilon$ is comparable to the gap $\Delta$. As $\delta\varepsilon$ is increased, the system crosses over from superconducting to normal…
We study the thermodynamics of ultrasmall metallic grains with level spacing $\delta$ comparable or smaller than the pairing correlation energy, at finite temperatures, $T \gsim \delta$. We describe a method which allows to find quantum…
Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an…
We examine the spectrum and boundary energy in boundary sine-Gordon theory, based on our recent results on the complete spectrum predicted by closing the boundary bootstrap. We check the spectrum and the reflection factors against truncated…
We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the $O(1/N)$ corrections in the replica…
BCS superconductivity is explained by a simple Hamiltonian describing an attractive pairing interaction between pairs of electrons. The Hamiltonian may be treated using a mean-field method, which is adequate to study equilibrium properties…