Exact Ground State of the 2D Hubbard Model at Half Filling for U=0+U=0^{+}

We solve analytically the $N\times N$ square lattice Hubbard model for even $N$ at half filling and weak coupling by a new approach. The exact ground state wave function provides an intriguing and appealing picture of the antiferromagnetic order. Like at strong coupling, the ground state has total momentum $K_{tot}=(0,0)$ and transforms as an $s$ wave for even $N/2$ and as a $d$ wave otherwise.Comment: 4 pages, typos in equation 5 correcte

"Spin-Disentangled" Exact Diagonalization of Repulsive Hubbard Systems: Superconducting Pair Propagation

By a novel exact diagonalization technique we show that bound pairs propagate between repulsive Hubbard clusters in a superconducting fashion. The size of the matrices that must be handled depends on the number of fermion configurations {\em per spin}, which is of the order of the square root of the overall size of the Hilbert space. We use CuO$_{4}$ units connected by weak O-O links to model interplanar coupling and c-axis superconductivity in Cuprates. The numerical evidence on Cu$_{2}$O$_{8}$ and Cu$_{3}$O$_{12}$ prompts a new analytic scheme describing the propagation of bound pairs and also the superconducting flux quantization in a 3-d geometry.Comment: 5 pages, 3 figure

Three-Body and One-Body Channels of the Auger Core-Valence-Valence decay: Simplified Approach

We propose a computationally simple model of Auger and APECS line shapes from open-band solids. Part of the intensity comes from the decay of unscreened core-holes and is obtained by the two-body Green's function $G^{(2)}_{\omega}$, as in the case of filled bands. The rest of the intensity arises from screened core-holes and is derived using a variational description of the relaxed ground state; this involves the two-holes-one-electron propagator $G_{\omega}$, which also contains one-hole contributions. For many transition metals, the two-hole Green's function $G^{(2)}_{\omega}$ can be well described by the Ladder Approximation, but the three-body Green's function poses serious further problems. To calculate $G_{\omega}$, treating electrons and holes on equal footing, we propose a practical approach to sum the series to all orders. We achieve that by formally rewriting the problem in terms of a fictitious three-body interaction. Our method grants non-negative densities of states, explains the apparent negative-U behavior of the spectra of early transition metals and interpolates well between weak and strong coupling, as we demonstrate by test model calculations.Comment: AMS-LaTeX file, 23 pages, 8 eps and 3 ps figures embedded in the text with epsfig.sty and float.sty, submitted to Phys. Rev.

Bouncing transient currents and SQUID-like voltage in nano devices at half filling

Nanorings asymmetrically connected to wires show different kinds of quantum interference phenomena under sudden excitations and in steady current conditions. Here we contrast the transient current caused by an abrupt bias to the magnetic effects at constant current. A repulsive impurity can cause charge build-up in one of the arms and reverse current spikes. Moreover, it can cause transitions from laminar current flow to vortices, and also change the chirality of the vortex. The magnetic behavior of these devices is also very peculiar. Those nano-circuits which consist of an odd number of atoms behave in a fundamentally different manner compared to those which consist of an even number of atoms. The circuits having an odd number of sites connected to long enough symmetric wires are diamagnetic; they display half-fluxon periodicity induced by many-body symmetry even in the absence of electron-phonon and electron-electron interactions. In principle one can operate a new kind of quantum interference device without superconductors. Since there is no gap and no critical temperature, one predicts qualitatively the same behavior at and above room temperature, although with a reduced current. The circuits with even site numbers, on the other hand, are paramagnetic.Comment: 7 pages, 10 figures, accepted by Phys. Rev.

Quantum Mechanics without Waves: a Generalization of Classical Statistical Mechanics

We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the theory). This is possible provided we adopt Feynman's suggestion of dropping the assumption that the probability for an event must always be a positive number. This approach has the advantage of allowing a reformulation of quantum theory in phase space without introducing the unphysical concept of probability amplitudes, together with all the problems concerning their ambiguous properties.Comment: 25 pages, Late

Repulsion-Sustained Supercurrent and Flux Quantization in Rings of Symmetric Hubbard Clusters

We test the response to a threading magnetic field of rings of 5-site $C_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each 5-site unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with 8 particles, we take advantage of a novel exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find Superconducting Flux Quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with W=0 pairing theory.Comment: 4 pages, 2 figure

Electronic screening and correlated superconductivity in carbon nanotubes

A theoretical analysis of the superconductivity observed recently in Carbon nanotubes is proposed. We argue that ultra-small (diameter $\sim 0.4 nm$) single wall carbon nanotubes (with transition temperature $T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$) can superconduct by an electronic mechanism, basically the same in both cases. By a Luttinger liquid -like approach, one finds enhanced superconducting correlations due to the strong screening of the long-range part of the Coulomb repulsion. Based on this finding, we perform a detailed analysis on the resulting Hubbard-like model, and calculate transition temperatures of the same order of magnitude as the measured ones.Comment: 6 pages, 1 figure, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in Phys. Rev.

SME perceptions of and responses to the recession

The UK has recently experienced the worst recession since the 1930s. Despite the severity of this recent recession, there are currently few studies of its effect on small and medium-sized enterprises (SMEs). However, small business growth and entrepreneurship are recognised as essential drivers for economic recovery (Matlay, 2012; Rae, 2010). Drawing on an online bi-monthly survey of SMEs in Lincolnshire and Rutland, this paper explores owner managers’ perceptions of the UK recession. We examine the views of businesses on various aspects of the recession, and how this has affected business performance, levels of confidence, and growth ambitions. The paper explores the role of business confidence in the economy as a determinant of business growth intentions, and draws a comparison between perceptions and behaviour