Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc

Universal Description of Granular Metals at Low Temperatures: Granular Fermi Liquid

We present a unified description of the low temperature phase of granular metals that reveals a striking generality of the low temperature behaviors. Our model explains the universality of the low-temperature conductivity that coincides exactly with that of the homogeneously disordered systems and enables a straightforward derivation of low temperature characteristics of disordered conductors.Comment: 4 pages, 1 figur

Consistency analysis of Kaluza-Klein geometric sigma models

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given metric field configuration which becomes the vacuum of the theory. Kaluza-Klein theories of the kind have been shown to be free of the classical cosmological constant problem, and to give massless gauge fields after dimensional reduction. In this paper, the consistency of dimensional reduction, as well as the stability of the internal excitations, are analyzed. Choosing the internal space in the form of a group manifold, one meets no inconsistencies in the dimensional reduction procedure. As an example, the SO(n) groups are analyzed, with the result that the mass matrix of the internal excitations necessarily possesses negative modes. In the case of coset spaces, the consistency of dimensional reduction rules out all but the stable mode, although the full vacuum stability remains an open problem.Comment: 13 pages, RevTe

A model for the accidental catalysis of protein unfolding in vivo

Activated processes such as protein unfolding are highly sensitive to heterogeneity in the environment. We study a highly simplified model of a protein in a random heterogeneous environment, a model of the in vivo environment. It is found that if the heterogeneity is sufficiently large the total rate of the process is essentially a random variable; this may be the cause of the species-to-species variability in the rate of prion protein conversion found by Deleault et al. [Nature, 425 (2003) 717].Comment: 5 pages, 2 figure

Computational challenges of systems biology

Progress in the study of biological systems such as the heart, brain, and liver will require computer scientists to work closely with life scientists and mathematicians. Computer science will play a key role in shaping the new discipline of systems biology and addressing the significant computational challenges it poses

Effects of fluctuations and Coulomb interaction on the transition temperature of granular superconductors

We investigate the suppression of superconducting transition temperature in granular metallic systems due to (i) fluctuations of the order parameter (bosonic mechanism) and (ii) Coulomb repulsion (fermionic mechanism) assuming large tunneling conductance between the grains $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$d$ granular samples and films. We demonstrate that if the critical temperature $T_c > g_T \delta$, where $\delta$ is the mean level spacing in a single grain the bosonic mechanism is the dominant mechanism of the superconductivity suppression, while for critical temperatures $T_c < g_T \delta$ the suppression of superconductivity is due to the fermionic mechanism.Comment: 12 pages, 9 figures, several sections clarifying the details of our calculations are adde

Evolution of SU(4) Transport Regimes in Carbon Nanotube Quantum Dots

We study the evolution of conductance regimes in carbon nanotubes with doubly degenerate orbitals (``shells'') by controlling the contact transparency within the same sample. For sufficiently open contacts, Kondo behavior is observed for 1, 2, and 3 electrons in the topmost shell. As the contacts are opened more, the sample enters the ``mixed valence'' regime, where different charge states are strongly hybridized by electron tunneling. Here, the conductance as a function of gate voltage shows pronounced modulations with a period of four electrons, and all single-electron features are washed away at low temperature. We successfully describe this behavior by a simple formula with no fitting parameters. Finally, we find a surprisingly small energy scale that controls the temperature evolution of conductance and the tunneling density of states in the mixed valence regime.Comment: 4 pages + supplementary info. The second part of the original submission is now split off as a separate paper (0709.1288

Local Moment Formation in the Superconducting State of a Doped Mott Insulator

A microscopic theory is presented for the local moment formation near a non-magnetic impurity or a copper defect in high-T_c superconductors. We use a renormalized meanfield theory of the t-J model for a doped Mott insulator and study the fully self-consistent, spatially unrestricted solutions of the d-wave superconducting (SC) state in both the spin S=0 and S=1/2 sectors. We find a transition from the singlet d-wave SC state to a spin doublet SC state when the renormalized exchange coupling exceeds a doping dependent critical value. The induced S=1/2 moment is staggered and localized around the impurity. It arises from the binding of an S=1/2 nodal quasiparticle excitation to the impurity. The local density of states spectrum is calculated and connections to NMR and STM experiments are discussed.Comment: 4 pages, 3 figures, revised version, to be published in Phys. Rev. Let

Collapse of Charge Gap in Random Mott Insulators

Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase transition due to randomness is observed associated with the collapse of the charge ordering. We also treat random Hubbard model focusing on the Mott gap. Although the randomness closes the Mott gap and low-lying states are created, which is observed in the charge compressibility, no (quasi-) Fermi surface singularity is formed. It implies localized nature of the low-lying states.Comment: RevTeX with 3 postscript figure

SU(4) and SU(2) Kondo Effects in Carbon Nanotube Quantum Dots

We study the SU(4) Kondo effect in carbon nanotube quantum dots, where doubly degenerate orbitals form 4-electron ``shells''. The SU(4) Kondo behavior is investigated for one, two and three electrons in the topmost shell. While the Kondo state of two electrons is quenched by magnetic field, in case of an odd number of electrons two types of SU(2) Kondo effect may survive. Namely, the spin SU(2) state is realized in the magnetic field parallel to the nanotube (inducing primarily orbital splitting). Application of the perpendicular field (inducing Zeeman splitting) results in the orbital SU(2) Kondo effect.Comment: 5 pages. Some material was previously posted in cond-mat/0608573, v