Mean Field Approach for a Statistical Mechanical Model of Proteins

We study the thermodynamical properties of a topology-based model proposed by Galzitskaya and Finkelstein for the description of protein folding. We devise and test three different mean-field approaches for the model, that simplify the treatment without spoiling the description. The validity of the model and its mean-field approximations is checked by applying them to the $\beta$-hairpin fragment of the immunoglobulin-binding protein (GB1) and making a comparison with available experimental data and simulation results. Our results indicate that this model is a rather simple and reasonably good tool for interpreting folding experimental data, provided the parameters of the model are carefully chosen. The mean-field approaches substantially recover all the relevant exact results and represent reliable alternatives to the Monte Carlo simulations.Comment: RevTeX-4, 11 pages, 6 eps-figures, To Appear on J.Chem.Phy

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

General solution of equations of motion for a classical particle in 9-dimensional Finslerian space

A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia for the Finslerian space is confirmed.Comment: 10 pages, LaTeX-2e, no figures; added 2 reference

Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long range character, resulting in $\log^2$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order, and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function, while all other quantities renormalize only logarithmically. We solve the RG flow equation for the Green function with logarithmic accuracy, and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge invariant quantities, such as the compressibility, remain finite to $\log^2$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the non-interacting value.Comment: 12 pages, 3 figure

Suppression of superconductivity in granular metals

We investigate the suppression of the superconducting transition temperature due to Coulomb repulsion in granular metallic systems at 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 depending on the parameters of superconducting grains, the corresponding granular samples can be divided into two groups: (i) the granular samples that belong to the first group may have only insulating or superconducting states at zero temperature depending on the bare intergranular tunneling conductance $g_T$, while (ii) the granular samples that belong to the second group in addition have an intermediate metallic phase where superconductivity is suppressed while the effects of the Coulomb blockade are not yet strong.Comment: 4 pages, 3 figure

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