Cliffordons

At higher energies the present complex quantum theory with its unitary group might expand into a real quantum theory with an orthogonal group, broken by an approximate $i$ operator at lower energies. Implementing this possibility requires a real quantum double-valued statistics. A Clifford statistics, representing a swap (12) by a difference $\gamma_1-\gamma_2$ of Clifford units, is uniquely appropriate. Unlike the Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein, and para- statistics, which are tensorial and single-valued, and unlike anyons, which are confined to two dimensions, Clifford statistics are multivalued and work for any dimensionality. Nayak and Wilczek proposed a Clifford statistics for the fractional quantum Hall effect. We apply them to toy quanta here. A complex-Clifford example has the energy spectrum of a system of spin-1/2 particles in an external magnetic field. This supports the proposal that the double-valued rotations --- spin --- seen at current energies might arise from double-valued permutations --- swap --- to be seen at higher energies. Another toy with real Clifford statistics illustrates how an effective imaginary unit $i$ can arise naturally within a real quantum theory.Comment: 15 pages, no figures; original title ("Clifford statistics") changed; to appear in J. Math. Phys., 42, 2001. Key words: Clifford statistics, cliffordons, double-valued representations of permutation groups, spin, swap, imaginary unit $i$, applications to quantum space-time and the Standard Model. Some of these results were presented at the American Physical Society Centennial Meeting, Atlanta, March 25, 199

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

Are Bosonic Replicas Faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.Comment: 4.3 pages; final version to appear in PR

FROM CHRONOLOGICAL NETWORKS TO BAYESIAN MODELS: CHRONOLOG AS A FRONT-END TO OXCAL

We present a new method for creating an OxCal Bayesian model that bypasses the complex task of writing OxCal code. Our methodology employs the recent ChronoLog software as a graphical front-end for generating OxCal scripts. This approach enables archaeologists to create complex Bayesian models—including termini post and ante quem, duration bounds and synchronisms—with the help of a user-friendly interface. The target audience can be divided into beginners, who might struggle to create chronological models using OxCal directly, and experienced OxCal users, who should find that ChronoLog saves time when coding complex models. Three case-studies from recent publications are presented

Critical behavior of density of states near Fermi energy in low-dimensional disordered metals

We study the effect of electron-electron interaction on the one-particle density of states (\emph{DOS}) $\rho^{(d)}(\epsilon,T)$ of low-dimensional disordered metals near Fermi energy within the framework of the finite temperature conventional impurity diagram technique. We consider only diffusive limit and by a geometric re-summation of the most singular first order self-energy corrections via the Dyson equation we obtain a non-divergent solution for the \emph{DOS} at low energies, while for higher energies the well-known Altshuler-Aronov corrections are recovered. At the Fermi level $\rho^{(d)}(\epsilon,T=0)\to 0$, this indicates that interacting disordered two- and quasi-one-dimensional systems are in insulating state at zero temperature. The obtained results are in good agreement with recent tunneling experiments on two-dimensional GaAs/AlGaAs heterostructures and quasi-one-dimensional doped multiwall carbon nanotubes.Comment: 8 pages, 4 figure

Renormalization of hole-hole interaction at decreasing Drude conductivity

The diffusion contribution of the hole-hole interaction to the conductivity is analyzed in gated GaAs/In$_x$Ga$_{1-x}$As/GaAs heterostructures. We show that the change of the interaction correction to the conductivity with the decreasing Drude conductivity results both from the compensation of the singlet and triplet channels and from the arising prefactor $\alpha_i<1$ in the conventional expression for the interaction correction.Comment: 6 pages, 5 figure

Giant suppression of the Drude conductivity due to quantum interference in disordered two-dimensional systems

Temperature and magnetic field dependences of the conductivity in heavily doped, strongly disordered two-dimensional quantum well structures GaAs/In$_x$Ga$_{1-x}$As/GaAs are investigated within wide conductivity and temperature ranges. Role of the interference in the electron transport is studied in the regimes when the phase breaking length $L_\phi$ crosses over the localization length $\xi\sim l\exp{(\pi k_Fl/2)}$ with lowering temperature, where $k_F$ and $l$ are the Fermi quasimomentum and mean free path, respectively. It has been shown that all the experimental data can be understood within framework of simple model of the conductivity over delocalized states. This model differs from the conventional model of the weak localization developed for $k_Fl\gg 1$ and $L_\phi\ll\xi$ by one point: the value of the quantum interference contribution to the conductivity is restricted not only by the phase breaking length $L_\phi$ but by the localization length $\xi$ as well. We show that just the quantity $(\tau_\phi^\ast)^{-1}=\tau_\phi^{-1}+\tau_\xi^{-1}$ rather than $\tau_\phi^{-1}$, where $\tau_\phi\propto T^{-1}$ is the dephasing time and $\tau_\xi\sim\tau\exp(\pi k_F l)$, is responsible for the temperature and magnetic field dependences of the conductivity over the wide range of temperature and disorder strength down to the conductivity of order $10^{-2} e^2/h$.Comment: 11 pages, 15 figure

Quantum creep and variable range hopping of one-dimensional interacting electrons

The variable range hopping results for noninteracting electrons of Mott and Shklovskii are generalized to 1D disordered charge density waves and Luttinger liquids using an instanton approach. Following a recent paper by Nattermann, Giamarchi and Le Doussal [Phys. Rev. Lett. {\bf 91}, 56603 (2003)] we calculate the quantum creep of charges at zero temperature and the linear conductivity at finite temperatures for these systems. The hopping conductivity for the short range interacting electrons acquires the same form as for noninteracting particles if the one-particle density of states is replaced by the compressibility. In the present paper we extend the calculation to dissipative systems and give a discussion of the physics after the particles materialize behind the tunneling barrier. It turns out that dissipation is crucial for tunneling to happen. Contrary to pure systems the new metastable state does not propagate through the system but is restricted to a region of the size of the tunneling region. This corresponds to the hopping of an integer number of charges over a finite distance. A global current results only if tunneling events fill the whole sample. We argue that rare events of extra low tunneling probability are not relevant for realistic systems of finite length. Finally we show that an additional Coulomb interaction only leads to small logarithmic corrections.Comment: 15 pages, 3 figures; references adde