Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.Comment: 58 pages; Acknowledgements added; small corrections in appendix A; minor changes & Note Adde

Mesoscopic transport beyond linear response

We present an approach to steady-state mesoscopic transport based on the maximum entropy principle formulation of nonequilibrium statistical mechanics. Our approach is not limited to the linear response regime. We show that this approach yields the quantization observed in the integer quantum Hall effect at large currents, which until now has been unexplained. We also predict new behaviors of non-local resistances at large currents in the presence of dirty contacts.Comment: 14 pages plus one figure (with an insert) (post-script codes appended), RevTeX 3.0, UCF-CM-93-004 (Revised

Remote site control of an active site fidelity checkpoint in a viral RNA-dependent RNA polymerase

The kinetic, thermodynamic, and structural basis for fidelity of nucleic acid polymerases remains controversial. An understanding of viral RNA-dependent RNA polymerase (RdRp) fidelity has become a topic of considerable interest as a result of recent experiments that show that a 2-fold increase in fidelity attenuates viral pathogenesis and a 2-fold decrease in fidelity reduces viral fitness. Here we show that a conformational change step preceding phosphoryl transfer is a key fidelity checkpoint for the poliovirus RdRp (3D pol). We provide evidence that this conformational change step is orientation of the triphosphate into a conformation suitable for catalysis, suggesting a kinetic and structural model for RdRp fidelity that can be extrapolated to other classes of nucleic acid polymerases. Finally, we show that a site remote from the catalytic center can control this checkpoint, which occurs at the active site. Importantly, similar connections between a remote site and the active site exist in a wide variety of viral RdRps. The capacity for sites remote from the catalytic center to alter fidelity suggests new possibilities for targeting the viral RdRp for antiviral drug development. © 2005 by The American Society for Biochemistry and Molecular Biology, Inc

Dynamics of barrier penetration in thermal medium: exact result for inverted harmonic oscillator

Time evolution of quantum tunneling is studied when the tunneling system is immersed in thermal medium. We analyze in detail the behavior of the system after integrating out the environment. Exact result for the inverted harmonic oscillator of the tunneling potential is derived and the barrier penetration factor is explicitly worked out as a function of time. Quantum mechanical formula without environment is modifed both by the potential renormalization effect and by a dynamical factor which may appreciably differ from the previously obtained one in the time range of 1/(curvature at the top of potential barrier).Comment: 30 pages, LATEX file with 11 PS figure

The stellar mass ratio of GK Persei

We study the absorption lines present in the spectra of the long-period cataclysmic variable GK Per during its quiescent state, which are associated with the secondary star. By comparing quiescent data with outburst spectra we infer that the donor star appears identical during the two states and the inner face of the secondary star is not noticeably irradiated by flux from the accreting regions. We obtain new values for the radial velocity semi-amplitude of the secondary star, Kk = 120.5 +- 0.7 km/s, a projected rotational velocity, Vksin i = 61.5 +- 11.8 km/s and consequently a measurement of the stellar mass ratio of GK Per, q = Mk/Mwd = 0.55 +- 0.21. The inferred white dwarf radial velocities are greater than those measured traditionally using the wings of Doppler-broadened emission lines suspected to originate in an accretion disk, highlighting the unsuitability of emission lines for mass determinations in cataclysmic variables. We determine mass limits for both components in the binary, Mk >= 0.48 +- 0.32 Msolar and Mwd >= 0.87 +- 0.24 Msolar.Comment: 8 pages, 8 figures, accepted by MNRA

On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes-Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral.Comment: 20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about Harish-Chandra-Itzykson-Zuber integrals. v4: Added Reference

Mesoscopic scattering in the half-plane: squeezing conductance through a small hole

We model the 2-probe conductance of a quantum point contact (QPC), in linear response. If the QPC is highly non-adiabatic or near to scatterers in the open reservoir regions, then the usual distinction between leads and reservoirs breaks down and a technique based on scattering theory in the full two-dimensional half-plane is more appropriate. Therefore we relate conductance to the transmission cross section for incident plane waves. This is equivalent to the usual Landauer formula using a radial partial-wave basis. We derive the result that an arbitrarily small (tunneling) QPC can reach a p-wave channel conductance of 2e^2/h when coupled to a suitable reflector. If two or more resonances coincide the total conductance can even exceed this. This relates to recent mesoscopic experiments in open geometries. We also discuss reciprocity of conductance, and the possibility of its breakdown in a proposed QPC for atom waves.Comment: 8 pages, 3 figures, REVTeX. Revised version (shortened), accepted for publication in PR

Simulation techniques for cosmological simulations

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure. In this paper we briefly review the current most effective techniques of large scale structure simulations, emphasising both their advantages and shortcomings. Starting with basics of the direct N-body simulations appropriate to modelling cold dark matter evolution, we then discuss the direct-sum technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and the tree algorithms. Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods. We briefly describe Eulerian grid methods, and also some variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.Comment: 42 pages, 16 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 12; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit

We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion spectrum correctly specifies the primary features of this system. Additional features are relatively small, indicating that the residual interaction between the composite fermions is weak. \footnote{Published in Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure

Long-term stress-strain response of chalk:a micro-mechanical interpretation

A long-term laboratory test programme of conventional compression and extension tests was carried out with test durations from 8 to 22-months, in a purpose built environmentally controlled facility, with specially designed loading frames and modified triaxial cells. In addition, Scanning Electron Microscope (SEM) techniques were employed in an effort to investigate the micro-mechanical res-ponse. Creep strains appeared to trigger an ageing process that produces elevated post-creep strength and stiffness irrespective of the ap-plied stress path