Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice, like a discrete version simple exclusion processes (ASEP), nonintersecting random walkers, lattice...

When a family of non symmetrical heterocycled compounds is investigated, a variety of mesophases can be observed with rather different features. Here we report the behaviour of seven different members among a family of such materials, that consists of mesomorphic oxadiazole compounds. In two of these compounds, the...

The magnetic spectrum at high-energies in heavily underdoped YBa$_{2}$Cu$_{3}$O$_{6.35}$ (T$_{c}$=18 K) has been determined throughout the Brillouin zone. At low-energy the scattering forms a cone of spin excitations emanating from the antiferromagnetic (0.5, 0.5) wave vector with an acoustic velocity similar to that of insulating cuprates. At high...

We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$ and with an arbitrary voltage $V_0$ applied across the barrier region. We demonstrate that the tunneling conductance of such a NIS junction is an oscillatory function of both $d$ and...

The present work is a brief review of the progressive search of improper delta-functions which are of interest in Quantum Mechanics and in the problem of motion in General Relativity Theory. Comment: LaTeX file, 15 pages no figures

We define the alternating sign matrix polytope as the convex hull of nxn alternating sign matrices and prove its equivalent description in terms of inequalities. This is analogous to the well known result of Birkhoff and von Neumann that the convex hull of the permutation matrices equals the...

A new class of cylindrically symmetric inhomogeneous string cosmological models is investigated. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the model is proportional to the eigen value $\sigma^{1}_{1}$ of the shear tensor $\sigma^{i}_{j}$. The physical and geometric aspects of the model...

We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide...

We discuss theoretically the properties of an electromechanical oscillator whose operation is based upon the cyclic, quasi-conservative conversion between gravitational potential, kinetic, and magnetic energies. The system consists of a strong-pinning type-II superconductor square loop subjected to a constant external force and to magnetic fields. The loop oscillates...

We use twisted sheaves to study the problem of index reduction for Brauer classes. In general terms, this problem may be phrased as follows: given a field $k$, a $k$-variety $X$, and a class $\alpha \in \Br(k)$, compute the index of the class $\alpha_{k(X)} \in \Br(X)$ obtained from...