Vector and axial vector mesons at finite temperature

We consider the thermal correlation functions of vector and axial-vector currents and evaluate corrections to the vector and axial-vector meson pole terms to one loop in chiral perturbation theory. As expected, the pole positions do not shift to leading order in temperature. But the residues decrease with temperature

Single molecule DNA sequencing via transverse electronic transport using a graphene nanopore: A tight-binding approach

We report a tight-binding model study of two-terminal graphene nanopore based device, for sequential determination of DNA bases. Using Greens function approach we calculate conductance spectra, I-V response and also the changes in local density of states (LDOS) profile as four different nucleobases inserted one by one into the pore embedded in the zigzag graphene nanoribbon (ZGNR). We find distinct features in LDOS profile for different nucleotides and the same is also present in conductance and I-V response. We propose the actual working principle of the device, by setting the bias across the pore to a fixed voltage (this voltage gives maximum discrimination between characteristic current of the four nucleotides) and translocating the ss-DNA through the nanopore using a transverse electric field while recording the characteristic current of the nucleotides. Not only the typical current output is much larger than previous results, but the seaparation between them for different bases are also definite. Our investigation provides high accuracy and significant amount of distinction between different nucleotides.Comment: 6 pages, 5 figure

Applications of Stein's method for concentration inequalities

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie--Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erd\H{o}s--R\'{e}nyi random graph $G(n,p)$ when $p\ge0.31$. Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures.Comment: Published in at http://dx.doi.org/10.1214/10-AOP542 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Central limit theorem for first-passage percolation time across thin cylinders

We prove that first-passage percolation times across thin cylinders of the form $[0,n]\times [-h_n,h_n]^{d-1}$ obey Gaussian central limit theorems as long as $h_n$ grows slower than $n^{1/(d+1)}$. It is an open question as to what is the fastest that $h_n$ can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of $(1,0,...,0)$, we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.Comment: Final version, accepted in Probability Theory and Related Fields. 40 pages, 7 figure

Power-law corrections to black-hole entropy via entanglement

We consider the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black-hole entropy. We examine possible deviations of black hole entropy from area proportionality. We show that while the area law holds when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. We compare our results with the other approaches in the literature.Comment: 10 pages, 5 figures, to appear in the Proceedings of "BH2, Dynamics and Thermodynamics of Blackholes and Naked Singularities", May 10-12 2007, Milano, Italy; conference website: http://www.mate.polimi.it/bh2