Particle diagrams and statistics of many-body random potentials

We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in Benet et al. (2001). We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with m$m$ bosons or fermions that interact through a random k$k$-body Hermitian potential (k≤m$k\le m$); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble   (eGUE) (Mon and French, 1975). Our results apply in the limit where the number l$l$ of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for m<2k$m<2k$ to Gaussian moments in the dilute limit k?m?l$k?m?l$. Regarding the form of this transition, we see that as m$m$ is increased, more and more diagrams become relevant, with new contributions starting from each of the points m=2k,3k,…,nk$m=2k,3k,\dots ,nk$ for the 2n$2n$th moment.     

Lattice Polytopes Associated to Certain Demazure Modules of sl n + 1

Let w be an element of the Weyl group of sl _{n + 1}. We prove that for a certain class of elements w (which includes the longest element w₀ of the Weyl group), there exist a lattice polytope R ^l(w) , for each fundamental weight _i of sl _{n + 1}, such that for any dominant weight = _{i = 1} ⁿ a _{i i} , the number of lattice points in the Minkowski sum _w = _{i = 1} ⁿ a _{i i} ^w is equal to the dimension of the Demazure module E _w (). We also define a linear map A ^w : R ^l(w) P _Z R where P denotes the weight lattice, such that char E _w () = e e^–A(x) where the sum runs through the lattice points x of ^w .     

Possible lattice distortions in the hubbard model for graphene

The Hubbard model on the honeycomb lattice is a well-known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most 6 atoms per unit cell as compared to two atoms for the undistorted lattice.     

Simulation of Laser Radiation Interaction with InSb Matrix Photodetector in the Software Package Logos

Russian Physics Journal - The article is devoted to simulation of the formation and evolution of the temperature field in an InSb matrix photodetector upon exposure of a part of its surface to...     

Nonexistence of Large Nuclei in the Liquid Drop Model

We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.     

Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. Our proofs utilize the technique of the original derivation of strong subadditivity of the von Neumann entropy.     

SUBSTRATE DEPENDENCE OF THE ACTION SPECTRUM FOR PHOTOENZYMATIC REPAIR OF DNA

Abstract— The absolute action spectrum has been determined for photoenzymatic splitting of cyclobutadipyrimidines ("pyrimidine dimers") from natural DNA, and from the synthetic polydeoxyribonucleotides poly(dA)·poly(dT) (forming only cyclobutadithymine) and poly(dG)·poly(dC) (forming only cyclobutadicytosine). These action spectra differ strikingly from each other, even when using the same enzyme preparations. On the other hand, the action spectrum for splitting cyclobutadithymine in natural DNA containing "dimers" of only this one type closely resembles the action spectrum for splitting the total mixture of "dimer" types in natural DNA, and is entirely different from the spectrum for splitting of the same photoproduct from poly(dA)·poly(dT). These results mean that the action spectrum is not simply the absorption spectrum of a chromophore carried by the photoreactivating enzyme, nor is it solely determined by the nature of the substrate photoproduct. It is at least partly determined by the over-all polynueleotide structure (viz. exact helical dimensions, pattern of neighboring bases to the "dimers," or both), affecting a ground state interaction between the enzyme and substrate in the enzyme-substrate complex.