Large-N analysis of (2+1)-dimensional Thirring model

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism the fermions acquire parity-violating mass dynamically in the range of the dimensionless coupling $\alpha$, $0 \leq \alpha \leq \alpha_c \equiv {1\over16} {\rm exp} (- {N \pi^2 \over 16})$. The symmetry breaking pattern is, however, in a way to conserve the overall parity of the theory such that the Chern-Simons term is not induced at any orders in $1/N$. $\alpha_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $\beta$ function is calculated to be $\beta (\alpha) = -2 (\alpha - \alpha_c)$ near the fixed point, and the UV-fixed point and the $\beta$ function are shown exact in the $1/N$ expansion.Comment: 14 pages Latex. (Revised version: some changes have been made and references added.) To appear in Phys. Rev. D, SNUTP 93-4

Broadband optical radiation detector

A method and apparatus for detecting optical radiation by optically monitoring temperature changes in a microvolume caused by absorption of the optical radiation to be detected is described. More specifically, a thermal lens forming material is provided which has first and second opposite, substantially parallel surfaces. A reflective coating is formed on the first surface, and a radiation absorbing coating is formed on the reflective coating. Chopped, incoming optical radiation to be detected is directed to irradiate a small portion of the radiation absorbing coating. Heat generated in this small area is conducted to the lens forming material through the reflective coating, thereby raising the temperature of a small portion of the lens forming material and causing a thermal lens to be formed therein

Double-beam optical method and apparatus for measuring thermal diffusivity and other molecular dynamic processes in utilizing the transient thermal lens effect

A sample material was irradiated by relatively high power, short pulses from a dye laser. Energy from the pulses was absorbed by the sample material, thereby forming a thermal lens in the area of absorption. The pulse repetition rate was chosen so that the thermal lens is substantially dissipated by the time the next pulse reaches the sample material. A probe light beam, which in a specific embodiment is a relatively low power, continuous wave (cw) laser beam, irradiated the thermal lens formed in the sample material. The intensity characteristics of the probe light beam subsequent to irradiation of the thermal lens is related to changes in the refractive index of the sample material as the thermal lens is formed and dissipated

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric