Orthogonal Polynomials and Exact Correlation Functions for Two Cut Random Matrix Models

Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support a $Z_2$ symmetric distribution is obtained. This results in an exact explicit expression for the kernel at large $N$ which determines all eigenvalue correlators. The oscillating and smooth parts of the two point correlator are extracted and the universality of local fine grained and smoothed global correlators is established.Comment: 15 pages, LaTex, a paragraph added in note added:, three references added. accepted in Nucl. Phys.

Strings and D-Branes at High Temperature

The thermodynamics of a gas of strings and D-branes near the Hagedorn transition is described by a coupled set of Boltzmann equations for weakly interacting open and closed long strings. The resulting distributions are dominated by the open string sector, indicating that D-branes grow to fill space at high temperature.Comment: 8 pages, LaTeX, 1 figur

Scattering phase shifts in quasi-one-dimension

Scattering of an electron in quasi-one dimensional quantum wires have many unusual features, not found in one, two or three dimensions. In this work we analyze the scattering phase shifts due to an impurity in a multi-channel quantum wire with special emphasis on negative slopes in the scattering phase shift versus incident energy curves and the Wigner delay time. Although at first sight, the large number of scattering matrix elements show phase shifts of different character and nature, it is possible to see some pattern and understand these features. The behavior of scattering phase shifts in one-dimension can be seen as a special case of these features observed in quasi-one-dimensions. The negative slopes can occur at any arbitrary energy and Friedel sum rule is completely violated in quasi-one-dimension at any arbitrary energy and any arbitrary regime. This is in contrast to one, two or three dimensions where such negative slopes and violation of Friedel sum rule happen only at low energy where the incident electron feels the potential very strongly (i.e., there is a very well defined regime, the WKB regime, where FSR works very well). There are some novel behavior of scattering phase shifts at the critical energies where $S$-matrix changes dimension.Comment: Minor corrections mad