Metastable Congested States in Multisegment Traffic Cellular Automaton

We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state dependence of the flow is observed. The essential feature of three-phased structure empirically found in real-world traffic flow is reproduced without elaborate assumptions.Comment: ReVTeX 5 Pages 8 Eps Fig

Spectroscopic studies in open quantum systems

The spectroscopic properties of an open quantum system are determined by the eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the Hamiltonian H_0 of the corresponding closed system and a non-Hermitian correction term W arising from the interaction via the continuum of decay channels. The eigenvalues E_R of H are complex. They are the poles of the S-matrix and provide both the energies and widths of the states. We illustrate the interplay between Re(H) and Im(H) by means of the different interference phenomena between two neighboured resonance states. Level repulsion along the real axis appears if the interaction is caused mainly by Re(H) while a bifurcation of the widths appears if the interaction occurs mainly due to Im(H). We then calculate the poles of the S-matrix and the corresponding wavefunctions for a rectangular microwave resonator with a scatter as a function of the area of the resonator as well as of the degree of opening to a guide. The calculations are performed by using the method of exterior complex scaling. Re(W) and Im(W) cause changes in the structure of the wavefunctions which are permanent, as a rule. At full opening to the lead, short-lived collective states are formed together with long-lived trapped states. The wavefunctions of the short-lived states at full opening to the lead are very different from those at small opening. The resonance picture obtained from the microwave resonator shows all the characteristic features known from the study of many-body systems in spite of the absence of two-body forces. The poles of the S-matrix determine the conductance of the resonator. Effects arising from the interplay between resonance trapping and level repulsion along the real axis are not involved in the statistical theory.Comment: The six jpg files are not included in the tex-fil

A "hybrid plane" with spin-orbit interaction

In this paper we attempt to reconstruct one of the last projects of Volodya Geyler which remained unfinished. We study motion of a quantum particle in the plane to which a halfline lead is attached assuming that the particle has spin $\frac12$ and the plane component of the Hamiltonian contains a spin-orbit interaction of either Rashba or Dresselhaus type. We construct the class of admissible Hamiltonians and derive an explicit expression for the Green function applying it to the scattering in such a system.Comment: LaTeX, 9 pages; in memoriam Vladimir A. Geyler (1943-2007