M. N. Hounkonnou — Page 2

arXiv2003

Relativistic Spectral Properties of Landau Operator with $δ$- and $δ'$- cylinder interactions

Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $δ$ and $δ'$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by the Hamiltonian $H^G_{B} = {(p-A)}^2 I + {\bfσ}.{\bf{B}+G}V(r),$ $\bigg(V(r) = δ(R-r)$ or $V(r) = δ' (R-r) \bigg),$ acting in $ L^2(\R^2)\bigotimes \C^2 $. $G$ a scalar $2\times 2$ real matrix. I is the identity matrix. The potential vector has the form $A= (B/2)(-y, x)$ and $B>0.$

math-ph↗

arXiv1998

A quantum statistical mechanics model of a three dimensional linear rigid rotator in a bath of oscillators: IV - steady state dielectric properties induced by a. c. and d. c. field coupling

The long time effect of a radio frequency (rf) a.c. field superimposed on a d.c. field on the electrical susceptibility and the Kerr optical functions of polarisable fluids in inert solvent is analysed. The results obtained for the classical Brownian limit, valid for dense solvent media, well reproduce classical results published in the literature with excellent precisions in inertia, density and temperature dependences. The low density limit yields absorption-dispersion lines whose widths and shifts are density, inertia and temperature dependent. While the low density and/or large inertia susceptibility is explicitly written out as a continued fraction got by solving an infinite hierarchy of differential coupled equations, that of the Kerr effect is given in the form of successive convergents of the solutions of an infinite hierarchy of differential difference triplets. The polarisation/a.c. field phase difference is analysed. The effects of the constant field strength and the a.c. field frequency on the Kerr function are explored. In this paper, which will be named paper IV, the derivation of some quoted equations will intensionally be left out as they exist in paper III (J. Phys. A, 30:6347, 1997) of which this work is its logical continuation.

cond-mat.stat-mech↗