Showing papers by "Aix-Marseille University published in 1973"
TL;DR: In this article, a lattice representation of the Schrodinger equation of an electron in the presence of an electrostatic periodic field and a uniform magnetic field is presented, which is only valid for rational fluxess/N per lattice cell.
Abstract: Utilizing the lattice representation of OCR introduced by Zak for the treatment of the Schrodinger equation of an electron in the presence of an electrostatic periodic field and a uniform magnetic field, this paper gives a decomposition of the space of states into spaces labelled by a constant of motionv1. Each of these spaces is constituted by functions that we shall call, in analogy with the case without magnetic field, the « magnetic Bloch functions ». The constant of motionv1 is related to the set of co-ordinates of the centres of the classical orbits whick are coupled by the periodic potential and form the Pippard network. The treatment is only valid for rational fluxess/N per lattice cell.
3 citations
TL;DR: In this article, the general form of the constitutive relations between conjugated forces and flows is examined within the framework of network thermodynamics, and a link between time delays and dissipation is established and can be visualized as an increase in entropy accompanying the redistribution of molecules after any local change in concentration.
Abstract: Within the framework of network thermodynamics the general form of the constitutive relations between conjugated forces and flows is examined. Since nonequilibrium processes are involved, time delays are assumed to take place between the variation of a concentration — or generalized displacement — and that of its conjugated force — or difference in potential. For example, a certain time is needed in a chemical mixture for the chemical potential X to follow changes in concentration c of a given compound. Thus, the concentration-potential relationships must be written in the form of retarded functions X(t) = f[c(t — Δt)]. A series expansion of such a function leads to a capacitive term independent of the delay Δt, resistive terms proportional to it, and an inductive term proportional to its square value. When applied to the network analysis of chemical reactions it is apparent, from inspection of the resistive, i.e. dissipative, term, that Δt is identical with the relaxation time of a reaction defined in chemical kinetics. Thus a link between time delays and dissipation is established and can be visualized as an increase in entropy accompanying the redistribution of molecules after any local change in concentration. As to the importance of the inductive terms, it depends upon particular circumstances where longer delays can take place so that second order terms cannot be neglected and inductance-like effects could, in principle, be observed.
2 citations