R. M. Kiehn

Periods on manifolds, quantization, and gauge

It is suggested that the quantization of flux, charge, and angular momentum be interpreted as a set of independent natural concepts which physically exhibit certain topological properties of the fields on a space–time manifold. These quantum, or topological, properties may be described in terms of one‐, two‐, and three‐dimensional periods, respectively. In terms of this viewpoint, topological constraints between the one‐, two‐, and three‐dimensional periods can be put into correspondence with various gauge theories. If a dynamical system is to be nondissipative, in the sense that its one‐, two‐, and three‐dimensional topological periods are reversible invariants of the motion, then it is proved herein that the dynamical field V must be a Hamiltonian vector field, the field currents must be proportional to V, and the Lagrangian difference between the elastic and inertial energy density must be twice the interaction energy density, respectively.

An extension of Hamilton's principle to include dissipative systems

The key idea of conservative Hamiltonian systems is the fact that the closed line integral of action is an absolute invariant of the motion. Dissipation effects may be included by considering those systems for which the closed integral of action is a parameter‐dependent, conformal invariant of the motion. An application of this idea to hydrodynamics is made, and the conditions required for the validity of the Liouville theorem with respect to conformal Hamiltonian flows are examined.

Are there three kinds of superconductivity

A Maxwell system of differential forms induces a coarse topology on a space time variety. This topology can be refined by certain extremal constraints of domain closure that lead to three topologically distinct, reactive impedances, Z1, Z2, Z3. These non-dissippative impedances are rational fraction ratios of topological invariants. The closure conditions induce physical constraints that permit Z1 to be identified with ordinary type I and II superconductive domains, and Z3 with the fractional quantum Hall effect. Only Z2 admits the time-reversal and parity symmetry breaking associated with Anyon theories.

Dual-polarized ring lasers

Simultaneous laser oscillation of four nondegenerate polarization and propagation direction eigenstates of a single TEM 00 mode was observed in a ring laser cavity. The observed polarization and frequency properties of the ring laser were analyzed in terms of the Jones matrix calculus.

Intrinsic hydrodynamics with applications to space-time fluids

Abstract Cartans methods of exterior differential forms are utilized to derive conformal and absolute conservation equations for various field quantities in relativistic hydromechanics. In particular, Fridmans results for the conservation of vector lines are extended to space time situations. The invariance concepts of Helmholtz and Bernoulli are formulated for arbitrary frames of reference, and the separate conservation concepts of total mass and total number in space time are distinguished and associated with the concept of turbulence.

Instability Patterns, Wakes and Topological Limit Sets

Many hydrodynamic instability patterns can be put into correspondence with a subset of characteristic surfaces of tangential discontinuities. These topological limits sets to systems of hyperbolic PDE’s are locally unstable, but a certain subset associated with minimal surfaces are globally stabilized, persistent and non-dissipative. Sections of these surfaces are the spiral scrolls so often observed in hydrodynamic wakes. This method of wake production does not depend explicitly upon viscosity.

Lifting of the four-fold em degeneracy and PT asymmetry☆

Abstract Solutions to Maxwells equations which lift the Lorentz degeneracies of propagation direction (T asymmetry) and helicity (P asymmetry) have been determined from the analysis of a valence four constitutive tensor density, χλνσϰ.

Conformal invariance and Hamilton Jacobi theory for dissipative systems

For certain dissipative systems, a comparison can be made between the Hamilton–Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton–Jacobi theory.

Entropy Production and Irreversible Processes -from the perspective of continuous topological evolution.

A concept of entropy production associated with continuous topological evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential velocities. An irreversible process can describe entropy production in terms of continuous topological evolution to non-equilibrium but stationary states. An equilibrium system can be defined topologically as a Lagrange submanifold of the 2n+2 topological space, upon which the change in entropy by continuous topological evolution is zero, dSequil=0.