Some studies on quantum equivalents of non-commutative operators via commutating eigenvalue relation: PT-symmetry

We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This universality relation is also equally valid for any matrix in any branch of physical or social science and also any operator involving co-ordinate$(x)$ or momentum$(p)$. Pictorially this is represented in fig. 1. Many interesting models including logarithmic potential have been considered.Comment: Since new submissions are not allowed, I have replaced my previous article, which may kindly be allowe

Measuring the Double Layer Capacitance of Electrolytes with Varied Concentrations

When electric potentials are applied from an electrolytic fluid to a metal, a double layer capacitor, Cdl, develops at the interface. The layer directly at the interface is called the Stern layer and has a thickness equal to roughly the size of the ions in the fluid. The next layer, the diffuse layer, arises from the gathering of like charges in the Stern layer. This layer is the distance needed for ionic concentrations to match the bulk fluid. This distance, called the Debye length, λ, depends on the square root of the electrolyte concentration. To study the properties of the diffuse layer, we measure C using different concentrations of electrolyte solutions in a cylindrical capacitor system we machined

Uncertainties and shortcomings of ground surface temperature histories derived from inversion of temperature logs

Analysing borehole temperature data in terms of ground surface history can add useful information to reconstructions of past climates. Therefore, a rigorous assessment of uncertainties and error sources is a necessary prerequisite for the meaningful interpretation of such ground surface temperature histories. This study analyses the most prominent sources of uncertainty. The diffusive nature of the process makes the inversion relatively robust against incomplete knowledge of the thermal diffusivity. Similarly the influence of heat production is small. It turns out that for investigations of the last 1000 to 100000 years the maximum depth of the temperature log is crucial. More than 3000 m are required for an optimal inversion. Reconstructions of the last one or two millennia require only modestly deep logs (>300 m) but suffer severely from noisy data.Comment: 28 pages, 18 figure, 3 table