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

Entanglement Wedge Cross Sections Require Tripartite Entanglement

We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well-supported conjectures about the entanglement wedge cross section surface $E_W$. If $E_W$ is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at $\mathcal{O}(\frac{1}{G_N})$. We prove that this implies holographic CFT states must have $\mathcal{O}(\frac{1}{G_N})$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.Comment: 20 pages, 5 figures, comments added in v

Zero energy correction method for non-Hermitian Harmonic oscillator with simultaneous transformation of co-ordinate and momentum: Wave function analysis under Iso-spectral condition

We present a complete analysis on energy and wave function of Harmonic oscillator with simultaneous non-hermitian transformation of co-ordinate ($(x \rightarrow \frac{(x+ i\lambda p)}{\sqrt{(1+\beta \lambda)}}$ and momentum $(p \rightarrow \frac{(p+ i\beta x)}{\sqrt{(1+\beta \lambda)}}$ for getting energy eigenvalue using perturbation theory under iso-spectral condition. Further we notice that two different frequency of oscillation ($w_{1}, w_{2}$)correspond to same energy eigenvalue, which can also be verified using Lie algebraic approach [Zhang et.al J.Math.Phys 56 ,072103 (2015)]. Interestingly wave function analysis using similarity transformation [F.M. Fernandez, Int. J. Theo. Phys. (2015)(in Press)] refers to a very special case.Comment: This paper for replacement .(i) Minor change in title reflecting wave function analysis(ii) Abstract-chaed suitably to refect wave function (iii) Text original work with information on wave function ,comparison and slight modification in references.Kindly accep