The random variable $1+z_1+z_1z_2+\dots$ appears in many contexts and was shown by Kesten to exhibit a heavy tail distribution. We consider natural extensions of this its associated recursion $N \times N$ matrices either real symmetric $\beta=1$ or complex Hermitian $\beta=2$. In the continuum limit recursion, we show that matrix distribution converges inverse-Wishart ensemble matrices. full dy...

In this paper, we study the massive Dirac equation with presence of Morse potential in polar coordinate. The Hamiltonian is written as two second-order differential equations terms spinor wavefunctions. Since motion electrons graphene propagated like relativistic fermionic quasi-particles, then one considered only pseudospin symmetry for aligned spin and unaligned by arbitrary $k$. Next, use co...

This paper introduces a general method for obtaining lower bounds for the total energy and the minimal inter-particle distance in optimal atom cluster problems with pair potential functions under weak general conditions on the pair potential. The bounds obtained are sharper than those previously known for both the Lennard-Jones potential and various Morse potentials. Statistics on the putative ...

Effect of defects on the melting profile of short heterogeneous DNA chains is calculated using the Peyrard-Bishop Hamiltonian. On-site potential on a defect site is represented by a potential that has only a short-range repulsion and a flat part without well of the Morse potential. Stacking energy between two neigbouring pairs involving a defect site is also modified. The results are found to b...