Zero-zero Transition and Electron-Neutron Interaction

ORTHOGONAL ZERO INTERPOLANTS AND APPLICATIONS

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...

Electron-Neutron Interaction.

Transmission zero in a semichaotic quantum dot with strong electron-electron interaction

The pioneering experiment [Nature 385, 417 (1997)] reported the measurement of the transmission phase of the electron traversing a quantum dot and found the intriguing feature of the sudden phase drop in conductance valleys. Based on the Friedel sum rule for a spinless effective one-dimensional system, it has been previously argued [Phys. Rev. Lett. 82, 2358 (1999)] that the sudden phase drop s...

Transmission zero in a quantum dot with strong electron-electron interaction: Perturbative conductance calculations

A pioneering experiment [E. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, and Hadas Shtrikman, Nature (London) 385, 417 (1997)] reported the measurement of the transmission phase of an electron traversing a quantum dot and found the intriguing feature of a sudden phase drop in the conductance valleys. Based on the Friedel sum rule for a spinless effective one-dimensional system, it has ...

Transition Operators of Diffusions Reduce Zero–crossing

If u(t, x) is a solution of a one–dimensional, parabolic, second– order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number of zero–crossings of the function u(t, ·) decreases (that is, does not increase) as time t increases. Such theorems have applications to the study of blow–up of solutions of semilinear PDE, time dependent Sturm Liouvill...