Dear Colleagues, 

You are most cordially invited to Yeditepe Mathematics Department 25th Year Seminars organized by the Department of Mathematics. The details of this week's talk are as follows.

Speaker: Oktay Pashaev (İHTE)

Topic: Quantum Calculus of Fibonacci Divisors applied to Classical Method of Images and Quantum Computational States

Abstract: Starting from divisibility problem for Fibonacci numbers, we introduce integer Fibonacci divisors, conjugate to $F_k$, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By the set of translation operators, we find the hierarchy of Golden binomials and related Golden analytic functions. In the limit $k \to 0,$ these functions reduce to classical holomorphic functions and quantum calculus of Fibonacci divisors to the usual one. The hierarchy of Golden periodic functions appearing in this calculus, we relate with classical method of images in planar hydrodynamics (electrostatics). Several applications of the calculus to quantum deformed algebras and quantum computation and information theory are discussed. In particular, we show that for repeated consecutive duplicated qubit states, probabilities are determined by Fibonacci numbers. We generalize these results for direct product of multiple qubit states and arbitrary position of repeated states. The calculations are based on structure of Fibonacci trees in space of qubit states, growing in the left and in the right directions, number of branches and allowed paths on the trees.

Date:  October 8, 2021, Friday

Time: 16:00

Zoom: Please contact Assist. Prof. Mehmet Akif ERDAL (mehmet.erdal@yeditepe.edu.tr) for the zoom address.

You may find a copy of the flyer from this link. For a full list of this semester's seminar schedule, click on the link below!

https://researchseminars.org/seminar/7tepemathseminars