Geometry of Cyclic Quantum Evolutions

Arun Kumar Pati

Andrzej Herdegen

Sharba Bhattacharjee, Biprateep Dey, Ashok Kumar Mohapatra

Abstract We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

Alejandro Romero-Osnaya

A geometric approach to the quantum states of light that is injected into a Mach- Zehnder interferometer is discussed. It is based on the Jordan-Schwinger representation of angular momentum and permits the identification of the photon states with cones in the threedimensional space that are rotated by the action of the optical devices. Some cases of the evolution loops, dynamical processes for which any state evolves cyclically, are presented.

Veeravalli S. Varadarajan

Qin Huang, Qiuju Diao, Shu Lin +1 more

This paper presents a technique to decompose a cyclic code given by a parity-check matrix in circulant form into descendant cyclic and quasi-cyclic codes of various length and rates. Based on this technique, cyclic finite geometry (FG) LDPC codes are decomposed into a large class of cyclic FG-LDPC codes and a large class of quasi-cyclic FG-LDPC codes.