Ufuk Taneri

The Relativistic Electrodynamics Least Action Principles Revisited: New Charged Point Particle and Hadronic String Models Analysis

The classical relativistic least action principle is revisited from the vacuum field theory approach. New physically motivated versions of relativistic Lorentz type forces are derived, a new relativistic hadronic string model is proposed and analyzed in detail. The reasonings of R. Feynman, who argued that the relativistic dynamical expressions obtain true physical sense only with respect to the proper rest reference frames, are supported by analyzing the dynamical stability of a relativistic charged string model.

Quantum field theory with application to Quantum nonlinear optics

Methods of Studying Quantum Optical Phenomena: Quantum States and Statistics Creation and Annihilation Operators The One-Particle Greens Function The Dyson Equations Polarization Operators The Hartree-Fock Approximation Nonlinear Quantum Optics Models and Their Applications: Nonlinear Quantum Optics Bose-Systems The Dicke Model A Degenerate Parametric Quantum Optical Amplifier A Nonlinear Quantum-Optical System at Equilibrium Radiative State and other topics.

A geometrical approach to quantum holonomic computing algorithms

The article continues a presentation of modern quantum mathematics backgrounds started in [Quantum Mathematics and its Applications. Part 1. Automatyka, vol. 6, AGH Publisher, Krakow, 2002, No. 1, pp. 234-2412; Quantum Mathematics: Holonomic Computing Algorithms and Their Applications. Part 2. Automatyka, vol. 7, No. 1, 2004]. A general approach to quantum holonomic computing based on geometric Lie-algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bundles it is shown that the associated holonomy groups properly realizing quantum computations can be effectively found concerning diverse practical problems. Two examples demonstrating two-form curvature calculations important for describing the corresponding holonomy Lie algebra are presented in detail.

Exact Computation of Spectral Densities for a Langevin Dynamic Modelling the Relaxation of a Protein Near Its Equilibrium

The relaxation motion of a protein nearby its equilibrium is enhanced by the heat bath in which the protein is embedded. A classical approach will realize this heat bath through a molecular dynamic including a large number of molecules of the solvent at the cost of a large computing time. Here, we propose a modelling of the heat bath by a Langevin random force. Under this Langevin dynamic, an exact mathematical computation of the spectral densities can be made.The mathematical expression will depend upon the normal modes of the potential nearby its minimum. The mathematical computation is exact; it is, therefore, unnecessary to run an effective simulation through a molecular dynamic. The spectral densities will peak at these normal modes. Our computation provides a theoretical ground to the experimental determination of normal modes through a peak searching of observed spectral densities.

On the structure of Picard–Fuchs type equations for Liouville–Arnold integrable Hamiltonian system on cotangent phase spaces

There are studied in detail the structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces and related with it so called Picard–Fuchs type equations. It is shown that these equations can be in general regularly constructed making use of a given a priori system of involutive invariants and proved that their solutions in the Hamolton–Jacobi separable variable case give rise exactly to the integral submanifold imbedding mapping being as known a main ingredient for Liouville–Arnold integrability by quadratures of the Hamiltonian system under regard.