Extended jordanian twists for Lie algebras

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebras ${\bf B}^{\vee}$ of $sl(N)$ the explicit expressions are obtained for the twist element ${\cal F}$, universal ${\cal R}$-matrix and the corresponding canonical element ${\cal T}$. It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ is self dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld-Jimbo quantization to the jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.Comment: 28 pages, LaTe

Quantum Computation as a Dynamical Process

In this paper, we discuss the dynamical issues of quantum computation. We demonstrate that fast wave function oscillations can affect the performance of Shor's quantum algorithm by destroying required quantum interference. We also show that this destructive effect can be routinely avoided by using resonant-pulse techniques. We discuss the dynamics of resonant pulse implementations of quantum logic gates in Ising spin systems. We also discuss the influence of non-resonant excitations. We calculate the range of parameters where undesirable non-resonant effects can be minimized. Finally, we describe the ``$2\pi k$-method'' which avoids the detrimental deflection of non-resonant qubits.Comment: 13 pages, 1 column, no figure

Stability of Nonlinear Normal Modes in the FPU-β\beta Chain in the Thermodynamic Limit

All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit, as well as its application for each of the above nonlinear normal modes are presented

Simulations of Quantum Logic Operations in Quantum Computer with Large Number of Qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.Comment: 13 pages, 15 figure

Non-Resonant Effects in Implementation of Quantum Shor Algorithm

We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our ``$2\pi k$''-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency.Comment: 11 pages, 13 figure

Charges and fields in a current-carrying wire

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and Special Relativity. Some consequences of the assumption that the net charge per unit length is zero in the electrons frame are also briefly discussed