Lossless propagation of optical pulses through N-level systems with SU(2) symmetry

Propagation of optical pulses through atomic media consisting of atoms with N transition levels and possessing the so-called SU(2) symmetry is studied. It is shown that there are generally N - 1 sets of conditions, each of which, when satisfied, would permit the appropriate Maxwell-Bloch equations to have a solution having the form of simultaneous different-wavelength optical solutions, so-called simulations. The first two sets of solutions were known previously, but the remaining sets are new

Adiabatic shape preservation and solitary waves in a five-level atomic medium

Adiabatically shape-preserving-wave and solitary-wave solutions for five-level atomic systems are presented. They give the idealized situations for the shape preserving propagation of optical waves through a five-level atomic medium, and provide some useful comparisons with the electromagnetically induced transparency experiments performed by Harris and his collaborators on atoms with hyperfine structure

N-level quantum systems with Gell-Mann dynamic symmetry

A set of conditions is presented for an N-level quantum system to possess the Gell-Mann-type dynamic symmetry, which was introduced in an earlier paper. The characteristic set of constants of motion that the system has when it possesses the symmetry and also the equivalent two-level system, which the system can be reduced to, are also presented

Lossless propagation of optical pulses through N-level systems with Gell-Mann symmetry

Propagation of optical pulses through atomic media consisting of atoms with N transition levels and possessing the so-called Gell-Mann symmetry is studied. An analytic solution of the appropriate Maxwell-Bloch equations having the form of simultaneous different wavelength optical solutions is presented. The special case of N = 3 was known previously

Erratum: Micellar-shape anisometry near isotropic–liquid-crystal phase transitions

In lieu of an abstract, below is the first paragraph: In our paper the binary sodium dodecyl (lauryl) sulfate (SLS)–water system was investigated by small-angle x-ray scattering in the isotropic (I) phase up to the I-hexagonal (Ha) transition and the ternary system (with decanol added to a binary system containing 26 wt% of SLS in water) up to what was considered to be an I-nematic cylindrical (Nc) phase transition. Our paper did not focus on the phase diagram of the studied system but rather on the detailed modeling of the scattering curves in the I phase in terms of particle form factor and interference function. The aim of the paper was to determine the particle anisometries in the I phase as I-liquid-crystal phase transitions were approached, and to compare it with theories that predicted I-(N)-H phase transitions in systems with self-association

Certain stability type and integrable two-dimensional Hamiltonian systems

We present the results of applying an analytical method, using a new concept involving a periodic stability around a line of initial values, to two Hamiltonian systems with two degrees of freedom each with several parameters. By requiring the systems to have this type of stability, we have been led to known integrable cases for the systems. For one of the systems, our analysis gives six other cases, two of which turn out to be nonintegrable. The status of the remaining four cases has not been established

Solitary Waves for N Coupled Nonlinear Schrodinger Equations

A hierarchy of exact analytic solitary-wave solutions for N coupled nonlinear Schrodinger equations fur which the nonlinear coupling parameters can change continuously and cover many regions is presented. Besides their potentially many practical applications to optical communication and multispecies Bose-Einstein condensates for couplings outside the special integrable cases, these analytically solvable cases for special initial conditions supplement and provide important links to and among the integrable cases

N-level quantum systems with SU(2) dynamic symmetry

We present an analytic solution of the coherent evolution of a laser-driven N-level quantum system that possesses an SU(2) dynamic symmetry

Stability-instability transitions in Hamiltonian systems of n dimensions

We show analytically that for a class of simple periodic motions in a general Hamiltonian system of n dimensions, if C is a parameter of the system and Cz one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent p as C approaches Ce from the unstable region is given by µ, =constX |~ C—Cp |β where β= 1/2, independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Harniltonian system which exhibits three types of stability-instability transitions, and for a two-dimensional Hamiltonian system which exhibits two types of transitions

Matched Optical Solitary Waves for 3-Level and 5-Level Systems

Exact analytic results are presented that give a general solution for a pair of solitary waves which can propagate through a three- and a five-level system with their shapes invariant. These solitary waves vary widely in shape and form: from ones for which the pulses have similar shape to ones which have very different but \u27\u27complementary\u27\u27 shapes. A general type of solitary-wave pair which is insensitive to small perturbations is identified