Representations of Uh(su(N))U_h(su(N)) derived from quantum flag manifolds

A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left \Uh -- module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of Leibniz rule. Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occuring in the diagonalization one can extract finite-dimensional irreducible representations of \Uh as cyclic submodules.Comment: LaTeX file, JMP (to appear

Quadrature entanglement and photon-number correlations accompanied by phase-locking

We investigate quantum properties of phase-locked light beams generated in a nondegenerate optical parametric oscillator (NOPO) with an intracavity waveplate. This investigation continuous our previous analysis presented in Phys.Rev.A 69, 05814 (2004), and involves problems of continuous-variable quadrature entanglement in the spectral domain, photon-number correlations as well as the signatures of phase-locking in the Wigner function. We study the role of phase-localizing processes on the quantum correlation effects. The peculiarities of phase-locked NOPO in the self-pulsing instability operational regime are also cleared up. The results are obtained in both the P-representation as a quantum-mechanical calculation in the framework of stochastic equations of motion, and also by using numerical simulation based on the method of quantum state diffusion.Comment: Subm. to PR

Conformal Symmetry on the Instanton Moduli Space

The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. It is shown that the conformal algebra closes only up to global gauge transformations, which generalizes the earlier discussion by Jackiw et al. An interesting 5-dimensional interpretation of the SU(2) single-instanton is also mentioned.Comment: 7 pages, LaTeX, version to appear in J. Phys. A: Math. Ge

Phase-sensitive quantum effects in Andreev conductance of the SNS system of metals with macroscopic phase breaking length

The dissipative component of electron transport through the doubly connected SNS Andreev interferometer indium (S)-aluminium (N)-indium (S) has been studied. Within helium temperature range, the conductance of the individual sections of the interferometer exhibits phase-sensitive oscillations of quantum-interference nature. In the non-domain (normal) state of indium narrowing adjacent to NS interface, the nonresonance oscillations have been observed, with the period inversely proportional to the area of the interferometer orifice. In the domain intermediate state of the narrowing, the magneto-temperature resistive oscillations appeared, with the period determined by the coherence length in the magnetic field equal to the critical one. The oscillating component of resonance form has been observed in the conductance of the macroscopic N-aluminium part of the system. The phase of the oscillations appears to be shifted by $\pi$ compared to that of nonresonance oscillations. We offer an explanation in terms of the contribution into Josephson current from the coherent quasiparticles with energies of order of the Thouless energy. The behavior of dissipative transport with temperature has been studied in a clean normal metal in the vicinity of a single point NS contact.Comment: 9 pages, 7 figures, to be published in Low Temp. Phys., v. 29, No. 12, 200

On the role of vortex stretching in energy optimal growth of three dimensional perturbations on plane parallel shear flows

The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane

Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.Comment: 5 pages, revtex4, 2 PS figures, title changed, final versio