871 research outputs found
On the geometry of Siegel-Jacobi domains
We study the holomorphic unitary representations of the Jacobi group based on
Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces
based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete
series of the Jacobi group for the Siegel-Jacobi disk is constructed and
polynomial orthonormal bases of the representation spaces are given.Comment: 15 pages, Latex, AMS fonts, paper presented at the the International
Conference "Differential Geometry and Dynamical Systems", August 25-28, 2010,
University Politehnica of Bucharest, Romani
A holomorphic representation of the Jacobi algebra
A representation of the Jacobi algebra by first order differential operators with polynomial
coefficients on the manifold is presented. The
Hilbert space of holomorphic functions on which the holomorphic first order
differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the
Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI:
10.1142/S0129055X12920018, references update
A convenient coordinatization of Siegel-Jacobi domains
We determine the homogeneous K\"ahler diffeomorphism which expresses the
K\"ahler two-form on the Siegel-Jacobi ball \mc{D}^J_n=\C^n\times \mc{D}_n as
the sum of the K\"ahler two-form on \C^n and the one on the Siegel ball
\mc{D}_n. The classical motion and quantum evolution on \mc{D}^J_n
determined by a hermitian linear Hamiltonian in the generators of the Jacobi
group G^J_n=H_n\rtimes\text{Sp}(n,\R)_{\C} are described by a matrix Riccati
equation on \mc{D}_n and a linear first order differential equation in
z\in\C^n, with coefficients depending also on W\in\mc{D}_n. denotes
the -dimensional Heisenberg group. The system of linear differential
equations attached to the matrix Riccati equation is a linear Hamiltonian
system on \mc{D}_n. When the transform is
applied, the first order differential equation in the variable
\eta=(\un-W\bar{W})^{-1}(z+W\bar{z})\in\C^n becomes decoupled from the motion
on the Siegel ball. Similar considerations are presented for the Siegel-Jacobi
upper half plane \mc{X}^J_n=\C^n\times\mc{X}_n, where \mc{X}_n denotes the
Siegel upper half plane.Comment: 32 pages, corrected typos, Latex, amsart, AMS font
Isospin equilibration processes and dipolar signals: Coherent cluster production
The total dipolar signal related to multi-break-up processes induced on the system 48Ca + 27Al at 40 MeV/nucleon has been investigated with the CHIMERA multi-detector. Experimental data related to semi-peripheral collisions are shown and compared with CoMD-III calculations. The strong connection between the dipolar signal as obtained from the detected fragments and the dynamics of the isospin equilibration processes is also shortly discussed
Study on the isospin equilibration phenomenon in nuclear reactions 40Ca + 40Ca, 40Ca + 46Ti, 40Ca + 48Ca, 48Ca + 48Ca at 25 MeV/nucleon by using the CHIMERA multidetector
We report on the results obtained by studying nuclear reactions between isotopes of Ca and Ti at 25MeV/nucleon. We used the multidetector CHIMERA to detect charged reaction products. In particular, we studied two main effects: the isospin diffusion and the isospin drift. In order to study these processes we performed a moving-source analysis on kinetic energy spectra of the isobar nuclei 3H and3He. This method allows to isolate the emission from the typical sources produced in reactions at Fermi energy: projectile like fragment (PLF), target like fragment (TLF), and mid-velocity (MV) emission. The obtained results are compared to previous experimental investigations and to simulations obtained with CoMD-II model
Multicomponent polariton superfluidity in the optical parametric oscillator regime
Superfluidity, the ability of a liquid or gas to flow with zero viscosity, is one of the most remarkable
implications of collective quantum coherence. In equilibrium systems like liquid 4He and ultracold
atomic gases, superfluid behaviour conjugates diverse yet related phenomena, such as persistency
of metastable flow in multiply connected geometries and the existence of a critical velocity for
frictionless flow when hitting a static defect. The link between these different aspects of superfluid
behaviour is far less clear in driven-dissipative systems displaying collective coherence, such as
microcavity polaritons, which raises important questions about their concurrency. With a joint
theoretical and experimental study, we show that the scenario is particularly rich for polaritons
driven in a three-fluid collective coherent regime so-called optical parametric oscillator. On the one
hand, the spontaneous macroscopic coherence following the phase locking of the signal and idler
fluids has been shown to be responsible for their simultaneous quantized flow metastability. On the
other hand, we show here that pump, signal and idler have distinct responses when hitting a static
defect; while the signal displays hardly appreciable modulations, the ones appearing in pump and
idler are determined by their mutual coupling due to nonlinear and parametric processes
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