Interfering Doorway States and Giant Resonances. II: Transition Strengths

The mixing of the doorway components of a giant resonance (GR) due to the interaction via common decay channels influences significantly the distribution of the multipole strength and the energy spectrum of the decay products of the GR. The concept of the partial widths of a GR becomes ambiguous when the mixing is strong. In this case, the partial widths determined in terms of the $K$- and $S$-matrices must be distinguished. The photoemission turns out to be most sensitive to the overlapping of the doorway states. At high excitation energies, the interference between the doorway states leads to a restructuring towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997

Quantum Resonances and Regularity Islands in Quantum Maps

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described the unitary unimodular group SU(q). The resonant energy growth of is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the non-zero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a non-linear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length, q << l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR

Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pade-Borel-Leroy and conformal mapping techniques. It is found that for N = 2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta-functions closer to each another. For N > 2 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N = 0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure

Compact objects in conformal nonlinear electrodynamics

In this paper we consider a special case of vacuum non-linear electrodynamics with a stress-energy tensor conformal to the Maxwell theory. Distinctive features of this model are: the absence of dimensional parameter for non-linearity description and a very simple form of the dominant energy condition, which can be easily verified in an arbitrary pseudo-riemannian space-time with the consequent constrains on the model parameters. In this paper we analyse some properties of astrophysical compact objects coupled to conformal vacuum non-linear electrodynamics