Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Dynamics of quantum systems

A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the $S$ matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.Comment: 21 pages 7 figure

Spectral Decorrelation of Nuclear Levels in the Presence of Continuum Decay

The fluctuation properties of nuclear giant resonance spectra are studied in the presence of continuum decay. The subspace of quasi-bound states is specified by one-particle one-hole and two-particle two-hole excitations and the continuum coupling is generated by a scattering ensemble. It is found that, with increasing number of open channels, the real parts of the complex eigenvalues quickly decorrelate. This appears to be related to the transition from power-law to exponential time behavior of the survival probability of an initially non-stationary state.Comment: 10 Pages, REVTEX, 4 PostScript figure

Dynamics of open quantum systems

The coupling between the states of a system and the continuum into which it is embedded, induces correlations that are especially large in the short time scale. These correlations cannot be calculated by using a statistical or perturbational approach. They are, however, involved in an approach describing structure and reaction aspects in a unified manner. Such a model is the SMEC (shell model embedded in the continuum). Some characteristic results obtained from SMEC as well as some aspects of the correlations induced by the coupling to the continuum are discussed.Comment: 16 pages, 5 figure

Collectivity Embedded in Complex Spectra of Finite Interacting Fermi Systems: Nuclear Example

The mechanism of collectivity coexisting with chaos in a finite system of strongly interacting fermions is investigated. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^{\pi}=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create strong transitions, even much stronger than those corresponding to a pure mean-field picture. Such an effect results from correlations among the off-diagonal matrix elements, is connected with locally reduced density of states and a local minimum in the information entropy.Comment: 16 pages, LaTeX2e, REVTeX, 8 PostScript figures, to appear in Physical Review

Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths

A phenomenological schematic model of multipole giant resonances (GR) is considered which treats the external interaction via common decay channels on the same footing as the coherent part of the internal residual interaction. The damping due to the coupling to the sea of complicated states is neglected. As a result, the formation of GR is governed by the interplay and competition of two kinds of collectivity, the internal and the external one. The mixing of the doorway components of a GR due to the external interaction influences significantly their multipole strengths, widths and positions in energy. In particular, a narrow resonance state with an appreciable multipole strength is formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997

Is stroke early supported discharge still effective in practice? A prospective comparative study

Objective: Randomised controlled trials have shown the benefits of Early Supported Discharge (ESD) of stroke survivors. Our aim was to evaluate whether ESD is still beneficial when operating in the complex context of frontline healthcare provision. Design: We conducted a cohort study with quasi experimental design. A total of 293 stroke survivors (transfer independently or with assistance of one, identified rehabilitation goals) within two naturally formed groups were recruited from two acute stroke units: ‘ESD’ n=135 and ‘Non ESD’ n=158 and 84 caregivers. The ‘ESD’ group accessed either of two ESD services operating in Nottinghamshire, UK. The ‘Non ESD’ group experienced standard practices for discharge and onward referral. Outcome measures (primary: Barthel Index) were administered at baseline, 6 weeks, 6 months and 12 months. Results: The ESD group had a significantly shorter length of hospital stay (P=0.029) and reported significantly higher levels of satisfaction with services received (P<0.001). Following adjustment for age differences at baseline, participants in the ESD group (n=71) had significantly higher odds (compared to the Non ESD group, n=85) of being in the ⩾90 Barthel Index category at 6 weeks (OR = 1.557, 95% CI 2.579 to 8.733), 6 months (OR = 1.541, 95% CI 2.617 to 8.340) and 12 months (OR 0.837, 95% CI 1.306 to 4.087) respectively in relation to baseline. Carers of patients accessing ESD services showed significant improvement in mental health scores (P<0.01). Conclusion: The health benefits of ESD are still evident when evidence based models of these services are implemented in practice

Observation of resonance trapping in an open microwave cavity

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.Comment: to be published in Phys. Rev. Let

New Discrete Basis for Nuclear Structure Studies

A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of weakly-bound orbitals are analyzed and the ground state properties of some spherical doubly-magic nuclei are studied. The basis of the transformed harmonic oscillator is a significant improvement over the harmonic oscillator basis, especially in studies of exotic nuclei where the coupling to the particle continuum is important.Comment: 13 pages, RevTex, 6 p.s. figures, submitted to Phys. Rev.