<i>Shell-Model Approach To Nuclear Reactions</i>

Mahaux, C.; Weidenmüller, Hans A.; Klein, Abraham

doi:10.1063/1.3022571

Cited by 506 publications

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“…The poles of the S-matrix are near to the real axis and ℑ(W ) is small. The effective Hamilton operator is H = H 0 + ℜ(W ) + ℑ(W ) = ℜ(H) − iV V † where the V are the coupling vectors between discrete and scattering states [19]. The level repulsion along the real energy axis is embodied in ℜ(H) by choosing, e.g., the Gaussian orthogonal ensemble.…”

Section: Discussionmentioning

confidence: 99%

Spectroscopic studies in open quantum systems

et al. 2000

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The spectroscopic properties of an open quantum system are determined by the eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the Hamiltonian H 0 of the corresponding closed system and a non-Hermitian correction term W arising from the interaction via the continuum of decay channels. The hermitian part of H is H 0 + ℜ(W ) while the anti-hermitian part is ℑ(W ). This holds for a many-particle system as well as for a microwave resonator. The eigenvalues E R of H are complex. They are the poles of the S-matrix and provide both the energies and widths of the states. We illustrate the interplay between ℜ(H) and ℑ(H) by means of the different interference phenomena between two neighboured resonance states. Level repulsion along the real axis appears if the interaction is caused mainly by (the non-diagonal part of) ℜ(H) while a bifurcation of the widths appears if the interaction occurs mainly due to (the non-diagonal part of) ℑ(H). We then calculate the poles of the S-matrix and the corresponding wavefunctions for a rectangular microwave resonator with a scatter as a function of the area of the resonator as well as of the degree of opening to a guide. The calculations are performed by using the method of exterior complex scaling. ℜ(W ) and ℑ(W ) cause changes in the structure of the wavefunctions which are permanent, as a rule. At full opening to the lead, short-lived collective states are formed together with long-lived trapped states. The wavefunctions of the short-lived states at full opening to the lead are very different from those at small opening. The resonance picture obtained from the microwave resonator shows all the characteristic features known from the study of many-body systems in spite of the absence of two-body forces. The poles of the S-matrix determine the conductance of the resonator. Effects arising from the interplay between resonance trapping and level repulsion along the real axis are not involved in the statistical theory (random matrix theory).

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Section: Discussionmentioning

confidence: 99%

Spectroscopic studies in open quantum systems

et al. 2000

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“…ImĜ(E + i0) and separate the channel and internal components of the Green functionĜ(E + i0) [29]. We obtain…”

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Fano interference and cross-section fluctuations in molecular photodissociation

et al. 2006

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We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.

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“…These systems are often described within the "effective non-Hermitian Hamiltonian" formalism [5]. The eigenvalues of the effective Hamiltonian are complex E n = E n −iΓ n /2, with the nonzero imaginary part, describing the rate with which an eigenstate of the open system (termed resonance state) decays in time due to the coupling to the "outside world".…”

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“…Our results (1,2,3) are confirmed numerically and are supported by theoretical arguments. A usual way to treat the coupling of bound states with continuum is to exclude the continuum degrees of freedom from consideration by the introduction of an effective Hamiltonian H eff acting within the subspace of bound states and implicitly taking into account their interaction with the continuum [5]. In the case of a dimer trap, it is natural to assume that the probability to escape in the continuum is proportional to the number of the bosons located at the site (say the second one) which is coupled to the continuum [24].…”

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confidence: 99%

“…The interplay of intrinsic dynamics with coupling to the continuum, radiation field or to any other external influence, such as measurement, is an important subject for various branches of modern physics: quantum chaos [1], nanoscale devices [2], quantum optics [3], theory of decoherence and quantum computing [4] up to nuclear [5], atomic and molecular physics [6] are some of the areas, seemingly far remote from each other, that boosted the research in open systems. These systems are often described within the "effective non-Hermitian Hamiltonian" formalism [5].…”

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Bifurcations in resonance widths of an open Bose-Hubbard dimer

2006

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We investigate the structure of resonance widths of a Bose-Hubbard Dimer with inter-site hopping amplitude k, which is coupled to continuum at one of the sites with strength γ. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term χ the resonances undergo consequent bifurcations. For Λ = k/γ ≥ 0.5, the bifurcation points follow a scaling lawχm ≡ χmN/k = fΛ(m − 0.5/Λ), where N is the number of bosons. For the function fΛ two different Λ dependences are found around the minimum and the maximum bifurcation point.

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Shell-Model Approach To Nuclear Reactions

Cited by 506 publications

References 0 publications

Spectroscopic studies in open quantum systems

Spectroscopic studies in open quantum systems

Fano interference and cross-section fluctuations in molecular photodissociation

Bifurcations in resonance widths of an open Bose-Hubbard dimer

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