Doorway Mechanism in Many-Body Systems and in Quantum Billiards

Abstract

Among the numerous different ways to excite many-body and other complex quantum systems, mechanisms are often found which are clearly distinguished by a simple, typically semiclassical interpretation. In nuclei, these are the collective excitations in which all or large groups of particles move coherently. They often act as "doorways" to other excitations of single-particle character. Examples for and the limitations of the doorway mechanism are discussed. Recent results show that superscars in the barrier billiard serve as perfect object to shed light on aspects of the doorway mechanism which are not directly accessible in traditional quantum systems. To this end, two new statistical observables are employed. Some open questions are addressed.

Envelope and phase distribution of a resonance transmission through a complex environment

“…The bulk of distribution ( 21 is essentially given by that at zero absorption, Eq. (11). The correction factor becomes crucial near the edges, where the exact distribution has an exponential cutoff ∼ e −(γ/4η) sec 2 θ .…”

“…The phase distribution (11) has a local maximum (minimum) at θ = 0 for η < 1 (η > 1) and becomes uniform at the special coupling η = 1. Note that this function has the following symmetry P 0 (θ)| η = P 0 (θ± π 2 )| η −1 under the involution η → η −1 .…”

“…In many situations, including examples from atomic and nuclear physics [5][6][7][8][9] and open mesoscopic systems [10][11][12][13], such a resonance state is embedded in the background of many complicated states. It represents a specific "simple" (deterministic) excitation [5], the amplitude of which spreads over the chaotic states.…”

Collective versus single-particle motion in quantum many-body systems from the perspective of an integrable model

“…A recent discussion can be found in Ref. [15]. Although successful in the qualitative description of collective excitation in nuclei, this model does not provide any explanation of the physical reasons that lead to the collective behavior.…”

Untitled

“…Although a recent discussion is available in Ref. [1], we briefly discuss the salient features by means of examples to make the present contribution self-contained. Consider anticrossing spectroscopy in molecular physics, see Ref.…”