Taksu Cheon

WAVE CHAOS IN QUANTUM BILLIARDS WITH A SMALL BUT FINITE-SIZE SCATTERER

We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is formulated in terms of self-adjoint extension theory of functional analysis. The condition for the appearance of so-called wave chaos is clarified. We then relate the pointlike scatterer to a finite-size scatterer through the appropriate truncation of basis. We show that the signature of wave chaos in low energy states is most prominent when the scatterer is weakly attractive. As an illustration, numerical results of a rectangular billiard with a small rectangular scatterer inside are exhibited.

Folded Bifurcation in Coupled Asymmetric Logistic Maps

A system of two coupled logistic maps, one periodic and the other chaotic, is studied. It is found that with the variation of the coupling strength, the system displays several curious features such as the appearance of quadrupling of period, occurrence of isolated period three attractor and the coexistence of the Hopf and pitchfork bifurcations. Possible applications and extensions are discus· sed. Chaos in higher dimensional systems is one of the focal subjects of physics today. Along with the approach starting from modeling physical systems with many degrees of freedom, there emerged a new approach, developed by Kaneko, to couple many one-dimensional maps 1 H> to study the behavior of the system as a whole. However, this model can only be applied to study the dynamics of a single medium such as pattern formation in a fluid. What happens if two media border each other? One may naturally be lead to a model of coupled logistic maps with different strength parameters. Thus it is appropriate to inquire whether loosening the condition of strict identity might bring any new feature while keeping both maps logistic to hold the redundant controlling parameters minimal. Even two logistic maps coupled to each other may serve as a dynamical model of driven coupled oscillators. It has been found that two coupled identical maps possess several characteristic features which are typical of higher dimensional chaos. 1 >. 4 > In this paper, we report the results of a numerical investigation of a system of two logistic maps with different strength parameters such that one map lies in a period one stable attractor or a bifurcation point and the other in chaotic region when decoupled. Several new features previously unobserved are found. Most notable among them is the appearance of a period four cycle straight from the stable period one cycle. The other peculiar feature is the almost simultaneous occurrence of periods four, eight and sixteen right after the Hopf bifurcation. This results in a very intriguing metamorxad phose of the attractor when one changes the coupling parameter. The system we study is two linearly coupled maps

Response function of asymmetric nuclear matter

Abstract The charge longitudinal response function is examined in the framework of the random-phase approximation in an isospin-asymmetric nuclear matter where proton and neutron densities are different. This asymmetry changes the response through both the particle-hole interaction and the free particle-hole polarization propagator. We discuss these two effects on the response function on the basis of our numerical results in detail.

Chaos and symmetry in the interacting boson model

Abstract The level spectra of the interacting boson model for the whole range of parameters which span over three dynamical symmetries are analyzed in terms of the nearest-neighbour level-spacing distribution, and the “quantum chaos map” is charted. Strongly chaotic level spectra are seen in between SU(3) and O(6) symmetries. Unexpected persistence of Poisson statistics is found along the line connecting U(5) and O(6) symmetries. We argue that this is to be identified with the Berry-Robnik distribution with high division number arising from the preserved O(5) subsymmetry.

Isospin-dependent effective interaction in nucleon-nucleus scattering.

We study the isospin-dependent component of the effective nucleon-nucleon interaction which causes the {Delta}{ital T}=1 ({ital p},{ital p}{prime}) and ({ital p},{ital n}) reactions off nuclei. It is shown that, at intermediate energies, the modification to the impulse approximation comes from the {ital g}-matrix-type correction and the rearrangement term. They are numerically estimated with the isospin-asymmetric nuclear-matter reaction matrix approach. The isobaric-analog transitions {sup 42}Ca({ital p},{ital n}){sup 42}Sc and {sup 48}Ca({ital p},{ital n}){sup 48}Sc are analyzed.

On relativistic and non-relativistic approaches to nucleon-nucleus scattering

Abstract The impulse approximation to the Dirac theory of nucleon-nucleus scattering is reduced to a non-relativistic formalism. It is shown that relativistic effects can be included on the same footing as the effects of the nuclear medium on the effective interaction. We apply the argument to spin observables in 200 MeV and 500 MeV proton elastic scattering on a 40 Ca target.

Resonance tunneling in double-well billiards with a point-like scatterer

Abstract Coherent tunneling is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a point-like scatterer inside the billiard, we can control the occurrence and the resonance tunneling rate. The key role of the avoided crossing is stressed.

Green Function Monte Carlo Method for Excited States of Quantum System

A novel scheme to solve the quantum eigenvalue problem through the imaginary-time Green function Monte Carlo method is presented. This method is applicable not only to the ground states, but also to the excited states of generic system. We demonstrate the actual utility of the method with the numerical examples on three simple systems. Typeset using REVTEX 1 The stochastic quantization has been successfully applied in recent years to the various problems of physics ranging from quantum chromo dynamics to the plasmon oscillation [1-3]. While it can handle very complex systems which is usually beyond the approach either by the direct diagonalization or by the perturbation, it has been only applicable to the calculation of the ground state properties of the system. In this paper, we propose a new method based on the imaginary-time Green function Monte Carlo approach, which is extendable to the excited states of Hamiltonian system. We have primarily in mind the non-relativistic quantum few body problem such as encountered in nuclear physics [4-6]. However, with suitable adaptation, it can also be applied to more general problems. The method is illustrated through the examples of the Morse oscillator and of a simple schematic deformed shell model with two interacting particles in two-dimension, and of a sine-Gordon coupled oscillators. Suppose we want to solve the eigenstate problem of a arbitrary Hamiltonian H , namely H |ψα〉 = Eα |ψα〉 (1) We assume that each eigenstate is normalized to unity. The evolution operator with an imaginary-time t operating on an arbitrary state φ1 will act as e |φ1〉 = ∑ α eα |ψα〉 〈ψα |φ1〉 (2) If we discretize the imaginary-time τ with the unit ∆τ , and name the state of the n-th step of the evolution as |φ1〉 (n) ≡ exp−n∆τH |φ1〉, the evolution at each step ∆τ is described by |φ1〉 (n+1) = e |φ1〉 (n) (3) Clearly, after the sufficient number of steps, all but the lowest energy state die out, and one finds |φ1〉 (n) → e ∆τ E1 |ψ1〉 〈ψ1| φ1〉 (n → ∞), (4) which is the basic relation to filter out the ground state in the imaginary time Green function approach. We consider a second sequence of states φ (n) 2 which satisfies the evolution equation 2 |φ2〉 (n+1) = e |φ2〉 (n) − |φ1〉 (n+1) (n) 〈φ1| e −∆τH |φ2〉 (n) (n) 〈φ1| φ1〉 (n+1) (5) The states φ (n) 1 and φ (n) 2 at adjacent time steps satisfy the orthogonality (n) 〈φ1| φ2〉 (n+1) = 0. Also, from eq. (4), we have the complimentary condition (n) 〈φ2| φ1〉 (n+1) → 0 for sufficiently large n. Expanding eq. (5) in the first order of ∆τ , we have |φ2〉 (n+1) ≈ e uf8f1

Irregular Scattering with Complex Target

The one-dimensional scatterings by a target with two internal degrees of freedom are investigat· ed. The damping of resonance peaks and the associated appearance of fluctuating background found in the quantum inelastic amplitudes are related to the disorderly reaction function in the analog classical system. The scattering experiments have always been one of the prime methods to extract the physical information from otherwise inaccessible world of microscopic scale. Naturally, one realizes the necessity of the fully quantum treatment of the scattering process in atomic, nuclear and particle physics. But in certain instances, the full treatment with extensive numerics is neither feasible nor is physically informative. The semiclassical treatment has been an indispensable rescue in those instances for the molecular and heavy-ion scatterings. The usefulness of the semiclassical theories of scattering has been highlighted in recent years from another perspective. Namely, the advent of the study of chaotic motion in classical mechanics and its quantum manifestation has opened up a new field of chaotic scatterings.) The study of the non-integrable scattering has been mostly done with the system with minimal comxad plexity, that is with the two degrees of freedom, one scattering and the other the internal (or the target) degree of freedom. 2 l This natural starting point has already yielded considerable fruits related to the understanding of Ericson fluctuation. 3 l But it is also very natural to look for the higher dimensional system for the unexplored aspects, and also for the understanding of the realistic system which has many internal degrees of freedom. In this paper, we intend to start this path with the study of a system with three degrees of freedom, one describing the scattering particle and two the remaining target motion. When there are two degrees of freedom in the target, the target motion can acquire multi-periodicity, and even chaotic motion. We shall show that this introduces some new features in the strucxad ture of the classical reaction functions. In the quantum scattering, we focus on the structure of the inelastic scattering amplitude as a function of excitation energy. There, our model displays the damping of the resonance peaks and the genesis of the fluctuating background, a phenomenon frequently encountered in atomic and nuclear scatterings. We present a simple semiclassical argument which relates this quantum behavior with the classical reaction function. We consider a projectile moving in one-dimensional space specified by the coordixad nate and its conjugate momentum (x, p). The particle is scattered by a system (or the target) which is described by the two internal degrees of freedom specified by two sets

Nuclear mass dependence of chaotic dynamics in the Ginocchio model

The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between the current approach and the earlier studies with bosonic models is discussed.