Universal power law in crossover from integrability to quantum chaos

We study models of interacting fermions in one dimension to investigate the crossover from integrability to nonintegrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size L -> infinity nonintegrability sets in for an arbitrarily small integrability-breaking perturbation. The crossover value of the perturbation scales as a power law similar to L-eta when the integrable system is gapless. The exponent eta approximate to 3 appears to be robust to microscopic details and the precise form of the perturbation. We conjecture that the exponent in the power law is characteristic of the random matrix ensemble describing the nonintegrable system. For systems with a gap, the crossover scaling appears to be faster than a power law.

Quantum chaos in ultracold collisions between Yb(¹S0) and Yb(³P2)

We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2) collisions as a function of an interatomic potential scaling factor λ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in λ, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Largely deformed dinuclear system formed in F-19+Al-27 dissipative collision

Excitation functions are measured for different charge products of the F-19+(27) Al reaction in the laboratory energy range 110.25-118.75MeV in steps of 250keV at theta(lab) = 57 degrees, 31 degrees and -29 degrees. The coherence rotation angular velocities of the intermediate dinuclear systems formed in the reaction are extracted from the cross section energy autocorrelation functions. Compared the angular velocity extracted from the experimental data with the ones deduced from the sticking limit, it is indicated that a larger deformation of the intermediate dinuclear system exists.

形变原子核系统中的量子混沌运动的研究

按照玻尔的对应原理，将量子力学应用到宏观运动上所得的结果应该与经典力学的结果一致。故而力学系统的混沌特征也必然要在其量子性质上有所表现。迄今，对量子混沌运动研究多局限于研究经典上混沌的系统对应的量子系统有什么量子表现，但这些量子表现的动力学根源仍然不清楚。应用量子可积系统H_0的最小测不准度态作为初绐态，研究了在扰动哈密顿量作用下波包随时间、空间的演化特征。在完全的量子力学动力学描述框架下，量子波包的空-时演化表现了与经典力学中一一对应的对初值的敏感性。对自治的哈密顿系统，选定初始位置的波包始终分布在确定的能区内。起始于经典上混沌的相空间内的相干态，在其时空演化时，所包含的能级呈现GOE分布，能级之间存在着大量的免交叉。免交叉处两能级对应的态函数发生强混杂，呈现非线性共振，因而态函数发生突变。正由于波包中一对对相邻能级、状态之间的这种非线性其振的出现，在确定的动力学方程描述下的波包的确定的空时演化特征变得非常复杂，以至于成为混沌的。我们用系统中一组完备的动力学变量的期望值及其相应的测不准度来描述波包在量子空间的拓扑性质。因此，量子混沌运动可以用与量子规则运动对比的方法进行研究，并用其渐近行为表示其特征。数值计算的结果表明，量子可积系统的最小测不准态波包的空时演化动力学性质确实表现了与相应的经典系统对应的初值敏感性及波包扩展宽度随时间指数式的扩散行为，后者保证了系统的混杂性。而在混杂之后，即波包宽度随时间指数式扩散之后，宽度达到稳定。这时，波包中各状态的分布趋于各态历经。由于采用了徐躬耦先生所建议的等效普朗克常数，我们的结果可方便地推广到经典极限。因此可明确地区分波包的空时演化特征中的量子效应和动力学效应。

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

Estudo da distribuição de espaçamentos de dubletos utilizando o modelo do bilhar anular

Pós-graduação em Física - IGCE

Caos e termalização na teoria de Yang-Mills com quebra espontânea de simetria

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Caos e termalização na teoria de Yang-Mills-Higgs em uma rede espacial

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)