We investigate dynamics of scalar field with non-minimal kinetic term. Nontrivial behavior of the field in the vicinity of singular points of kinetic term is observed. In particular, the singular points could serve as attractor for classical solutions.
We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and harmonic oscillator. By unfolding of the spectrum of such matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe Poissonian behavior in the integrable case and Wignerian behavior in the chaotic case. We present numerical evidence that the action matrix of the stadium billiard displays GOE behavior and give an explanation for it. The findings present evidence for universality of level fluctuations -known from quantum chaos -also to hold in classical physics. [7] states that in time-reversal invariant quantum systems with fully chaotic classical counterpart, the energy level spacing distribution is the same as that obtained from random matrices of a certain symmetry (Gaussian orthogonal ensembles GOE), resulting in a Wignerian distribution. This paper is about classical chaos occuring widely in nature, for example in astro physics, meteorology and dynamics of the atmosphere, fluid and ocean dynamics, climate change, chemical reactions, biology, physiology, neuroscience, or medicine. Traditionally, classical chaos is described by tools of nonlinear dynamics like Lyapunov exponents, Kolmogorov-Sinai entropy and phase space portraits (Poincaré sections). In this work we present evidence that fully chaotic classical systems show univer-
We investigate chaotic behavior in a 2-D Hamiltonian system -oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincaré sections and compute Lyapunov exponents for the quantum system. We find that the quantum system is globally less chaotic than the classical system. We also observe with increasing energy the distribution of Lyapunov exponts approaching a Gaussian with a strong correlation between its mean value and energy. Introduction. Quantum chaos has been experimentally observed in irregular energy spectra of nuclei, of atoms perturbed by strong electromagnetic fields [1], and in billiard systems [2,3,4]. Irregular patterns have been found in the wave functions of the quantum mechanical stadium billard [5], where scars are reminders of classical motion [6]. Recently, dynamical tunneling in atoms between regular islands has been observed. The transition is enhanced by chaos [7,8]. Spectra of fully chaotic quantum systems can statistically be described by random matrices [9], which corresponds to a level density distribution of Wigner-type, while integrable (nonchaotic) quantum system yield a Poissonian distribution. Here we ask: What happens between these two extremes? For example, an hydrogen atom exposed to a weak exterior magnetic field shows a level distribution, which is neither Poissonian nor Wignerian. Can we compare classical chaos with quantum chaos? And is the quantum system more or less chaotic than the corresponding classical system? Also we address the following problem: An understanding of how classically regular and chaotic phase space is reflected in quantum systems is an open problem. Semiclassical methods of quantisation (EKB, Gutzwiller's trace formula) are not amenable to mixed dynamical systems [10]. Here we suggest a solution using the concept of the quantum action [13,14]. It parametrizes quantum transition amplitudes in
We investigate chaotic behavior in a 2-D Hamiltonian system -oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincaré sections and compute Lyapunov exponents for the quantum system. We find that the quantum system is globally less chaotic than the classical system. We also observe with increasing energy the distribution of Lyapunov exponts approaching a Gaussian with a strong correlation between its mean value and energy.
We compute numerically the quantum action for the inverse square potential and compare the global fit method with a new method, the flow equation. We investigate the error of fitting quantum-mechanical transition amplitudes by the quantum action. The flow equation works well in the regime of large T giving results consistent with the global fit method.
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