Related papers: Towards chaos criterion in quantum field theory
Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics.
We discuss the necessity and demonstrate the validity of introduction the notion of deterministic chaos in quantum field theory. Brief review of the existing approaches to this problem is given. We compare proposed chaos criterion for…
The earlier suggested criterion of quantum chaoticity, borrowed from the nuclear compound resonance theory, is used in the analysis of the quantum diamagnetic Kepler problem (the spinless charged particle motion in the Coulomb and…
A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory, and to use erratic behavior of the…
A semiclassical method to determine if the classical limit of a quantum system is chaotic or not, based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow--type model and it is concluded that its classical…
We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincar\'e sections etc. be carried over to…
Based on the Hilbert space approach to the theory of nonlinear dynamical systems developed by the author a hypothesis is formulated concerning the "quantal" criterion for classical ordinary differential systems to exhibit chaotic behaviour.
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
We propose a formalism which makes the chaos to be quantized. Quantum mechanical equation is derived for describing the chaos for a particle moving in an electromagnetic field.
We discuss how the concept of the quantum action can be used to characterize quantum chaos. As an example we study quantum mechanics of the inverse square potential in order to test some questions related to quantum action. Quantum chaos is…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to…
We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of…
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…