Chaos quantum

Stookmann Fl-J 1999 Quantum Chaos An Introduction (Cambridge Cambridge University Press)... 

The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. 

There were 29 one-hour talks and a total of seven half-hour talks, mostly by the students. In addition two round table discussions were organised to bring the important topics that still need careful consideration. One was devoted to questions and unsolved problems in Chaos, in particular Quantum Chaos. The other round table discussion considered the outstanding problems in Fundamental Interactions. There were extensive discussions during the two hours devoted to each area. Applications and development of new and diverse techniques was the real focus of these discussions. 

Casati, G. and B.V. Chirkov. Quantum chaos between order and disorder a selection of papers. Cambridge University Press, New York, 1995. 

Signatures of quantum chaos in open chaotic billiards... 

The complex scattering wave function can be specified by nodal points at which u = 0,v = 0. They have great physical significance since they are responsible for current vortices. We have calculated distribution functions for nearest distances between nodal points and found that there is a universal form for open chaotic billiards. The form coincides with the distribution for the Berry function and hence, it may be used as a signature of quantum chaos in open systems. All distributions agree well with numerically computed results for transmission through quantum chaotic billiards. 

The nature of quantum chaos in a specific system is traditionally inferred from its classical counterpart. It is an interdisciplinary field that extends into, for example, atomic and molecular physics, condensed matter physics, nuclear physics, and subatomic physics (H.-... 

These results nicely agree with the Berry conjecture (M.V. Berry, 1977) of quantum chaos according to which the wave function in the chaotic billiard has to be expressed as a sum over an infinite number of plane waves... 

Stockmann, H.-J. Quantum Chaos An Introduction Cambridge University Press, Cambridge, UK, 1999. 

Quantum chaos in floppy molecular systems The LiCN molecule... 

Keywords Quantum chaos, Scar theory, Semiclassical theories, Excited vibrational states, Vibrational spectroscopy... 

Keywords Quantum chaos, finite-temperature, quantum billiard... 

Another development in the quantum chaos where finite-temperature effects are important is the Quantum field theory. As it is shown by recent studies on the Quantum Chromodynamics (QCD) Dirac operator level statistics (Bittner et.al., 1999), nearest level spacing distribution of this operator is governed by random matrix theory both in confinement and deconfinement phases. In the presence of in-medium effects... 

It should be noted that there is no universal approach for the study of finite-temperature effects in quantum chaos, in particular for quantum billiards. One of the way for introducing temperature in billiards is to consider softer-wall Gaussian boundaries. Relation (Stockmann et. ah, 1997) between billiard geometry and the temperature has been considered. 

The role of finite temperature in quantum chaos is studied within the imaginary time formalism via quantum action approach (Caron et al 2001). 

Cvitanovic P. and Eckhardt B. Phys. Rev. Lett. 63, 823 (1989) Eckhardt B. et al Pinball scattering Quantum chaos between order and disorder, eds G. Casati and B. Chirikov (Cambridge University press, Cambridge, 1995) P. 405. 

Taking the experimentally measured mass spectrum of hadrons up to 2.5 GeV from the Particle Data Group, Pascalutsa (2003) could show that the hadron level-spacing distribution is remarkably well described by the Wigner surmise for / = 1 (see Fig. 6). This indicates that the fluctuation properties of the hadron spectrum fall into the GOE universality class, and hence hadrons exhibit the quantum chaos phenomenon. One then should be able to describe the statistical properties of hadron spectra using RMT with random Hamiltonians from GOE that are characterized by good time-reversal and rotational symmetry. 

Bittner, E., Harald Markum and Reiner Pullrich Quantum chaos in physical systems from super conductors to quarks, hep-lat/0110222 Berman, G. P., G. M. Zaslavskii, and A. R. Kolovskii. Sou. Phys. JETP, 61 925, 1985. 

Abstract. Quantum chaos at finite-temperature is studied using a simple paradigm, two-dimensional coupled nonlinear oscillator. As an approach for the treatment of the finite-temperature a real-time finite-temperature field theory, thermofield dynamics, is used. It is found that increasing the temperature leads to a smooth transition from Poissonian to Gaussian distribution in nearest neighbor level spacing distribution. 

In this work we give a simple presciption for the treatment of finite-temperature effects in quantum chaos using a well-known paradigm of nonlinear dynamics, nonlinear oscillator. 

Seligman, T. H., and Nishioka, H. (Eds.) (1986), Quantum Chaos and Statistical Nuclear Physics, Springer-Verlag, Berlin. 

MSN. 134.1. Prigogine and T. Petrosky, Quantum chaos—Towards the formulation of an alternate quantum theory, Proceedings, H International Wigner Symposium, H. D. Doebner, W. Scherer, and F. Schroeck Jr., eds., World Scientihc, Singapore, 1992. 

MSN. 139. T. Petrosky and I. Prigogine, Complex spectral representations and quantum chaos, in Research Trends in Physics Chaotic Dynamics and Transport in Fluids and Plasmas, Institute of Advanced Studies, La Jolla, 1992. 

MSN.141. I. Prigogine, From classical chaos to quantum chaos, Vistas in Astron. 37, 7—25 (1993). 

MSN. 145. T. Petrosky and I. Prigogine, Quantum chaos, complex spectral representations and time symmetry breaking, Chaos, Solitons and Fractals 4, 311-359 (1994). 

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