The $1/r^2$ Integrable system: The Universal Hamiltonian for Quantum Chaos

Details The $1/r^2$ Integrable system: The Universal Hamiltonian for Quantum Chaos The $1/r^2$ Integrable system: The Universal Hamiltonian for Quantum Chaos

1994-02-16

arxiv.org/abs/cond-mat/9402065v1

Physics

Condensed Matter

bss@physics.att.com from March , Physics Department, Indian Institute of Science, BANGALORE,560012 India bss@physics.iisc.erne

Scientific paper

We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their eigenvalues under changes of parameters. The robustness of bulk space-time correlations of a many particle system to changing boundary conditions is suggested to be at the root of the universality. The explicit density-density correlation functions of the $1/r^2$ model, now available through the above mapping at two values of the coupling constant, are interpreted in the light of Bethe's {\it Ansatz}, giving a vivid picture of the fractionalization of bare particles or holes into ``quark'' like Bethe quasi-particles and holes.

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