2016
DOI: 10.1088/0951-7715/29/2/325
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Classical foundations of many-particle quantum chaos

Abstract: In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however, the scope of this approach has been mainly limited to systems of a few particles with low-dimensional phase spaces. In the present work we consider Nparticle chaotic systems with local homogeneous interactions, where N is not necessarily small. Based on a model of coupled c… Show more

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Cited by 28 publications
(81 citation statements)
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“…the embedded many-body ensembles [39,40] or ensembles sensitive to the spacial structure of the problem. An example for a situation where the spacial structure is important is the continuum limit with diverging number of sites; additional orbit correlations relevant in this case were identified in [41].…”
Section: Systems Without a Spectral Gapmentioning
confidence: 99%
“…the embedded many-body ensembles [39,40] or ensembles sensitive to the spacial structure of the problem. An example for a situation where the spacial structure is important is the continuum limit with diverging number of sites; additional orbit correlations relevant in this case were identified in [41].…”
Section: Systems Without a Spectral Gapmentioning
confidence: 99%
“…The huge dimension of the Hilbert space might seem to raise an impenetrable barrier for the applicability of semiclassical tools such as the Gutzwiller trace formula [32]. We demonstrate that this problem can be circumvented by a suitable generalization of the recently discovered duality relation [28,33] that maps properties of the time evo-arXiv:1611.05749v1 [nlin.CD] 17 Nov 2016 lution and of the enlargement of the system (by adding further particles) onto each other. Second, we wish to demonstrate the importance of collective motion.…”
mentioning
confidence: 99%
“…These six constraints fully fix the even spins, (30) and (33) hold for each of the spins separately, while (31) and (32) impose only two further conditions.…”
Section: Periodic Orbit Manifoldsmentioning
confidence: 99%