3 research outputs found
Quantum Entanglement and fixed point Hopf bifurcation
We present the qualitative differences in the phase transitions of the
mono-mode Dicke model in its integrable and chaotic versions. We show that a
first order phase transition occurs in the integrable case whereas a second
order in the chaotic one. This difference is also reflected in the classical
limit: for the integrable case the stable fixed point in phase space suffers a
bifurcation of Hopf type whereas for the second one a pitchfork type
bifurcation has been reported
Universal geometric approach to uncertainty, entropy and information
It is shown that for any ensemble, whether classical or quantum, continuous
or discrete, there is only one measure of the "volume" of the ensemble that is
compatible with several basic geometric postulates. This volume measure is thus
a preferred and universal choice for characterising the inherent spread,
dispersion, localisation, etc, of the ensemble. Remarkably, this unique
"ensemble volume" is a simple function of the ensemble entropy, and hence
provides a new geometric characterisation of the latter quantity. Applications
include unified, volume-based derivations of the Holevo and Shannon bounds in
quantum and classical information theory; a precise geometric interpretation of
thermodynamic entropy for equilibrium ensembles; a geometric derivation of
semi-classical uncertainty relations; a new means for defining classical and
quantum localization for arbitrary evolution processes; a geometric
interpretation of relative entropy; and a new proposed definition for the
spot-size of an optical beam. Advantages of the ensemble volume over other
measures of localization (root-mean-square deviation, Renyi entropies, and
inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10)
of published version