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Beyond quantum microcanonical statistics
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View: Figures


Image of FIG. 1.
FIG. 1.

Time evolution and distribution of the first diagonal element μ0, 0 of the reduced density matrix for an oscillator in the randomly perturbed Einstein oscillator model. The following parameters have been employed: n = 5, E max /ℏω0 = 5.1 (corresponding to a dimension N = 252 of the active Hilbert space), λ/ℏω0 = 10−3. Panels A and B display the evolution μ0, 0(t) for two different random choices of the initial wavefunction, with the corresponding statistical distributions of μ0, 0 reported in panels C and D. The asymptotic time average is indicated by the red dotted line.

Image of FIG. 2.
FIG. 2.

Distribution within RPSE of first element, , of the equilibrium reduced density matrix of a single oscillator of the randomly perturbed Einstein oscillator model as obtained from the sampling of population sets. The distributions refer to systems composed of different number of oscillators (n = 5, 6, 7, 8), with E max /nℏω0 = 2 and λ/ℏω0 = 10−3. In the inset we have reported the numerically determined variance (in a logarithmic scale) as a function of the number n of oscillators.

Image of FIG. 3.
FIG. 3.

Scaled internal energy per component U/nℏω0 (panel A) and entropy per component S/nk B (panel B) as functions of the scaled cutoff energy e max /ℏω0 per component, for systems of n = 5 (red points), n = 10 (black points), and n = 50 (blue points) oscillators. The asymptotic n → ∞ profiles are represented with black continuous lines.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Beyond quantum microcanonical statistics