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Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system
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10.1063/1.3456000
/content/aip/journal/jcp/133/3/10.1063/1.3456000
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/3/10.1063/1.3456000
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Domain for the independent occupation numbers represented as the gray area.

Image of FIG. 2.
FIG. 2.

Gaussian density of states of ten identical spins (solid line). The histogram shows the degeneracy calculated according to Eq. (7).

Image of FIG. 3.
FIG. 3.

Average FEEE entropy per spin as a function of the internal energy per spin for a system composed of three levels systems. The continuous line represents the asymptotic behavior described by Eq. (23), while the other lines are the results of calculation according to Eq. (20) for finite systems: (dashed line), (dashed-dotted line), and (dotted line).

Image of FIG. 4.
FIG. 4.

Parameter [Eq. (27)] which quantifies the deviations from the canonical form of the reduced density matrix as a function of the internal energy. The dashed and the dotted lines refer to a system with and with spins, while the continuous line represents the asymptotic result Eq. (29) for a large number of spins.

Image of FIG. 5.
FIG. 5.

Ratio between the dimensions of RPSE active space and of the overall Hilbert space, in a logarithmic scale, as function of the scaled cutoff energy. Dotted lines: Eq. (32) resulting from the Gaussian density of states; continuous lines: exact calculations for a system of and of spins, respectively.

Image of FIG. 6.
FIG. 6.

Logarithm of the dimensions of RPSE active space, divided by the number of spin, as a function of the energy cut off. Continuous line: asymptotic dependence [Eqs. (49) and (45)]; dotted lines: exact results for finite systems approaching the asymptotic profile for an increasing number of spins: , 30, and 100.

Image of FIG. 7.
FIG. 7.

RPSE internal energy a function of the energy cutoff. Continuous line: asymptotic behavior described by Eqs. (56) and (58). The dotted lines represent the result for finite system approaching the asymptotic profile for an increasing number of spins: , 50, and 150.

Image of FIG. 8.
FIG. 8.

Inverse temperature as function of the internal energy from RPSE.

Image of FIG. 9.
FIG. 9.

Dependence of the RPSE average of the reduced density matrix elements on the scaled cutoff energy. The asymptotic function which describes the dependence of the typical values on the energy Eq. (71) is reported as continuous lines. The other lines represent the result for finite system approaching the asymptotic profile for an increasing number of spins: , 30, and 100.

Image of FIG. 10.
FIG. 10.

Plot of the location of maximum with respect to (continuous line) within the existence domain of the function (gray area).

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/content/aip/journal/jcp/133/3/10.1063/1.3456000
2010-07-20
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/3/10.1063/1.3456000
10.1063/1.3456000
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