A thermodynamic analysis of energy eigenvalues

Shriner, J. F.; Pato, M. P.; Mitchell, G. E.; Tufaile, Alberto

doi:10.1016/j.nima.2007.08.171

Cited by 5 publications

(9 citation statements)

References 18 publications

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“…To determine V , the connection between level density ρ and potential V implied by Dyson's mean field equation [13] has been employed [15]:…”

Section: The Internal Energy U Generalmentioning

confidence: 99%

“…The details of this unfolding procedure are given in [15]. Ensembles of 2500 GOE and Poisson spectra ranging in size from N = 10 levels to N = 1000 levels were generated.…”

Section: The Internal Energy U Generalmentioning

confidence: 99%

“…[15]). To ensure that these conditions are met exactly, we apply two more transformations to the energy eigenvalues (for both GOE and Poisson spectra), the first to set the average spacing and the second to center the eigenvalues (see ref.…”

Section: The Internal Energy U Generalmentioning

confidence: 99%

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Thermodynamic analysis of spectra

Mitchell¹,

Shriner²

2008

AIP Conference Proceedings

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A new combination of replica exchange Monte Carlo and histogram analysis for protein folding and thermodynamics Abstract.Although random matrix theory had its initial application to neutron resonances, there is a relative scarcity of suitable nuclear data. The primary reason for this is the sensitivity of the standard measures used to evaluate spectra -the spectra must be essential pure (no state with a different symmetry) and complete (no states missing). Additional measures that are less sensitive to these experimental limitations are of significant value. The standard measure for long range order is the ∆ 3 statistic. In the original paper that introduced this statistic, Dyson and Mehta also attempted to evaluate spectra with thermodynamic variables obtained from the circular orthogonal ensemble. We consider the thermodynamic "internal energy" and evaluate its sensitivity to experimental limitations such as missing and spurious levels. Monte Carlo simulations suggest that the internal energy is less sensitive to mistakes than is ∆ 3 , and thus the internal energy can serve as a addition to the tool kit for evaluating experimental spectra.

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“…To determine V , the connection between level density ρ and potential V implied by Dyson's mean field equation [13] has been employed [15]:…”

Section: The Internal Energy U Generalmentioning

confidence: 99%

“…The details of this unfolding procedure are given in [15]. Ensembles of 2500 GOE and Poisson spectra ranging in size from N = 10 levels to N = 1000 levels were generated.…”

Section: The Internal Energy U Generalmentioning

confidence: 99%

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Thermodynamic analysis of spectra

Mitchell¹,

Shriner²

2008

AIP Conference Proceedings

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“…The problem of spurious levels is addressed in Ref. [5] with both A3(L) and the thermodynamic internal energy. A search for missed levels was performed on opened spectra using RMT methods, keeping in mind that a search for intruders would give the same results.…”

Section: Introductionmentioning

confidence: 99%

Open quantum systems and random matrix theory

Mulhall

2015

Phys. Rev. C

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A simple model for open quantum systems is analyzed with random matrix theory. The system is coupled to the continuum in a minimal way. In this paper the effect on the level statistics of opening the system is seen. In particular the A3(L) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a super-radiant transition is observed. The level spacing and A3(L) statistics exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed.

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“…In [4] it was seen that the effect on ∆ 3 (L) of intruder levels or missed levels was the same. The problem of spurious levels is addressed in [5] with both ∆ 3 (L) and the thermodynamic internal energy.…”

Section: Introductionmentioning

confidence: 99%

Open quantum systems and random matrix theory

Mulhall

2014

AIP Conference Proceedings

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A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper the effect of opening the system on the level statistics is seen. In particular the ∆ 3 (L) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a superradiant transition is observed. The level spacing and ∆ 3 (L) statistic exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed. * Electronic address: mulhalld2@scranton.edu

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A thermodynamic analysis of energy eigenvalues

Cited by 5 publications

References 18 publications

Thermodynamic analysis of spectra

Thermodynamic analysis of spectra

Open quantum systems and random matrix theory

Open quantum systems and random matrix theory

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