Quantum chaos in compact lattice QED

Berg, Bernd A.; Markum, H.; Pullirsch, Rainer

doi:10.1103/physrevd.59.097504

Cited by 23 publications

(24 citation statements)

References 22 publications

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“…In particular, this has been confirmed by the analysis of the low-energy effective theory [4,5,6,7], universality studies [8,9,10,11,12], lattice QCD simulations [13,4,14,15,17,18,16,19,20,21,22] and the study two-sublattice theories with disorder [23,24,25,26]. This means that the dynamical details of QCD are not important on energy scales of the order of the average level spacing.…”

Section: Introductionsupporting

confidence: 48%

“…Spectral correlations have been studied in great detail for both lattice QCD simulations [4,14,15,19,17,20,21] and instanton-liquid simulations [5] (see [2] for a recent review). In lattice QCD they were studied by means of the disconnected scalar susceptibility [22], and complete agreement with partially quenched chiral perturbation theory was found.…”

Section: Comparison With Instanton Simulationsmentioning

confidence: 99%

“…and summing the geometric series after using the explicit expression (20) for the ω n . Instead of working with the canonical ensemble we eliminate the constraint on the sum over the n i by working with the grand canonical ensemble.…”

Section: Definition Of the Modelmentioning

confidence: 99%

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Chiral random matrix model for critical statistics

García-García

Verbaarschot

2000

Nuclear Physics B

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We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a noninteracting Fermi-gas we show that for energy differences less than a critical energy E c the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than E c the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained.

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Section: Introductionsupporting

confidence: 48%

Section: Comparison With Instanton Simulationsmentioning

confidence: 99%

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Chiral random matrix model for critical statistics

García-García

Verbaarschot

2000

Nuclear Physics B

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“…The properties of the Dirac spectrum have been analyzed in many lattice QCD simulations [ 33,3,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] [ 49,50,51,52,53,54] and have been found to be in complete agreement with the conclusions of the previous section. We only show three representative examples.…”

Section: Lattice Resultssupporting

confidence: 73%

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Toublan¹,

Verbaarschot²

2002

Continuous Advances in QCD 2002

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We show that QCD Dirac spectra well below Λ QCD , both at zero and at nonzero chemical potential, can be obtained from a chiral Lagrangian. At nonzero chemical potential Goldstone bosons with nonzero baryon number condense beyond a critical value. Such superfluid phase transition is likely to occur in any system with a chemical potential with the quantum numbers of the Goldstone bosons. We discuss the phase diagram for one such system, QCD with two colors, and show the existence of a tricritical point in an effective potential approach.

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“…The agreement extends on both sides of the confinement-deconfinement phase transition [23,36]. However, to the authors' knowledge there is no analytical prediction from chRMT for the level spacing distribution when focusing on the soft edge or at T c .…”

Section: B Level Spacing Distributionmentioning

confidence: 78%

Microscopic universality and the chiral phase transition in two flavor QCD

et al. 2000

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We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator for SU(3) lattice gauge theory with dynamical fermions are examined. We consider temperatures below, near, and above the critical temperature Tc for the chiral phase transition. Below and above Tc the statistics are in agreement with the exact analytical predictions in the microscopic scaling regime. Above Tc we observe a gap in the spectral density and a distribution compatible with the Airy distribution. Near Tc the eigenvalue correlations appear inconsistent with chRMT.

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Quantum chaos in compact lattice QED

Cited by 23 publications

References 22 publications

Chiral random matrix model for critical statistics

Chiral random matrix model for critical statistics

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Microscopic universality and the chiral phase transition in two flavor QCD

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