Binary ionic mixtures and a solvable model

Jancovici, B.

doi:10.1080/00268978400101921

Cited by 10 publications

(14 citation statements)

References 13 publications

(14 reference statements)

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“…Our model gives a natural chiral extension of the ensemble treated in [8,9]. Although our main motivation is the application to QCD lattice calculations with µ = 0 the new correlation functions we derive may find other applications as well, such as in the fractional Quantum Hall effect [20] or two-dimensional charged plasmas [21]. We restrict ourselves to work with a Gaussian chiral RMM.…”

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confidence: 99%

Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

Akemann

2002

Phys. Rev. Lett.

118

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A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac operator eigenvalues at zero virtuality. The parameter which measures the non-Hermiticity of the Dirac matrix is identified with the chemical potential.In the phase with broken chiral symmetry all spectral correlations of the Dirac eigenvalues are calculated as functions of quark flavors and chemical potential. The derivation uses the orthogonality of the Laguerre polynomials in the complex plane. Explicit results are given for any finite matrix size N as well in the large-N limit for weak and strong non-Hermiticity. Much less is known so far for spectral correlations of complex eigenvalues derived from RMM. Although the first results date back to Ginibre [5] where the correlations for the complex Unitary Ensemble labeled by the Dyson index β = 2 were calculated, progress has been slow. The correlation functions of the ensemble with real non-symmetric matrices (β = 1) are still unknown. Results for quaternion matrices (β = 4) were obtained more recently in [6,7] and the inclusion of Dirac mass terms for β = 2 in [8]. Furthermore, it has been realized by works of Fyodorov and collaborators [9] that different regimes of complex eigenvalues exist, the weak and strong nonHermiticity limit. In the present work we wish to extend the knowledge about complex matrix models to the socalled chiral models.Chiral RMM of real eigenvalues have been introduced to describe the local fluctuation properties of the Dirac operator in QCD at the origin [10]. The low energy spectrum of the QCD Dirac operator is a very sensitive tool to study the phenomenon of chiral symmetry breaking [11]. The predictions of the different chiral RMM ensembles have been very successful in describing the dependence on the gauge group and its representation, the number of quark flavors and masses and the topology [12]. In particular the topology dependence has been very useful in comparison with new developments in lattice gauge theory, admitting to incorporate an exact chiral symmetry [13]. By now the field theoretic origin of the RMM description has also been well understood [14].On the other hand lattice simulations in the presence of a chemical potential µ, which renders the Dirac eigenvalues complex, remain extremely difficult, as reviewed in [15]. Although recent progress has been made [16] along the phase transition line the general phase diagram remains unexplored for µ = 0. It is in this context that analytical knowledge of microscopic correlation functions from complex chiral RMM could be very useful, in view of its success in predicting real eigenvalue correlations.Chiral RMM including a chemical potential have been already studied in several works [4,17,18,19]. In [4] the nature of the quenched limit has been analyzed in such a model, and the global density of complex eigenvalues together with its boundary hav...

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confidence: 99%

Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

Akemann

2002

Phys. Rev. Lett.

118

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“…[10] correlation functions for a charged two-dimensional plasma with fractional charges at the origin have been obtained, in what we call strong non-Hermiticity limit. However, since the interaction term induced by the Vandermonde determinant of squared arguments in our model eq.…”

Section: The Strong Non-hermiticity Limitmentioning

confidence: 99%

“…On the other hand for eq. (2.8) the macroscopic density has been calculated in [8], 10) where the eigenvalues are bounded by the following curve 2…”

Section: The Modelmentioning

confidence: 99%

“…As examples we mention localization in superconductors [6], dissipation and scattering in Quantum Chaos [7] or Quantum Chromodynamics (QCD) with a non-vanishing chemical potential [8]. Other possible applications include the fractional Quantum Hall Effect as in [9] or a two-dimensional plasma of charged particles [10,11]. A classification of all models with non-Hermitian matrices has been achieved more recently [12] and the number of possible cases exceeds by far those with real eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

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The solution of a chiral random matrix model with complex eigenvalues

Akemann

2003

J. Phys. A: Math. Gen.

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We describe in detail the solution of the extension of the chiral Gaussian Unitary Ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. Applications to the Dirac operator eigenvalue spectrum in QCD with non-vanishing chemical potential are briefly discussed. This is an extended version of hep-th/0204068.

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“…All potential moments are available for the present system due to the knowledge of the induced charge density around the guest charge [18,1]:…”

Section: One-component Plasma At βE 2 =mentioning

confidence: 99%

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Jancovici

Šamaj

2008

J Stat Phys

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A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases.

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Binary ionic mixtures and a solvable model

Cited by 10 publications

References 13 publications

Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

The solution of a chiral random matrix model with complex eigenvalues

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

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