A supersymmetry approach to billiards with randomly distributed scatterers

Stoeckmann, H.J.

doi:10.1088/0305-4470/35/25/302

Cited by 4 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a particular example, we consider an intermediate ensemble from arbitrary unitarily invariant ensembles over Hermitian matrices to a rotation invariant ensemble over one of the symmetric spaces. This generalizes the known results [39][40][41][42][43][44][45][46][47]. For this example we use the supersymmetry method.…”

Section: Introductionsupporting

confidence: 68%

Derivation of determinantal structures for random matrix ensembles in a new way

Kieburg¹,

Guhr²

2010

J. Phys. A: Math. Theor.

121

View full text Add to dashboard Cite

Abstract. There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques.Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can coin our approach "supersymmetry without supersymmetry" because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.

show abstract

Section: Introductionsupporting

confidence: 68%

Derivation of determinantal structures for random matrix ensembles in a new way

Kieburg¹,

Guhr²

2010

J. Phys. A: Math. Theor.

121

View full text Add to dashboard Cite

show abstract

“…Otherwise the deviations from this behavior are significant due to the unitarity of the S matrix [4,10,38,39]. The complexity involved in the calculations of the correlation functions [9,10,40] indicates that those of the distributions of the S-matrix elements constitute a challenging task. However, this was partially accomplished in [17] where the distribution of the diagonal S-matrix elements was derived.…”

mentioning

confidence: 99%

Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering

Kumar¹,

Nock²,

Sommers³

et al. 2013

Phys. Rev. Lett.

View full text Add to dashboard Cite

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory, the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices. A long-standing problem was the computation of the distribution of the off-diagonal scattering-matrix elements. We report here an exact solution to this problem and present analytical results for systems with preserved and with violated time-reversal invariance. Our derivation is based on a new variant of the supersymmetry method. We also validate our results with scattering data obtained from experiments with microwave billiards.

show abstract

A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations

Guhr

Stöckmann

2004

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

In a previous contribution (H.J. Stöckmann, J. Phys. A35, 5165 (2002)), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian Unitary Ensemble (GUE) of random matrices. In passing from the band centre to the tail states, The density of states is depleted considerably and the twopoint correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as similar to a mobility edge.

show abstract

A supersymmetry approach to billiards with randomly distributed scatterers

Cited by 4 publications

References 27 publications

Derivation of determinantal structures for random matrix ensembles in a new way

Derivation of determinantal structures for random matrix ensembles in a new way

Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering

A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations

Contact Info

Product

Resources

About