Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9504048

Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles

C. M. Canali·V. E. Kravtsov
View original source ↗Read source document ↗Export metadata ↓

Abstract

It is shown that the two-level correlation function $R(s,s')$ in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term ${\rm var}(n)=ηn$ that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, $η$ playing the role of an order-parameter.

Explore related subjects

cond-mat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. M. Canali, V. E. Kravtsov. 1995-04-12. Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles. https://doi.org/10.1103/physreve.51.r5185

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2017

Random-Matrix Theory of Quantum Size Effects on Nuclear Magnetic Resonance in Metal Particles

The distribution function of the local density of states is computed exactly for the Wigner-Dyson ensemble of random Hamiltonians. In the absence of time-reversal symmetry, precise agreement is obtained with the "supersymmetry" theory by Efetov and Prigodin of the NMR lineshape in disordered metal particles. Upon breaking time-reversal symmetry, the variance of the Knight shift in the smallest particles is reduced by a universal factor of 2/3. ***To be published in Physical Review B.****

cond-mat↗
arXiv2017

Andreev Reflection In Ferromagnet-Superconductor Junctions

The transport properties of a ferromagnet-superconductor (FS) junction are studied in a scattering formulation. Andreev reflection at the FS interface is strongly affected by the exchange interaction in the ferromagnet. The conductance G_FS of a ballistic point contact between F and S can be both larger or smaller than the value G_FN with the superconductor in the normal state, depending on the ratio of the exchange and Fermi energies. If the ferromagnet contains a tunnel barrier (I), the conductance G_FIFS exhibits resonances which do not vanish in linear response -- in contrast to the Tomasch oscillations for non-ferromagnetic materials.

cond-mat↗
arXiv2017

Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which diffuse in a $ d $-dimensional disordered metallic conductor of characteristic Thouless energy $ E_c. $ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $ f(\varepsilon ). $ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $ \varepsilon E_c, $ $ f(\varepsilon ) $ vanishes as a power law in $ \varepsilon /E_c $ with exponents $ -{1 \over 2},-2, $ and $ -{3 \over 2} $ for $ d=1,2, $ and 3, respectively. While for $ d=1,2 $ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion.

cond-mat↗