Related papers: Distribution of the k-th smallest Dirac operator e…
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are…
We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in…
We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density…
Using a chiral random matrix theory we can now derive the low energy partition functions and Dirac eigenvalue correlations of QCD with different chemical potentials for the dynamical and valence quarks. The results can also be extended to…
We investigate the spectrum of the staggered Dirac operator in 4d quenched U(1) lattice gauge theory and its relationship to random matrix theory. In the confined as well as in the Coulomb phase the nearest-neighbor spacing distribution of…
The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
We consider rectangular random matrices of size $p\times n$ belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble appears in many applications like QCD, mesoscopic physics, and…
We compare eigenvalue correlations of the Dirac operator with a chemical potential obtained from lattice simulations of quenched QCD with analytic predictions obtained from chiral effective theories in the zero-momentum limit. By comparing…
In quantum chromodynamics (QCD) at nonzero chemical potential, the eigenvalues of the Dirac operator are scattered in the complex plane. Can the fluctuation properties of the Dirac spectrum be described by universal predictions of…
It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
We apply a complex chiral random matrix model as an effective model to QCD with a small chemical potential at zero temperature. In our model the correlation functions of complex eigenvalues can be determined analytically in two different…
We summarize the analytical solution of the Chiral Perturbation Theory for the Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in the fundamental representation. Results have been obtained for the quenched microscopic spectral…
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…
We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential \mu for a…
The degree of entanglement of random pure states in bipartite quantum systems can be estimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of size M\geq N, these are distributed according to a…
The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger…
In the epsilon-regime of lattice QCD one can get an accurate measurement of the pion decay constant F_pi by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources.…
We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…