Related papers: Chiral Random Band Matrices at Zero Energy
Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…
Random Matrix Theory has been a unifying approach in physics and mathematics.In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview…
According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a…
Heavy quark symmetry predicts the value of $B \rightarrow D$ and $B \rightarrow D^*$ transition matrix elements of the current $\bar c \gamma_\mu (1 - \gamma_5)b$, at zero recoil (where in the rest frame of the $B$ the $D$ or $D^*$ is also…
Energy band structure of the bilayer graphene superlattices with $\delta$-function magnetic barriers and zero average magnetic flux is studied within the four-band continuum model, using the transfer matrix method. The periodic magnetic…
We prove a limiting absorption principle at zero energy for two-body Schr\"odinger operators with long-range potentials having a positive virial at infinity. More precisely, we establish a complete asymptotic expansion of the resolvent in…
The phase transition of chiral symmetry restoration in strange hadronic matter is studied in the chiral SU(3) quark mean field model. When the baryon density is larger than a critical density $\rho_c$, the minimal energy density of the…
We update lattice QCD results for second order cumulants of conserved charge fluctuations and correlations at non-zero temperature and vanishing values of the conserved charge chemical potentials. We compare these results to hadron…
In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\frac{1}{\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the…
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of…
The flux-across-surfaces conjecture represents a corner stone in quantum scattering theory because it is the key-assumption needed to prove the usual relation between differential cross section and scattering amplitude. We improve a recent…
A quantitative form of the Nullity Theorem is presented, which establishes a linear relation between the singular values of the two submatrices involved in the theorem up to the first order. The theorem is then extended to function spaces…
A one-parameter family of static and spherically symmetric solutions to Einstein equations with a traceless energy-momentum tensor is found. When the nonzero parameter $\beta$ lies in the open interval $(0,1)$ one obtains traversable…
We study a single 2d Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1d chiral fermions (associated to each point…
Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able…
We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to…
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 first part of these lectures we discuss the infrared limit of the spectrum of the QCD Dirac operator. We discuss the global symmetries of the QCD partition function and show that the Dirac spectrum near zero virtuality is determined…
The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac operator shows a strong dependence on the chemical potential. The…
The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)_L*SU(n)_R symmetry of the…