Related papers: Subsets and the canonical partition functions
We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition…
We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective…
In this lecture we give a brief review of chiral Random Matrix Theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from…
A pseudoclassical model, reproducing, upon quantization, the dynamics of the chiral sectors of the massless spin-1/2 field theory is proposed. The discrete symmetries of the action are studied in details. In order to reproduce the positive…
The distribution of canonical determinants in QCD is determined by means of chiral perturbation theory. For a non-zero quark charge the canonical determinants take complex values. In the dilute pion gas approximation, we compute all moments…
We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set Z included in C^k with C an algebraic closed field. We…
Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…
We further pursue an approach to the sign problem of quantum chromodynamics at nonzero chemical potential, in which configurations of the lattice path integral are gathered into subsets. In the subset construction we multiply each temporal…
In this talk we discuss the microscopic limit of QCD at nonzero chemical potential. In this domain, where the QCD partition function is under complete analytical control, we uncover an entirely new link between the spectral density of the…
We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this…
We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in…
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 infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient…
We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a…
We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem that the chiral condensate at zero temperature does not depend…
We study the relation between the scale of chiral symmetry spontaneously breaking and constituent quark mass. We argue that this relation partly reveals strong interaction origination of chiral symmetry breaking. We show that the relation…
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…
At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with fixed quark number via the imaginary chemical potential region with few ansatzs.…
The canonical partition function approach was designed to avoid the overlap problem that affects the lattice simulations of nuclear matter at high density. The method employs the projections of the quark determinant on a fix quark number…
In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…