scholarly journals Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

2002 ◽  
Vol 89 (7) ◽  
Author(s):  
G. Akemann
Keyword(s):  
Dirac Operator ◽  
Correlation Functions ◽  
Chemical Potential

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
G. Akemann ◽  
T. R. Würfel
Keyword(s):  
Dirac Operator ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Chiral Condensate ◽  
Effect Of Temperature ◽  
Specific Class ◽  
Chiral Phase ◽  
Determinantal Representation ◽  
Matrix Ensemble

Abstract In the ε-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 matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting kernel and correlation functions in this class, which is the class of polynomial ensembles. We prove the equivalence between this new determinantal representation of the microscopic eigenvalue correlation functions and existing results in terms of determinants of different sizes, for an arbitrary number of quark flavours, with and without temperature, and extend them to non-zero topology. These results all agree and are thus universal when measured in units of the temperature dependent chiral condensate, as long as we stay below the chiral phase transition.

scholarly journals Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

2018 ◽  
Vol 175 ◽  
pp. 05003 ◽  
Author(s):  
Michael Wagman
Keyword(s):  
Lattice Qcd ◽  
Correlation Functions ◽  
Chemical Potential ◽  
Time Correlation ◽  
Time Interval ◽  
Signal To Noise ◽  
Complex Phase ◽  
Sign Problem ◽  
Heavy Tailed ◽  
Potential Sign

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.

scholarly journals Coherent Transport in Periodically Driven Mesoscopic Conductors: From Scattering Amplitudes to Quantum Thermodynamics

2020 ◽  
Vol 75 (5) ◽  
pp. 483-500
Author(s):  
Kay Brandner
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Frequency Noise ◽  
Perturbation Scheme ◽  
Quantum Thermodynamics ◽  
Mean Values ◽  
Periodically Driven ◽  
The Mean

AbstractScattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic fields. Our approach is based on an extension of the conventional Lippmann–Schwinger formalism to systems with a periodically time-dependent Hamiltonian. As a key result, we obtain a systematic perturbation scheme for the Floquet scattering amplitudes that describes the transition of a transport carrier through a periodically driven sample. Within a general multi-terminal setup, we derive microscopic expressions for the mean values and time-integrated correlation functions, or zero-frequency noise, of matter and energy currents, thus recovering the results of earlier studies in a unifying framework. We show that this framework is inherently consistent with the first and the second law of thermodynamics and prove that the mean rate of entropy production vanishes only if all currents in the system are zero. As an application, we derive a generalized Green–Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. Finally, we discuss potential topics for future studies and further reaching applications of the Floquet scattering approach to quantum transport in stochastic and quantum thermodynamics.

scholarly journals CHIRAL SYMMETRY BREAKING AT NONZERO CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (04) ◽  
pp. 859-864 ◽  
Author(s):  
J. C. Osborn ◽  
K. Splittorff ◽  
J. J. M. Verbaarschot
Keyword(s):  
Partition Function ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Dirac Spectrum

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 on the chemical potential while this is not the case for the Dirac spectrum and the weight of the partition function.

Sign in / Sign up

Export Citation Format

Share Document