Related Experiment Video
Updated: May 25, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Eigenvalue density of the non-Hermitian Wilson Dirac operator.
Mario Kieburg1, Jacobus J M Verbaarschot, Savvas Zafeiropoulos
1Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3800, USA.
Physical Review Letters
|February 14, 2012
Summary
We analyzed the eigenvalue density of the non-Hermitian Wilson Dirac operator. Our findings reveal its lattice spacing dependence and provide an analytical expression for real modes.
Area of Science:
- Quantum Chromodynamics (QCD)
- Lattice Field Theory
- Non-Hermitian Physics
Background:
- Understanding the behavior of Dirac operators in non-Hermitian systems is crucial for various areas of physics.
- The ϵ-domain provides a unique theoretical framework for studying critical phenomena in quantum field theories.
Purpose of the Study:
- To investigate the lattice spacing dependence of the eigenvalue density for the non-Hermitian Wilson Dirac operator.
- To analyze the distribution of complex and real eigenvalues, including chiral separation.
- To derive an analytical expression for the number of additional real modes.
Main Methods:
- Utilizing the joint probability density from random matrix theory as a starting point.
- Calculating the density of complex eigenvalues.
- Separately determining the density of real eigenvalues for positive and negative chiralities.
Main Results:
- The study successfully determined the lattice spacing dependence of the eigenvalue density.
- An explicit analytical expression for the number of additional real modes was derived.
- The distribution of complex and real eigenvalues was analyzed in detail.
Conclusions:
- The findings provide valuable insights into the spectral properties of non-Hermitian Dirac operators in lattice QCD.
- The derived analytical expression offers a new tool for theoretical investigations in this field.
- This work contributes to a deeper understanding of chiral symmetry breaking and related phenomena in non-Hermitian systems.
Related Concept Videos
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
01:22Energy Carried By Electromagnetic Waves
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...
01:26Susceptibility, Permittivity and Dielectric Constant
When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
01:16Second Uniqueness Theorem
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
01:21Energy Associated With a Charge Distribution
The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.