Browsing by Author "Verbaarschot, Jacobus"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Continuous Insights in Wilson Fermions
    (2012-02-07) Verbaarschot, Jacobus
  • Thumbnail Image
    Item
    Lessons From Random Matrix Theory for QCD at Finite Density
    (2008-07-30) Verbaarschot, Jacobus
  • Thumbnail Image
    Item
    Spectral Properties of the SYK Model
    (2018-05) Verbaarschot, Jacobus
    The Sachedev-Ye-Kitaev model provides us with a new window on strongly interacting many-body systems. In particular, it is a variant of the two-body random ensemble which captures the main features of nuclear interactions. One of main successes of recent work on the SYK model is that it shows that the Bethe formula for the nuclear level density is a direct consequence of the conformal symmetry of the low-energy sector of this model. We study the spectrum of the q-body SYK model by means of the moment method, and have obtained analytical results for all moments up to order 1/ N^3 in the number of Majorana fermions N. We elucidate the structure of the moments and how they relate to the free energy including $1/q$ corrections. For fixed $q^2/N$, the spectral density is given by the weight function of the Q-Hermite polynomials, which for large $N$ and $q$ simplifies to $exp( -N arcsin^2(E/E_0) / q^2)$. This spectral form reproduces the free energy obtained by path integral methods in the same limit. From applications to nuclear physics, it is clear that the SYK model has to be chaotic, which is also one of the main reasons why it is of interest to black hole physics. We study the chaotic dynamics by means of the number variance and the closely related spectral form factor. We show that the asymptotic quadratic dependence of the number variance results in a $1/t^2$ peak of the spectral form factor for short times, while random matrix spectral statistics is found for longer time scales.
  • Thumbnail Image
    Item
    Topology and the Dirac Spectrum for One-Flavor QCD
    (2016-05-13) Verbaarschot, Jacobus
    The chiral condensate of one-flavor QCD is continuous when the quark mass|crosses zero. In the sector of fixed topological charge though, the chiral condensate becomes discontinuous at zero mass in the the thermodynamical|limit. To reconcile these contradictory observations, we have evaluated|the spectral density of the Dirac operator in the epsilon domain of |one-flavor QCD. In this domain, we have obtained exact analytical expressions which show that the spectral density at $\theta = 0$ becomes a |strongly oscillating function for negative quark mass with an amplitude|that increases exponentially with the volume. As is the case for QCD at|nonzero chemical potential, these strong oscillations invalidate the|Banks-Casher formula and result in a chiral condensate that is continuous|as a function of the quark mass. An additional subtlety is the effect|of the topological zero modes which will be discussed as well.