201 citations · 1.3k across the 41 of their papers we have counts for
40 papers
Lapse singularities, caustics and entanglement
Zachary Guralnik
We study diffraction catastrophes of wave functions in diffeomorphism invariant quantum theories, for which . These wave functions can be represented in terms of integra…
Geometry and Perturbative Sensitivity of non-Smooth Caustics of the Helmholtz Equation
Zachary Guralnik, Charles Spofford, Katherine Woolfe
The geometry of non-smooth caustics in solutions of the Helmholtz equation is analyzed using a Fock-Schwinger proper-time formulation. In this description, or cusp…
A new look at the Helmholtz equation: Lefschetz thimbles and the einbein action
Zachary Guralnik
Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of sums of integrals of a proper-time, or `einbein', wave function $Ψ(Λ) = \exp(i\mat…
Holography, Fractals and the Weyl Anomaly
Gerald Guralnik, Zachary Guralnik, Cengiz Pehlevan
We study the large source asymptotics of the generating functional in quantum field theory using the holographic renormalization group, and draw comparisons with the asymptotics of…
On exact statistics and classification of ergodic systems of integer dimension
Zachary Guralnik, Cengiz Pehlevan, Gerald Guralnik
We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and ar…
On the Asymptotics of the Hopf Characteristic Function
Zachary Guralnik, Cengiz Pehlevan, Gerald Guralnik
We study the asymptotic behavior of the Hopf characteristic function of fractals and chaotic dynamical systems in the limit of large argument. The small argument behavior is determ…