Papers by Alexander A Migdal
arXiv (Cornell University), Sep 25, 2022
Proceedings of the fourth symposium on Virtual reality modeling language, 1999
Fractal and Fractional
We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equat... more We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension d>2. This solution family is equivalent to a fractal curve in complex space Cd with random steps parametrized by N Ising variables σi=±1, in addition to a rational number pq and an integer winding number r, related by ∑σi=qr. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in Rd space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size N→∞ or its chemical potential μ→0. The system with fixed N has diffe...
arXiv (Cornell University), Aug 4, 2019
arXiv (Cornell University), May 4, 2020
Journal of Experimental and Theoretical Physics, 1969
Nuclear Physics B - Proceedings Supplements, 1989
Nuclear Physics B, 1981
The Fermi string theory which was earlier conjectured to be equivalent to QCD is revised and inve... more The Fermi string theory which was earlier conjectured to be equivalent to QCD is revised and investigated in detail. The precise correspondence between the loop average in QCD at N = ∞ and the propagator of the Fermi string with some special boundary conditions for a bispinor field is established. The effective string tension as a function of the bare fermion mass satisfies the scaling law with the critical index 1211.
The relation between the Fermi energy and number of particles is extended to the case of a gas in... more The relation between the Fermi energy and number of particles is extended to the case of a gas in a potential well with a diffuse edge. The results are employed for calculating the boundary Fermi energy of neutrons in heavy nuclei with an accuracy approximates 1 Mev. The mean distance between the levels and the nuclear surface energy are calculated for the last elements of the Mendeleyev table. The calculations are performed for the optical model potential. (auth)
International Journal of Modern Physics A, 2021
We revise the steady vortex surface theory following the recent finding of asymmetric vortex shee... more We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the...
Physics Letters B, 1973
Abstract Models are proposed, which have an explicit solution at any space-time dimension with no... more Abstract Models are proposed, which have an explicit solution at any space-time dimension with nontrivial conformal interaction, but in general with ghost states. At two dimensions ghosts can be removed, and one obtains the Thirring model. The problem of ghosts at four dimensions remains open.
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Papers by Alexander A Migdal