Regular and chaotic interactions of two BPS dyons at low energy

Abstract

We identify and analyze quasiperiodic and chaotic motion patterns in the time evolution of a classical, non-Abelian Bogomol'nyi-Prasad-Sommerfield (BPS) dyon pair at low energies. This system is amenable to the geodesic approximation which restricts the underlying SU(2) Yang-Mills-Higgs dynamics to an eight-dimensional phase space. We numerically calculate a representative set of long-time solutions to the corresponding Hamilton equations and analyze quasiperiodic and chaotic phase space regions by means of Poincaré surfaces of section, high-resolution power spectra and Lyapunov exponents. Our results provide clear evidence for both quasiperiodic and chaotic behavior and characterize it quantitatively. Indications for intermittency are also discussed.

Loop Expansion in Yang–Mills Thermodynamics

“…As a consequence, no breaking of rotational symmetry is introduced by the regularization of the azimuthal angular integration. 8 No freedom of shifting the ground-state energy density exists because of the BPS saturation of the field φ, and the inertness of φ already is a consequence of the nonpropagating nature of (anti)calorons: their energy-momentum tensor vanishes identically. of the theory, 9 the former is subject to an evolution in temperature.…”

“…Finally, one shows the above-mentioned fluctuation inertness of the field φ by means of its effective action whose potential is uniquely fixed. 8 Two parameters, the ef fective coupling e and the Yang-Mills scale (through the potential V(φ)), enter the effective action. While the latter is a free parameter 7 The dimensionless quantityφ depends on temperature only via the periodicity in τ .…”

Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

“…Finally, we recall that the full YMH dynamics in temporal gauge is only recovered after supplementing Hamilton's equations (17), (19) and (26)…”

“…Studies of this type could provide new insights into the corresponding quantum theories. Applied to multimonopole configurations of YMH theory with an adjoint Higgs field, whose chaotic interactions we have recently studied [17], they may for example help to clarify the role of chaotic monopole ensembles in disordering the gauge-theory vacuum.…”

A Planck-scale axion and SU(2) Yang–Mills dynamics: present acceleration and the fate of the photon

“…Obviously, its derivation in terms of complex dynamics governed by eq. (8) is an extremely complicated task, see for example [36]. It may or may not be accomplished in the future.…”