arXiv subjects

Lee Johnson

Publications and source records attributed to Lee Johnson.

3 recordsLinked to original sources

arXiv2024

Quantum analog of Landau-Lifshitz-Gilbert dynamics

The Landau-Lifshitz-Gilbert (LLG) and Landau-Lifshitz (LL) equations play an essential role for describing the dynamics of magnetization in solids. While a quantum analog of the LL dynamics has been proposed in [Phys. Rev. Lett. 110, 147201 (2013)], the corresponding quantum version of LLG remains unknown. Here, we propose such a quantum LLG equation that inherently conserves purity of the quantum state. We examine the quantum LLG dynamics of a dimer consisting of two interacting spin-1/2 particles. Our analysis reveals that, in the case of ferromagnetic coupling, the evolution of initially uncorrelated spins mirrors the classical LLG dynamics. However, in the antiferromagnetic scenario, we observe pronounced deviations from classical behavior, underscoring the unique dynamics of becoming a spinless state, which is non-locally correlated. Moreover, when considering spins that are initially entangled, our study uncovers an unusual form of revival-type quantum correlation dynamics, which differs significantly from what is typically seen in open quantum systems.

quant-ph↗

arXiv2014

Generation of multi-terawatt vortex laser beams

We report the fabrication of large-area phase masks on thin fused-silica substrates that are suitable for shaping multi-terawatt femtosecond laser beams. We apply these phase masks for the generation of intense femtosecond optical vortices. We further quantify distortions of the vortex beam patterns that result from several common types of mask defects.

physics.optics↗

arXiv2012

The Theory of Pseudoknots

Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that point. A pseudodiagram is a knot diagram that may be missing crossing information at some of its crossings. At these crossings, it is undetermined which strand passes over. Pseudodiagrams were first introduced by Ryo Hanaki in 2010. Here, we introduce the notion of a pseudoknot, i.e. an equivalence class of pseudodiagrams under an appropriate choice of Reidemeister moves. In order to begin a classification of pseudoknots, we introduce the concept of a weighted resolution set, an invariant of pseudoknots. We compute the weighted resolution set for several pseudoknot families and discuss notions of crossing number, homotopy, and chirality for pseudoknots.

math.GT↗