![]() ![]() You have unlimited access to preview, modify, share, and import these building blocks in any of your Möbius classes! Summary of Möbius FoundationsĬheck out Add Möbius Foundations to your class for more details on how to access and use any of the Möbius Foundations content in your class. Since you’ll have access to this content inside of your Möbius site, this means that you can even take a look behind the scenes at how this content is authored! There's even student and instructor onboarding materials to get you and your students started with Möbius! ![]() These supplementary STEM lessons, assignments and questions are an engaging showcase of Möbius' features, especially the interactive and exciting aspects of the platform like: Interactive Narratives, Math Apps, Maple-graded questions, 3-D plots, algorithmic questions, and more! This new technique has enabled important advances in the field of nonlinear spin dynamics, including the discovery of parity-time ( \(\) symmetry 10.Möbius Foundations is a collection of Möbius building blocks that you can use as a starting point to build out the rest of your course or supplement content that you've already purchased or authored. Within this framework, the nonconservative effects of Gilbert damping and applied Slonczewski STT 3 originate from the imaginary part of the system’s Hamiltonian. It has recently been shown that nonequilibrium classical spin dynamics described by the LLGS equation naturally follows from the non-Hermitian extension of Hamiltonian formalism 10. On the fundamental side, complete quantitative understanding of single-spin dynamics provides the essential tool for predictive description of many complex spin systems.Īnalytical studies of nonlinear spin dynamics in nanomagnetic devices and structures have been the focus of active research for many decades (see, e.g., refs 8, 9 and references therein). On the application side, spin controlled by the applied spin-polarized current is an elemental unit for a wealth of spintronic applications 4, 5, 6, 7. The interest to dissipative spin-transfer torque (STT)-driven dynamics of a spin, described by Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation 1, 2, 3 is two-fold. ![]() This establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space. We identify the parity-time symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Möbius transformations, with the critical point of the transition corresponding to the parabolic transformation. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Möbius transformation in complex stereographic coordinates. Here we report that the time evolution of a single classical spin (e.g. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |