Upcoming Events
Ezio Iacocca
Northumbria University
Wed 2nd October 2019, 3pm
MAGIC room (ELD201)
Rapid dynamics in solid-state magnetism
Rapid dynamics in solid-state magnetism
Magnetism in solids is a fascinating yet complex phenomenon that encompasses vastly different length and time scales. This complexity is typically resolved by establishing equations that are valid at different scales. For example, magnetic dynamics at the atomic level can be described by a discrete system of Schrödinger equations while microscopic magnetisation dynamics is described by a vectorial partial differential equation known as the Landau-Lifshitz equation. However, such a distinction of scales is challenged when considering the problem of a magnetic material that dynamically evolves towards equilibrium from a randomised state. In this talk, I will give an overview of solid-state magnetism at these extreme conditions, the experimental capabilities available, and the current theoretical understanding of the underlying physical phenomena. I will also discuss the advantages of a dispersive hydrodynamic interpretation of magnetisation dynamics in the context of rapid magnetic soliton nucleation and evolution. Finally, I will outline future research directions and outstanding challenges of the research field towards technological applications.
Alexander Tovbis
University of Central Florida
Wed 9th October 2019, 3pm
MAGIC room (ELD201)
Soliton and breather gases for the focusing nonlinear Schrödinger equation
Soliton and breather gases for the focusing nonlinear Schrödinger equation
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles" of complex statistical objects called soliton and breather gases. In this talk, we discuss spectral theory of a generalized breather gas by considering a special, thermodynamic type limit of multi-phase (finite-gap) solutions of the focusing nonlinear Schrödinger (fNLS) equation. The family of generalized breather gases includes gas of fundamental solitons and gas of conventional breathers (solitons on finite background) as particular cases. We consider several particular cases of the generalized breather gas including the so-called bound state soliton gas, as well as some transitional regimes (condensate and ideal gas limits
Cornelis van der Mee
University of Cagliari
Wed 16th October 2019, 3pm
MAGIC room (ELD201)
Reflectionless Solutions for Square Matrix Nonlinear Schroedinger equation with Vanishing Boundary Conditions
Reflectionless Solutions for Square Matrix Nonlinear Schroedinger equation with Vanishing Boundary Conditions
After a quick review of the direct and inverse scattering theory of the focusing Zakharov-Shabat system with symmetric nonvanishing boundary conditions, we derive the reflectionless solutions of the 2 + 2 matrix NLS equation with vanishing boundary conditions and four different symmetries by using the Marchenko theory. Since the Marchenko integral kernel has separated variables, the matrix triplet method - consisting of representing the Marchenko integral kernel in a suitable form - allows us to find the exact expressions of the reflectionless solutions in terms of a triplet of matrices. Moreover, since these exact expressions contain matrix exponentials and matrix inverses, computer algebra can be used to "unpack" and graph them. Finally, it is remarkable that these solutions are also verified by direct substitution in the 2 + 2 NLS equation.
This is a joint work with Francesco Demontis (University of Cagliari, Italy) and Alyssa Ortiz (University of Colorado at Colorado Springs, USA).
This is a joint work with Francesco Demontis (University of Cagliari, Italy) and Alyssa Ortiz (University of Colorado at Colorado Springs, USA).