ITS Theory Seminar
Three theory talks at the ITS with lunch served in between. Please RSVP your lunch preference. See below for the title and content of the talks. Zoom link will be provided on the day of the seminar on this webpage.
Michal Shavit (11-12 am)
The role of sign indefinite invariants in shaping turbulent energy cascades
Non linear systems with two quadratic invariants might appear exceptional. Yet alongside two dimensional hydrodynamics, classical geophysical systems at various scales conserve quadratic energy, despite being governed by quadratic nonlinear equations. Energy conservation is accompanied by an additional quadratic invariant that is not necessarily sign-definite. These systems include internal gravity waves on a vertical plane, Rossby waves in the mid-latitude beta-plane and inertial waves.
Unlike two-dimensional hydrodynamics, where no waves can exist, waves are a prominent part of energy transfer in geophysical systems and play an essential dynamical role in the local environment. These systems are non isotropic, which complicates their analytical study with respect to isotropic wave systems. I will demonstrate that the mathematical structure of the PDE's governing these systems suggests a non canonical choice of variables for writing a kinetic equation for the energy density. This choice enables an efficient derivation of the kinetic equation while describing the system in terms of physically natural variables. I will show that the existence of a second quadratic invariant, regardless of its sign-definiteness, significantly simplifies the kinetic equation and leads to additional conservation laws for resonant interactions. This simplification allows me to find analytically the isotropic part of the turbulent energy spectrum (integrated over the angle). I will show that it has a Kolmogorov-Zakharov scaling analogously to isotropic systems. If time permits, I will discuss physically relevant scenarios in which the sign indefinite quadratic invariant of internal gravity and inertial waves can play a role akin to the enstrophy of two-dimensional hydrodynamics in driving an inverse energy cascade from small to large scales. (This talk is based on a joint work with Jalal Shatah and Oliver Buhler)
Ilya Esin (1-2 pm)
Taming heating and energy dissipation in driven topological systems
In this talk, I will discuss energy dissipation and heating in slowly driven quantum systems, focusing on topological driving schemes. In the first part of my talk, I will present a system in which many-body dynamics lead to the emergence of a quasi-steady state with a high entropy density and yet robust topological transport. I will explain the mechanisms behind this phenomenon and demonstrate the emergence of the quasi-steady state on an exactly solvable strongly coupled fermionic model. In the second part of my talk, I will show that the dissipation of energy in nearly adiabatic quantum systems is linked to the quantum geometry of the problem. Interestingly, this result implies a topological bound on the energy dissipation rate in a class of topological systems. Our findings uncover new connections between topology and dissipation in slowly driven quantum systems, shedding light on their fundamental properties and potential for practical applications, such as the development of optimized driving protocols for topological drives.