Dissipative flow equations

We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We introduce and discuss three different generators of the flow that transform a linear non-Hermitian operator into a diagonal one. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode. We then move to problems with many fermionic modes and discuss the interplay between coherent (disordered) dynamics and localized losses. Our method can also be applied to non-Hermitian Hamiltonians.

The generic matrix Revenge tragedy, history play, murder pamphlet and conversion narrative

This chapter processes a variety of different sorts of contemporary concerns, such as political, confessional and religious issues. It examines how William Shakespeare's plays elicit from its audience and then manipulates a series of narrative expectations derived from a range of different contemporary genres. It also looks into the irruptive intervention of the ghost that has cut Hamlet off from the values and traditions out of which the narrative quest for life is sustained. The chapter points out how the play has utterly undermined all the canons of Renaissance humanist assumption that had hitherto underpinned Hamlet's existence and sense of himself as an actor or social, political and moral agent in the world. It also explains how Hamlet exploits the void by offering the audience a variety of different sorts of story or narrative template with which to make sense of what is happening to the characters.

A Generic Matrix Method to Model the Magnetics of Multi-Coil Air-Cored IPT Systems

This paper deals with a generic methodology to evaluate the magnetic parameters of contactless power transfer systems. Neumann's integral has been used to create a matrix method that can model the magnetics of single coils (circle, square, rectangle). The principle of superposition has been utilised to extend the theory to multi-coil geometries such as double circular, double rectangle and double rectangle quadrature assuming linearity of magnetics. Numerical and experimental validation has been performed to validate the analytical models developed. A rigorous application of the analysis has been carried out to study misalignment and hence the efficacy of various geometries to misalignment tolerance. Comparison of single-coil and multi-coil shapes considering coupling variation with misalignment, power transferred and maximum efficiency is carried out.

Characters of equivariant -modules on spaces of matrices

We compute the characters of the simple $\text{GL}$-equivariant holonomic ${\mathcal{D}}$-modules on the vector spaces of general, symmetric, and skew-symmetric matrices. We realize some of these ${\mathcal{D}}$-modules explicitly as subquotients in the pole order filtration associated to the $\text{determinant}/\text{Pfaffian}$ of a generic matrix, and others as local cohomology modules. We give a direct proof of a conjecture of Levasseur in the case of general and skew-symmetric matrices, and provide counterexamples in the case of symmetric matrices. The character calculations are used in subsequent work with Weyman to describe the ${\mathcal{D}}$-module composition factors of local cohomology modules with determinantal and Pfaffian support.