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Convergent Quantum Normal Forms, ${\mathcal P}{\mathcal T}$-symmetry and reality of the spectrum
Convergent Quantum Normal Forms reality of the spectrum Mathematical Physics
2012/6/19
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed t...
Classical Bethe Ansatz and Normal Forms in the Jaynes-Cummings Model
Classical Bethe Ansatz Normal Forms the Jaynes-Cummings Model
2011/7/28
Abstract: The Jaynes-Cummings-Gaudin model describes a collection of $n$ spins coupled to an harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each ...
On Urn Models, Non-commutativity and Operator Normal Forms
Urn Models Non-commutativity Operator Normal Forms
2010/11/5
Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation rel...
Conservation laws and normal forms of evolution equations
Conservation laws normal forms evolution equations
2010/4/6
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Exampl...