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9 papers · 1 filter
New solutions of Heun general equation
Artur Ishkhanyan, Kalle-Antti Suominen
We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this p…
Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
Jani Lukkarinen, Herbert Spohn
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method develope…
Random walks in space time mixing environments
Jean Bricmont, Antti Kupiainen
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by t…
From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
B. Aneva, M. Chaichian, P. P. Kulish
Within the quantum affine algebra representation theory we construct linear covariant operators that generate the Askey-Wilson algebra. It has the property of a coideal subalgebra,…
Approach to equilibrium for the phonon Boltzmann equation
Jean Bricmont, Antti Kupiainen
We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the ini…
A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations
Emiliano De Simone
We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuou…