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13 papers · 2 filters
Parametrisations of elements of spinor and orthogonal groups using exterior exponents
Nikolay Marchuk
We present new parametrizations of elements of spinor and orthogonal groups of dimension 4 using Grassmann exterior algebra. Theory of spinor groups is an important tool in theoret…
Renormalization, isogenies and rational symmetries of differential equations
A. Bostan, S. Boukraa, S. Hassani +4
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illust…
Functional Classical Mechanics and Rational Numbers
A. S. Trushechkin, I. V. Volovich
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. Howev…
Universality in the 2D Ising model and conformal invariance of fermionic observables
Dmitry Chelkak, Stanislav Smirnov
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. H…
Adiabatic theorem for finite dimensional quantum mechanical systems
M. O. Katanaev
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is co…
The arctic curve of the domain-wall six-vertex model
F. Colomo, A. G. Pronko
The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scali…