Remarks on the notion of quantum integrability

JS Caux, J Mossel - Journal of Statistical Mechanics: Theory and …, 2011 - iopscience.iop.org
We discuss the notion of integrability in quantum mechanics. Starting from a review of some
definitions commonly used in the literature, we propose a different set of criteria, leading to a …

New integrable generalizations of Calogero-Moser quantum problem

OA Chalykh, M Feigin, AP Veselov - Journal of Mathematical …, 1998 - eprints.gla.ac.uk
New integrable generalizations of Calogero-Moser quantum problem - Enlighten Publications
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[HTML][HTML] Parameterized Picard–Vessiot extensions and Atiyah extensions

H Gillet, S Gorchinskiy, A Ovchinnikov - Advances in Mathematics, 2013 - Elsevier
Generalizing Atiyah extensions, we introduce and study differential abelian tensor
categories over differential rings. By a differential ring, we mean a commutative ring with an …

Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case

PC Argyres, O Chalykh, Y Lü - arxiv preprint arxiv:2309.12760, 2023 - arxiv.org
We consider generalisations of the elliptic Calogero--Moser systems associated to complex
crystallographic groups in accordance to\cite {EFMV11ecm}. In our previous work\cite …

Galoisian approach to supersymmetric quantum mechanics

PB Acosta-Humanez - arxiv preprint arxiv:0906.3532, 2009 - arxiv.org
This thesis is concerning to the Differential Galois Theory point of view of the
Supersymmetric Quantum Mechanics. The main object considered here is the non …

Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations

A Minchenko, A Ovchinnikov… - International Mathematics …, 2015 - academic.oup.com
We develop the representation theory for reductive linear differential algebraic groups
(LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in …

Algebro-geometric Schrödinger operators in many dimensions

O Chalykh - … Transactions of the Royal Society A …, 2008 - royalsocietypublishing.org
Algebro-geometric Schrödinger operators in many dimensions | Philosophical Transactions of
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On elliptic Calogero–Moser systems for complex crystallographic reflection groups

P Etingof, G Felder, X Ma, A Veselov - Journal of Algebra, 2011 - Elsevier
To every irreducible finite crystallographic reflection group (ie, an irreducible finite reflection
group G acting faithfully on an abelian variety X), we attach a family of classical and …

The Schur–Sato Theory for Quasi-elliptic Rings

AB Zheglov - Proceedings of the Steklov Institute of Mathematics, 2023 - Springer
The notion of quasi-elliptic rings appeared as a result of an attempt to classify a wide class of
commutative rings of operators arising in the theory of integrable systems, such as rings of …

Commuting differential operators and higher-dimensional algebraic varieties

H Kurke, D Osipov, A Zheglov - Selecta Mathematica, 2014 - Springer
Several algebro-geometric properties of commutative rings of partial differential operators
(PDOs) as well as several geometric constructions are investigated. In particular, we show …