Remarks on the notion of quantum integrability
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 …
definitions commonly used in the literature, we propose a different set of criteria, leading to a …
New integrable generalizations of Calogero-Moser quantum problem
New integrable generalizations of Calogero-Moser quantum problem - Enlighten Publications
Skip to main content Accessibility information Site navigation Study Research About us Student …
Skip to main content Accessibility information Site navigation Study Research About us Student …
[HTML][HTML] Parameterized Picard–Vessiot extensions and Atiyah extensions
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 …
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 …
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 …
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 …
(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
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …
On elliptic Calogero–Moser systems for complex crystallographic reflection groups
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 …
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 …
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 …
(PDOs) as well as several geometric constructions are investigated. In particular, we show …