Related papers: Note on Superintegrability of TTW model
A general procedure is outlined which allows one to construct superintegrable models of Winternitz type. Some examples are presented.
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
Recently proposed procedure of constructing maximally superintegrable systems of Winternitz type is further developed and illustrated by an example of system admitting an explicit construction of angle variables and additional integrals of…
Construction and classification of 2D superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of…
Recent progress in the gauge-mediated supersymmetry breaking is reviewed, with emphasis on the theoretical problems which gauge-mediated models so successfully solve, as well as those problems which are endemic to the models themselves and…
We outline the basic ideas of the topological mechanisms of superconductivity. A gauged model of correlated electronic system where a topological fluid is formed as a result of a strong interaction is discussed.
We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…
The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational…
Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some…
A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ and for a family of systems defined on constant curvature manifolds. The…
For a class of Hamiltonian systems naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional integrals of motion.
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
We present new examples of superintegrable matrix/eigenvalue models. These examples arise as a result of the exploration of the relationship between the theory of superintegrability and multivariate orthogonal polynomials. The new…
By use of geometrical methods of surface theory we demonstrate links of Green-Schwarz superstring dynamics with supersymmetric exactly-solvable nonlinear systems and super-WZNW models reduced in an appropriate way.
The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of higher-order in the momenta that can be obtained as the…
Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…
Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Staeckel transform. In this paper a…
Model merging, particularly through weight averaging, has shown surprising effectiveness in saving computations and improving model performance without any additional training. However, the interpretability of why and how this technique…
We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…