Related papers: On Haantjes tensors for second-order superintegrab…
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…
In this contribution we have collected some facts about Killing and Killing-Yano tensors that we feel are of general interest for researchers working on problems that rely on differential geometry. We also include some of our recent studies…
The influence of a Zeeman magnetic field on the superconducting characteristics of the attractive Hubbard model was investigated. The ground state and temperature phase diagrams were obtained for a fixed number of particles. Two critical…
Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are non-holonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological…
Using an analysis similar to that of Imry and Wortis, it is shown that the apparent first order superconductor to metal transition, which has been claimed to exist at low values of the magnetic field in a two-dimensional field-tuned system…
We study mechanical cooling in systems of coupled passive (lossy) and active (with gain) optical resonators. We find that for a driving laser which is red-detuned with respect to the cavity frequency, the supermode structure of the system…
A recently found (gr-qc/0303036) 2-index, symmetric, trace-free, divergence-free tensor is introduced for arbitrary source-free electromagnetic fields. The tensor can be constructed for any test Maxwell field in Einstein spaces (including…
Nijenhuis tensors $N$ on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form $N+N^*=aI$ for irreducible Courant algebroids, in particular for the extended tangent bundles…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
Two-component second and third-order Burgers type systems with nondiagonal constant matrix of leading order terms are classified for higher symmetries. New symmetry integrable systems with their master symmetries are obtained. Some third…
In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive…
We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated…
Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the…
The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl-regular Nijenhuis operators. We prove the splitting Theorem for symmetries and conservation laws of Nijenhuis operators, show that…
The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field…
Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of…
We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast with the case without vector potential, the corresponding integrals may no…
Exponential small splitting of separatrices in the singular perturbation theory leads generally to nonvanishing oscillations near a saddle--center point and to nonexistence of a true homoclinic orbit. It was conjectured long ago that the…
In this work, we uncover a collection of non invertible topological operators linked to the 0-, 2-, 4- and 6-form symmetries related to the type IIB superstring effective theory. By pinpointing the $\text{SL}(2,\mathbb{Z})$-covariant…
We calculate the quasiparticle contribution to the zero temperature Hall conductance of two-dimensional extreme type-II superconductors in a high magnetic field, using the Landau basis. As one enters the superconducting phase the Hall…