Related papers: On Haantjes tensors for second-order superintegrab…
Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy tensors for arbitrary fields is presented, having good mathematical and physical properties. Remarkably, there appear quantities with…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
We show that all density operators of 2$\times N$--dimensional quantum systems that remain invariant after partial transposition with respect to the first system are separable. Based on this criterion, we derive a sufficient separability…
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
Consider a strictly hyperbolic $n\times n$ system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup…
The classical dynamics of antisymmetric second-rank tensor matter fields is analyzed. The conformally invariant action for the tensor field leads to a positive-definite hamiltonian on the class of the solutions that are bounded at the time…
Valiant's Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets $\mathcal{F}$ and $\mathcal{G}$ of tensors (a.k.a. constraint functions or signatures) are related by a…
We show the vanishing of higher extension groups and torsion groups between linearisation of additive functors from a semi-additive category satisfying some conditions to a category of vector spaces. In particular, we apply our results to…
In this paper we apply hydrodynamics for systems with continuous broken symmetries to heavy ion collisions in the framework of (1+1) dimensional Bjorken model. The temperature profile with respect to proper time determined in that context…
A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved,…
In this paper, we study invariants of second order tensors in an $n$-dimensional flat Riemannian space. We define eigenvalues, eigenvectors and characteristic polynomials for second order tensors in such an $n$-dimensional Riemannian space…
We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
Perovskite oxides are already widely used in industry and have huge potential for novel device applications thanks to the rich physical behaviour displayed in these materials. The key to the functional electronic properties exhibited by…
In non-interacting or weakly-interacting 2D electron systems, the energy of the extended states increases as the perpendicular magnetic field approaches zero: the extended states "float up" in energy, giving rise to an insulator. However,…
For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of…
We construct a local gauge transformation to show how, in confined systems, a generic, weak nonhomogeneous SU(2) spin-orbit Hamiltonian reduces to two U(1) Hamiltonians for spinless fermions at opposite magnetic fields, to leading order in…
The definition of ``Lie derivative'' of spinors with respect to Killing vectors is extended to all kinds of Lorentz tensors. This Lie-Lorentz derivative appears naturally in the commutator of two supersymmetry transformations generated by…
Self-organization of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion is investigated. In the mean-field approximation without Coulomb interaction, the system displays a…
We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural…