Related papers: Quantum Exotic PDE's
Quantum knot invariants (like colored HOMFLY-PT or Kauffman polynomials) are a distinguished class of non-perturbative topological invariants. Any known way to construct them (via Chern-Simons theory or quantum R-matrix) starts with a…
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
In this paper, we investigate the concept of local homeomorphism in Esakia spaces. We introduce the notion of etale Heyting H-algebra and establish category-theoretic duality for etale Heyting H-algebra in the case of finite Heyting algebra…
The finite set of subsystems of a finite quantum system with variables in ${\mathbb Z}(n)$, is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more…
We describe firstly the basic features of quantum $\kappa$-Poincar\'{e} symmetries with their Hopf algebra structure. The quantum $\kappa$-Poincar\'{e} framework in any basis relates rigidly the quantum $\kappa$-Poincar\'{e} algebra with…
Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang--Baxter equation, from which…
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to…
We construct a deformed $C_{\lambda}$-extended Heisenberg algebra in two-dimensional space using non-commuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is…
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painleve transcendent P$_{\rm IV}$, obtained in the context of second-order supersymmetric quantum mechanics and…
We show how some classical r-matrices for the D=4 Poincare algebra can be supersymmetrized by an addition of part depending on odd supercharges. These r-matrices for D=4 super-Poincare algebra can be presented as a sum of the so-called…
To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of…
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on…
We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…