Showing papers in "Reports on Mathematical Physics in 2001"

TL;DR: In this article, the notion of symmetry for implicit generalized Hamiltonian systems with respect to a generalized Dirac structure was studied and the reduction of these systems admitting a symmetry Lie group with corresponding quantities was investigated.

TL;DR: In this article, a universal symplectic structure for a constrained system can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics, which preserves symbiotic character among derivability from a variational principle, Lie algebra and symplectic geometry.

TL;DR: In this article, a Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined, and Jacobi's identity is fulfilled for forms of degree n − 1, where n is the dimension of space time.

TL;DR: In this paper, a family of torsion-free affine connections is introduced, in analogy with the classical α-connections defined by Amari, and the dual connections with respect to the metric are found.

TL;DR: In this paper, a vertical exterior derivative is constructed for a graded Poisson structure on multisymplectic manifolds over nontrivial vector bundles, and the properties of the Poisson bracket are proved and first examples are discussed.

TL;DR: In this article, a brief review of an (optical) holonomic quantum computer (or computation) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and Chountasis, and a mathematical reinforcement to their works is given.

TL;DR: In this article, the Nockel model of an open quantum dot has been studied and a sufficient condition for the discrete spectrum of such a system to survive the presence of a strong magnetic field is given.

TL;DR: In this article, exact solutions to the generalized Fisher equation were found using the classical Lie approach and the method of additional generating conditions, and the exact solutions were applied next to solving a nonlinear boundary value problem with the zero Neumann conditions.

TL;DR: In this article, a general method for the determination of Lie symmetry groups of integro-differential equations is presented, which is a natural extension of the Ovsiannikov method developed for differential equations.

TL;DR: In this article, the authors investigate some classes of (α, β)-metric spaces obtaining Randers class, Kropina class and Matsumoto class and provide a means to generate new concrete examples of Finsler spaces with (β, ε)-metrics.

TL;DR: In this article, it was shown that any bijective transformation on the set of all density operators on a Hilbert space preserving fidelity is implemented by either a unitary or an anti-unitary operator on the underlying Hilbert space.

TL;DR: In this article, it was shown that the space of a proper action of a symmetry group of a distributional Hamiltonian system is a differential space partitioned by smooth manifolds preserved by the evolution.

TL;DR: In this article, the authors consider the question when coexisting observables are functionally coexistent and give partial answers for special classes of observables on effect algebras, in particular on the Hilbert space effects.

TL;DR: In this paper, the idea of V. Sokolov's hereditary algebra of symmetries was used to construct recursion operators and hereditary algebra for many field and lattice systems.

TL;DR: In this paper, the Konstant-Kirillov co-adjoint orbits method for connected Lie groups and the Borel-Weil-Bott representation algorithm for semisimple groups are introduced.

TL;DR: In this paper, the integrability of N-body systems with δ-interactions and point spin couplings is investigated, and the cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.

TL;DR: In this paper, the authors give simple examples of applications in physics of the result of the theorem by Lie and Scheffers concerning systems of differential equations admitting a superposition function allowing us to write the general solution in terms of a set of arbitrary, but independent, particular solutions.

TL;DR: By means of the variational method, a probability distribution of noncommuting observables which minimizes or maximizes their β-entropic sum is determined, which gets the upper and lower bounds of their Shannon entropy sum.

TL;DR: In this paper, the authors derived and discussed equations of motion of rigid bodies of infinitesimal size in a Riemann space, where the rigorous meaning of "infinitisemal size" consists in replacing an extended body by the structured material point with internal degrees of freedom.

TL;DR: ψ-extension of Rota's finite operator calculus delivers an elementary umbral underpinning for a model of q-deformed quantum oscillator and its possible generalisations.

TL;DR: By using Weyl systems associated with symplectic vector spaces, this paper showed an association between bi-Hamiltonian classical systems and corresponding quantum systems, carried on the example of the harmonic oscillator.

TL;DR: In this paper, the authors construct Hilbert systems for the action of the circle group T using subgroups of implementable Bogoljubov unitaries w.r.t.

TL;DR: In this paper, the concepts of Q-valued measures, observables and states are introduced for ring-like quantum logics providing a unified approach to the basic notions of axiomatic quantum mechanics.

TL;DR: In this paper, a systematic geometric approach to integration of generalized Henon-Heiles system is presented, which is defined by a nonlinear system of four differential equations admitting two polynomial first integrals.

TL;DR: In this article, it was shown that every local automorphism (affine 1-local, or non-affine 2-local) of the sets of all states on a Hilbert space is an automomorphism.

TL;DR: In this article, complete exact analytical solutions of the inhomogeneous Burgers equation in the special case of inhomogenous term are proposed, and the stability of the obtained solution is discussed.

TL;DR: In this paper, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics, which enables a consistent picture of classical point charges with finite electromagnetic self-energy.

TL;DR: In this article, the negative eigenvalues problem for the generalized Laplace operator − Δ = −Δ+ + αT, α Δ ) is shown to be finite or infinite.

TL;DR: In this article, the Calogero-Degasperis-Fokas (CDF) equation is extended to (2+1) dimensions by a dimensional extension of the Lax pair.

TL;DR: In this paper, a quantum deformation of corresponding to the deformation parameter, where N is an even natural number, was constructed at the Hopf *-algebra, Hilbert space and C * algebra levels.