K. Pachucki,1 V. A. Yerokhin,2 and P. Cancio Pastor3, 4 Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg 195251, Russia Istituto Nazionale di Ottica-CNR (INO-CNR), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy 4 European Laboratory for Non-Linear Spectroscopy (LENS) and Dipartimen...

Quantum Mechanics in the non-commutative plane is shown to admit the “exotic” symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, the system becomes singular, and “Faddeev-Jackiw” reduction yields the “Chern-Simons” mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves a...

We find soliton solutions in the 2+1 dimensional non-commutative Maxwell Chern-Simons Higgs theories. In the limit of the Chern-Simons coefficient going to zero, these solutions go over to the previously found solutions in the non-commutative Maxwell Higgs theories. The new solutions may have relevance in the theory of the fractional quantum Hall effect and possibly in string vacua correspondin...

The notions of side-effect-freeness and commutativity are typical for probabilistic models, as subclass of quantum models. This paper connects these notions to properties in the theory of monads. A new property of a monad (‘strongly affine’) is introduced. It is shown that for such strongly affine monads predicates are in bijective correspondence with side-effect-free instruments. Also it is sh...

In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The cryptographic security is assured as long the GSDP problem is computationally hard to solve in non-commutative algebraic structures and belongs currently to the P...

We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. The Nielsen quantity controls the transition between commutative and non-commutative propagation in time. The quasiperiodically kicked ...

In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asymptotic commutativity property, generalizing the notion of relative locality proved by Borch...

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observ...

Quantum field planes furnish a noncommutative differential algebra Ω which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data requirered in their construction come from a quantum field theory. The basic idea is to replace the ground field C of quantum planes by the noncommutative algebra A of observables of the quantum field theory. HUTMP 94-B335...

By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdSd+1 space. We have found that in the boundary of two layers AdSd+1 space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry. e-mail:kaviani,[email protected]...