The acceleration-dependent system with noncommuting coordinates, proposed by Lukier-ski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's classical electron [Acta Physica Polonica 6, 218 (1937)], further discussed by Weyssenhoff and Raabe [Acta Physica Polonica 9, 7 (1947)]. The two-parameter centrally extended Galilean symmetry of the ...

We construct a Bell inequality for coincidence probabilities on a three three-dimensional (qutrit) system. We show that this inequality is violated when each observer measures two noncommuting observables, defined by the so-called unbiased six-port beam splitter, on a maximally entangled state of two qutrits. The strength of the violation agrees with the numerical results presented by Kaszlikow...

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group GL q,p (2). The q-deformed differential calculus on the phase space is formulated and using this, both the Hamiltonian and Lagrangian forms of dynamics have been constructed. In contrast to earlier forms of q-dynamics, our formalism has the advantage of pr...

Given a finite group G, we consider the problem of finding the maximal size nc(G) of subsets of G that have the property that no two of their elements of commute. After constructing a large noncommuting subset of Sn, we consider the definition and classification of extraspecial p-groups and focus on such a group: S(p.n). We show that nc(S(2, n)) = 2n+ 1 and that S(p, n) ≥ pn+ 1.

This behavior has been seen in some notable cases. Kirillov [3] shows that elementary symmetric polynomials in noncommuting variables commute (and, in some cases, all Schur functions) when elementary symmetric polynomials of degree at most three commute when restricted to at most three of the variables. Generalizing this, Blasiak and Fomin [1] give a wider theory for rules of three of generatin...

Using electromagnetically induced transparency in a cesium vapor, we demonstrate experimentally that the quantum state of a light beam can be mapped into the long-lived Zeeman coherences of an atomic ground state. Two noncommuting variables carried by light are simultaneously stored and subsequently read out, with no noise added. We compare the case where a tunable single sideband is stored ind...

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying...

We consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommu...

By using finite resolution measurements it is possible to simultaneously obtain noisy information on two noncommuting polarization components of a single photon. This method can be applied to a pair of entangled photons with polarization statistics that violate Bell’s inequalities. The theoretically predicted results show that the non-classical nature of entanglement arises from negative joint ...