This work will be devoted to the quantisation of the classical Bernoulli random walk over Z. As this random walk is isomorphic to the classical chaotic dynamical system x 7→ 2x mod 1 with x ∈ [0, 1], we will explore the rôle of classical periodic orbits of this chaotic map in relation with a non commutative algebra associated with the quantisation of the Bernoulli walk. In particular we show th...

A many-body coherent potential approximation (CPA) previously developed for the double exchange (DE) model is extended to include coupling to local quantum phonons. The Holstein-DE model studied (equal to the Holstein model for zero Hund coupling) is considered to be a simple model for the colossal magnetoresistance manganites. We concentrate on eeects due to the quantisation of the phonons, su...

Absolute radial positions of the main features in Saturn’s ring system have been calculated by adapting the quantum theory of atomic spectra. Fine rings superimposed upon broad rings are found to be covered by a harmonic series of the form N α A(r) 1/2 , where N and A are integers. Fourier analysis of the ring system shows that the spectral amplitude fits a response profile which is characteris...

Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with decreasing one-parameter family translated subspaces is convex for given (not necessarily smooth) vector in underlying Hilbert space. In second quantisation, this infers convexity vacuum relative respect to translation parameter tunnel von Neumann algebras. This result allows us study...

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H eff ({S i }) derived from the coherent-state integral is highly singular: the quasiprobability density exp(−βH eff), a Wigner function, imposes quantisation through derivatives of delta f...

We review aspects of quantisation of the 11-dimensional su-permembrane world volume theory. We explicitly construct vertex operators for the massless states and study interactions of supermembranes. The open supermembrane and its vertex operators are discussed. We show how our results have direct applications to Matrix theory by appropriate regularisation of the supermembrane.