We evaluate the leading asymptotic contributions to the traces of the quantum baker's map propagator. Besides the usual Gutzwiller periodic orbit contribution, we identify boundary paths giving rise to anomalous log(hbar) terms. Some examples of these anomalous terms are calculated both numerically and analytically.

F. Toscano R. O. Vallejos M. Saraceno

A proof is given for the observation that the equations of motion for the companion Lagrangian without a square root, subject to some constraints, just reduce to the equations of motion for the companion Lagrangian with a square root in one less dimension. The companion Lagrangian is just an extension of the Klein-Gordon Lagrangian to more fields in order to provide a field description for strings and branes.

L. M. Baker

For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top points, also in the quantum case, at a universal distribution.

M. Fannes P. Spincemaille

We show that the class of quantum baker's maps defined by Schack and Caves have the proper classical limit provided the number of momentum bits approaches infinity. This is done by deriving a semi-classical approximation to the coherent-state propagator.

Mark M. Tracy A. J. Scott

For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian function with respect to the Fourier transformation. We show that the value of properly normalised Baker-Akhiezer function at the origin can be given by an integral of Macdonald-Mehta type and explicitly compute these integrals for all known Baker-Akhiezer arrangements. We use the Dotsenko-Fateev integrals to extend this calculation to all deformed root systems, related to the non-exceptional basic classical Lie superalgebras.

M. V. Feigin M. A. Hallnas A. P. Veselov

The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each subsystem has power-of-two Hilbert space dimension. We here study the particular example of two baker maps that interact via a controlled-not interaction. Numerical evidence indicates that the control subspace becomes an ideal Markovian environment for the target map in the limit of large Hilbert space dimension.

Raul O. Vallejos P. R. del Santoro A. M. Ozorio de Almeida

Let $M$ be a $3$--dimensional handlebody of genus $g$. This paper gives examples of hyperbolic knots in $M$ with arbitrarily large genus $g$ bridge number which admit Dehn surgeries which are boundary-reducible manifolds.

Kenneth L. Baker R. Sean Bowman John Luecke

The quantum spin ice model applied to Tb2Ti2O7 predicts that magnetic fields applied along the [111] axis will induce a partial magnetization plateau [H. R. Molavian and M. J. P. Gingras, J. Phys.: Condens. Matter 21, 172201 (2009)]. We test this hypothesis using ac magnetic susceptibility and muon-spin relaxation measurements, finding features at 15 and 65 mT agreeing with the predicted boundaries of the magnetization plateau. This suggests that Tb2Ti2O7 is well described by a quantum spin ice model with an effective exchange constant of Jeff = 0.17(1) K.

P. J. Baker M. J. Matthews S. R. Giblin P. Schiffer C. Baines D. Prabhakaran

We show there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1.

Kenneth L. Baker Cameron Gordon John Luecke

The aim of this manuscript is to present the proof given by Michel M\'erigot in 1974 for an enlarged convergence domain of the Campbell-Baker-Hausdorff-Dynkin series in the Lie algebra of a Banach-Lie group. This proof is based on a theorem, of independent interest, on the lifetime of the solution of a Cauchy problem. We furnish all the details for this ODE result in Appendix A.

Stefano Biagi