Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

Mathematical constraints on a theory of human memory - Response

Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of specifying memory operations in set theoretic notation, as it would have been difficult if not impossible to formulate such an objection at the algorithmic level.

Macroscopic test of quantum mechanics versus stochastic electrodynamics

We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

Odorant-induced currents in intact patches from rat olfactory receptor neurons: Theory and experiment

Odorant-induced currents in mammalian olfactory receptor neurons have proved difficult to obtain reliably using conventional whole-cell recording. By using a mathematical model of the electrical circuit of the patch and rest-of-cell, we demonstrate how cell-attached patch measurements can be used to quantitatively analyze responses to odorants or a high (100 mM) K+ solution. High K+ induced an immediate current flux from cell to pipette, which was modeled as a depolarization of similar to 52 mV, close to that expected from the Nernst equation (56 mV), and no change in the patch conductance. By contrast, a cocktail of cAMP-stimulating odorants induced a current flux from pipette into cell following a significant (4-10 s) delay. This was modeled as an average patch conductance increase of 36 pS and a depolarization of 13 mV, Odorant-induced single channels had a conductance of 16 pS. In cells bathed with no Mg2+ and 0.25 mM Ca2+, odorants induced a current flow from cell to pipette, which was modeled as a patch conductance increase of similar to 115 pS and depolarization of similar to 32 mV, All these results are consistent with cAMP-gated cation channels dominating the odorant response, This approach, which provides useful estimates of odorant-induced voltage and conductance changes, is applicable to similar measurements in any small cells.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential

We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Quantum chaos in the atomic gravitational cavity

We report quantum chaos phenomena in the atomic gravitational cavity. We consider the reflection of cold atoms from a temporally modulated evanescent wave. In the globally chaotic regime, for small modulation, the squared energy distribution as a function of time demonstrates dynamical localization. However, for larger modulation delocalization occurs.

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

Measuring macromolecular diffusion using heteronuclear multiple-quantum pulsed-field-gradient NMR

We have previously shown that H-1 pulsed-field-gradient (PFG) NMR spectroscopy provides a facile method for monitoring protein self-association and can be used, albeit with some caveats, to measure the apparent molecular mass of the diffusant [Dingley et al. (1995) J. Biomol. NMR, 6, 321-328]. In this paper we show that, for N-15-labelled proteins, selection of H-1-N-15 multiple-quantum (MQ) coherences in PFG diffusion experiments provides several advantages over monitoring H-1 single-quantum (SQ) magnetization. First, the use of a gradient-selected MQ filter provides a convenient means of suppressing resonances from both the solvent and unlabelled solutes. Second, H-1-N-15 zero-quantum coherence dephases more rapidly than H-1 SQ coherence under the influence of a PFG. This allows the diffusion coefficients of larger proteins to be measured more readily. Alternatively, the gradient length and/or the diffusion delay may be decreased, thereby reducing signal losses from relaxation. In order to extend the size of macromolecules to which these experiments can be applied, we have developed a new MQ PFG diffusion experiment in which the magnetization is stored as longitudinal two-spin order for most of the diffusion period, thus minimizing sensitivity losses due to transverse relaxation and J-coupling evolution.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.