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We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.

This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book.

We report exact results for one-dimensional reaction-diffusion models A + A → inert, A + A → A, and A + B → inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasized anisotropy of hopping rates; no changes in universal properties were found, due to anisotropy, in all three

Experimental data on the dependence of the surface tension of water on the adsorption of n-alkanes (methane to butane) from the vapor phase over a range of temperatures are re-interpreted to obtain improved estimates of the two-dimensional second virial coefficients for comparison with calculations based on the Lennard-Jones (L-J) formalism in two dimensions. The analysis includes the fugacity corrections for the alkane gases and takes the L-J parameters as known for the three-dimensional gases. The new L-J calculations use a closed-form analytical solution of the basic equation for the two-dimensional second virial coefficient. These older published computations are correct and, as expected, are in complete agreement with the results by numerical integration with modern computer software. Together with estimates of the standard entropies of adsorption, the results indicate that no significant structuring of the surface water molecules occurs upon adsorption of the alkanes. The two-dimensional second virial coefficients are in fair accord with the L-J predictions, except for butane. The reduction of the attractive component of the potentials of mean force between physisorbed molecules arising from the frequencydependent interaction with their electrostatic images in the bulk aqueous phase, as described by McLachlan (Mol. Phys. 1964, 7, 381), or from the polarization of the adsorbates by a surface electric field (surface field polarization) is minor for methane, ethane, and propane. For butane, these effects may be significant but possible changes in conformation upon adsorption may weaken the validity of the gas-phase L-J parameters in estimating the two-dimensional virial coefficients for this alkane.