Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. [S1050-2947(98)51110-9].

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

Three-dimensional solution structure of alpha-conotoxin MII by NMR spectroscopy: Effects of solution environment on helicity

alpha-Conotoxin MII, a 16-residue polypeptide from the venom of the piscivorous cone snail Conus magus, is a potent and highly specific blocker of mammalian neuronal nicotinic acetylcholine receptors composed of alpha 3 beta 2 subunits. The role of this receptor type in the modulation of neurotransmitter release and its relevance to the problems of addiction and psychosis emphasize the importance of a structural understanding of the mode of interaction of MII with the alpha 3 beta 2 interface. Here we describe the three-dimensional solution structure of MIT determined using 2D H-1 NMR spectroscopy. Structural restraints consisting of 376 interproton distances inferred from NOEs and 12 dihedral restraints derived from spin-spin coupling constants were used as input for simulated annealing calculations and energy minimization in the program X-PLOR. The final set of 20 structures is exceptionally well-defined with mean pairwise rms differences over the whole molecule of 0.07 Angstrom for the backbone atoms and 0.34 Angstrom for all heavy atoms. MII adopts a compact structure incorporating a central segment of alpha-helix and beta-turns at the N- and C-termini. The molecule is stabilized by two disulfide bonds, which provide cross-links between the N-terminus and both the middle and C-terminus of the structure. The susceptibility of the structure to conformational change was examined using several different solvent conditions. While the global fold of MII remains the same, the structure is stabilized in a more hydrophobic environment provided by the addition of acetonitrile or trifluoroethanol to the aqueous solution. The distribution of amino acid side chains in MII creates distinct hydrophobic and polar patches on its surface that may be important for the specific interaction with the alpha 3 beta 2 neuronal nAChR. A comparison of the structure of MII with other neuronal-specific alpha-conotoxins provides insights into their mode of interaction with these receptors.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

NMR structure of C-terminally tagged gramicidin channels

A biotin group was covalently attached to the C terminus of gramicidin A (gA) through a linker arm comprising a glycine residue with either one (gAXB) or two caproyl groups (gAXXB). High-resolution two-dimensional NMR spectroscopy was used to determine the structure of these modified gA analogues and [Lys(16)]gramicidin A (gA-Lys) in sodium dodecyl-d(25) sulphate micelles. Gated gA ion channels based on linking a receptor group to these gA analogues have been used recently as a component in a sensing device. The conformations of the gA backbones and amino acid side chains of lysinated gA and biotinylated gA in detergent micelles were found to be almost identical to that of native gA, i.e. that of an N-terminal to N-terminal (head to head) dimer formed by two right-handed, single-stranded beta(6.3) helices. The biotin tail of the gAXB and gAXXB and the lysine extremity of gA-Lys appeared to lie outside the micelle. Thus it appears that the covalent attachment of functional groups to the C terminus of gA does not disrupt the peptide's helical configuration. Further, single channel measurements of all three gA analogues showed that functioning ion channels were preserved within a membrane environment. (C) 1999 Elsevier Science B.V. All rights reserved.

Quantum oscillations in quasi-one-dimensional metals with spin-density-wave ground states

We consider the magnetoresistance oscillation phenomena in the Bechgaard salts (TMTSF)(2)X, where X = ClO4, PF6, and AsF6 in pulsed magnetic fields to 51 T. Of particular importance is the observation of a new magnetoresistance oscillation for X = ClO4 in its quenched state. In the absence of any Fermi-surface reconstruction due to anion order at low temperatures, all three materials exhibit nonmonotonic temperature dependence of the oscillation amplitude in the spin-density-wave (SDW) state. We discuss a model where, below a characteristic temperature T* within the SDW state, a magnetic breakdown gap opens. [S0163-1829(99)00904-2].

Quantum open-systems approach to current noise in resonant tunneling junctions

A quantum Markovian master equation is derived to describe the current noise in resonant tunneling devices. This equation includes both incoherent and coherent quantum tunneling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict subshot noise statistics for strong tunneling between the wells. The method is an alternative to Green's function methods and population master equations for very small coherently coupled quantum dots.

H-1-NMR structural studies of a cystine-linked peptide containing residues 71-93 of transthyretin and effects of a Ser84 substitution implicated in familial amyloidotic polyneuropathy

The Ile-->Ser84 substitution in the thyroid hormone transport protein transthyretin is one of over 50 variations found to be associated with familial amyloid polyneuropathy, a hereditary type of lethal amyloidosis. Using a peptide analogue of the loop containing residue 84 in transthyretin, we have examined the putative local structural effects of this substitution using H-1-NMR spectroscopy. The peptide, containing residues 71-93 of transthyretin with its termini linked via a disulfide bond, was found to possess the same helix-turn motif as in the corresponding region of the crystallographically derived structure of transthyretin in 20% trifluoroethanol (TFE) solution. It therefore, represents a useful model with which to examine the effects of amyloidogenic substitutions. In a peptide analogue containing the Ile84-->Ser substitution it was found that the substitution does not greatly disrupt the overall three-dimensional structure, but leads to minor local differences at the turn in which residue 84 is involved. Coupling constant and NOE measurements indicate that the helix-turn motif is still present, but differences in chemical shifts and amide-exchange rates reflect a small distortion. This is in keeping with observations that several other mutant forms of transthyretin display similar subunit interactions and those that have been structurally analysed possess a near native structure. We propose that the Ser84 mutation induces only subtle perturbations to the transthyretin structure which predisposes the protein to amyloid formation.

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

NMR studies of the low-density lipoprotein receptor-binding peptide of apolipoprotein E bound to dodecylphosphocholine micelles

Circular dichroism and NMR spectroscopy have been used to determine the structure of the low-density lipoprotein (LDL) receptor-binding peptide, comprising residues 130-152, of the human apolipoprotein E. This peptide has little persistent three-dimensional structure in solution, but when bound to micelles of dodecylphosphocholine (DPC) it adopts a predominantly alpha-helical structure. The three-dimensional structure of the DPC-bound peptide has been determined by using H-1-NMR spectroscopy: the structure derived from NOE-based distance constraints and restrained molecular dynamics is largely helical. The derived phi and psi angle order parameters show that the helical structure is well defined but with some flexibility that causes the structures not to be superimposable over the full peptide length. Deuterium exchange experiments suggest that many peptide amide groups are readily accessible to the solvent, but those associated with hydrophobic residues exchange more slowly, and this helix is thus likely to be positioned on the surface of the DPC micelles. In this conformation the peptide has one hydrophobic face and two that are rich in basic amino acid side chains. The solvent-exposed face of the peptide contains residues previously shown to be involved in binding to the LDL receptor.