Table of contents

Using the recently developed technique of integration within an ordered product (IWOP) of operators, we derive some new expressions for single-mode and one- and two-mode squeezed states. They provide the possibility of finding new ways of generating squeezing.

By variational and diffusion fixed-node quantum Monte Carlo we compute the correlation energy of the uniform electron gas in the density range 1 ⩽ r_s ⩽ 5. We consider several intermediate values of the spin polarization, and we compare our results to three parametrizations for the correlation energy used in Local Spin Density computations.

We investigate cellular automata where some global quantity varies periodically or quasi-periodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We conclude that this is not a collective phenomenon–where different subsystems are supposed to synchronize–but rather like many very weakly coupled oscillators fluctuating around one exact frequency. The global quantity measured is a mean taken over all these subsystems, and gets more precise the larger the system is.

Binary Zn-TM (TM = Zr, Nb, Mo) alloys have been prepared by mechanical alloying from elemental powders in a planetary ball mill. The structure and thermal behaviour were investigated by X-ray diffraction and differential thermal analysis. Completely amorphous powders were obtained in the Zn-Zr and Zn-Nb systems, whereas for the Zn-Mo system mechanical alloying results in a crystalline Mo-based solid solution. Furthermore the factors related to the possibility and rate of amorphization were discussed.

The general phenomenological free energy is derived for a liquid crystalline elastomer under arbitrary strain and orientational distortions. Using the group representations method we obtained all invariants, describing the coupling of translational and orientational deformations and/or external electric field. It is shown that in centrosymmetric materials (nematic rubbers) the only contribution to the free energy which is linear in (small) gradients of the director, is the coupling with electric field and the strain tensor (16 independent terms analogous to the flexoelectric effect). In chiral materials (cholesterics) the electric field couples with the strain tensor for uniform nematic director (piezoelectric effect, 3 invariants) and, in the absence of an electric field, translational and linear orientational distortions interact with each other (couple-stress effects, 6 invariants). Experimental observations and previous models are critically analysed.

We have studied a hopping process in perfect icosahedral Al₆₂Cu_25.5Fe_12.5 powder samples by time-of-flight (TOF) quasi-elastic neutron scattering. Within the (ℏω, ℏQ)-window of the present experiment the signal observed is entirely due to copper motion. Its dependence on the neutron momentum transfer ℏQ suggests that this process remains confined in space and that it has a characteristic length of (3.9 ± 0.25) Å. Its dependence on the temperature T is interpreted as giving evidence for a depinning energy of 0.75 eV.

The transient dynamics of a bound electron in a crystal, linearly coupled to the lattice and excited by femtosecond light absorption, is studied in the presence of the whole phonon spectrum and of a complex electron structure. Use is made of a numerical method which allows the evaluation of the resulting non-linear dynamics. Different regimes of relaxation are found.

We present a study of contact line configurations on a completely wetted vertical plate near non-wetting vertical-line defects of varying width. The contact line shape is compared with a recently obtained solution for distortions caused by a localized force. Fits to the theory are excellent after the introduction of a new characteristic length scale depending on the defect width w. Two regimes are observed as w is varied: for narrow defects, the behaviour of the characteristic healing length correlates well with the defect width, while for wide defects, the healing length saturates to a constant value.

We infer scaling of the shape and energy of a space-enclosing elastic sheet such as a large fullerene ball of linear dimension R. Stretching deformation is crucial in determining the optimal shape, in conjunction with bending. The asymptotic shape of a symmetrical fullerene ball is a flat-sided polyhedron whose edges have an average curvature radius of order R^2/3. The predicted asymptotic energy is concentrated in these edges and is of order R^1/3. Analogous edges with this scaling property should occur generally in elastic sheets with discrete disclinations.

The superconductivity of Li₂MC₆₀ and Na₂MC₆₀ (where M is Cs, Rb and K) compounds with small lattice parameters is studied in detail. The results reveal that Na₂CsC₆₀ and Na₂RbC₆₀ are superconducting at 12 K and 3.5 K with large superconducting fractions (70% for Na₂CsC₆₀ and more than 20% for Na₂RbC₆₀), while Li₂MC₆₀ compounds are not superconducting down to 2 K. The large variation in T_c observed over a wide range of lattice parameter is explained in the framework of the McMillan equation, and the phonon frequency involved in electron pairing is discussed.

We present ¹³C NMR results on K₃C₆₀ showing that nuclear relaxation is exponential only above 250 K where molecular motion narrows the NMR line. The non-exponential nuclear relaxation at low temperatures is an intrinsic property of the frozen state and is associated with intramolecular variations of the electron spin density distribution. Dipolar coupling to the electron spins at the Fermi level of the carbon pπ-t_1u band is identified as the dominant source of ¹³C relaxation. The measured mean value of (T₁T)^-1 is determined not only by the total density of states at the Fermi level, but also by the intramolecular electron spin density distribution.

We determine the dispersion relation for a fluid bilayer membrane, taking into account the coupling between bending and the local density of the two monolayers. Apart from important corrections to the conventional bending mode, we obtain a second slow mode which is essentially a fluctuation in the density difference of the two monolayers, damped by inter-monolayer friction. Estimates for a stack of membranes show reasonable agreement with a recent spin-echo study of membrane undulations.