Table of contents

The quantum version of de Finetti's theorem implies the existence of a large class of correlation inequalities for indistinguishable particles, e.g. Bell's inequalities. Systems which violate these inequalities are in a state that is compatible with a finite number of particles only.

For quantum systems whose Hamiltonian is formed by a Fibonacci sequence alternating over unit intervals in space or time we present an efficient algorithm for the computation of correlation functions at very long distances equal to the Fibonacci numbers. As an application we show that the correlation function of a quasi-periodically driven 2-level system is nondecaying over time intervals of order 10⁸.

We demonstrate that the principle of adaptation enables us to prescribe the appropriate performance function for optimal robustness against random dilution, in both the entire or restricted space of synaptic weights. It also enables us to improve the network robustness against clipping. However, we clarify that clipping and annealed dilution result in different optimal networks, although they have increasing resemblance at low dilution.

We present a method to analyse the properties of a synchronous stochastic neural network with asymmetric connections. We obtain an equivalence between the dynamics of the network and the iteration defined by a deterministic continuous mapping. This approach enables us to predict the existence of a bifurcation from a stable fixed point to an attracting cycle in a simple case.

We consider the many-body initial-value problem for the reversible single-species diffusion-controlled reaction X + X ⇌ X. A mapping to a dual process is identified which reduces the N-body problem to the dynamics of interfaces, which for general initial conditions is reduced to simple quadratures. The diffusion-controlled limit and the continuous space limit are taken as leading orders in power series expansions. The spectrum of the reaction operator is given explicitly and its use for the calculation of corrections to the diffusion-controlled limit is explained. A closed form is given for the time- and space-dependent concentration ρ(R, t) in one dimension following an arbitrary initial state.

The directional total emittance ε' of coated float glass (fluorine-doped tin oxide coating 300 nm thick) and uncoated float glass was measured at 283 K and in the angular range 10° to 84°. The direct method was employed in which the radiation emitted by the sample was measured using a broad-band Golay detector. A novel scheme of discriminating against unwanted radiation allows fractional uncertainties of ±1% or better (1 s.d.) to be achieved. The uncoated glass, the directional total emittance of which can be calculated accurately, was used to test the apparatus, and the difference between the measured and the calculated values was found to be not greater than ±1%, fractional, for angles less than 80°.

Differential cross-sections are measured for autoionising double capture (ADC) and true double electron capture (TDC) in collision of multiply charged ions with rare-gas targets. Angular profiles and energy gain spectra are identical for both processes suggesting a similar primary mechanism. ADC is well understood in the framework of the independent electron model. To populate TDC a secondary mechanism is suggested which involves electron-electron interaction and feeds very asymmetrical nonautoionising configurations from the quasi-symmetrical one initially populated.

State-selective single-electron capture in slow (1.5 keV/a.m.u.) collisions of He²⁺ ions with laser-excited Na*(3p) atoms has been investigated by means of translational energy spectroscopy. Laser-prepared excitation of the target atoms changes drastically in the final-state distribution of the electron capture process as compared to the ground-state target atoms. For the excited Na*(3p) target atoms strong enhancement has been found for capture into He⁺(n = 4) and He⁺ (n = 5) states, while capture into He⁺ (n = 3) (i.e. the dominant final state for capture from Na(3s)) decreased significantly.

By solving Maxwell's equations for the propagation of electromagnetic waves in periodic dielectric structures (with dielectric constant ε_b in a uniform background ε_a), we found that several classes of periodic dielectric structures possess full photonic gaps, as in the case of dielectric spheres arranged in the diamond structure. These new structures have the additional advantage that they can be easily fabricated experimentally.

Two-photon persistent hole burning is observed at T = 296 K in ⁵D₁–⁷F₀ and ⁵D₀–⁷F₀ transitions of Sm²⁺ ions in substitutionally disordered SrFCl_1/2 single crystals, showing the ratio of inhomogeneous to homogeneous linewidth of 20 ÷ 25. The minimum hole widths of 3.5 cm^-1 and 2.6 cm^-1, respectively, were determined for these transitions. In fact, the applicability of persistent spectral hole burning, known as a low-temperature high-resolution spectroscopic method and a potential basis for the use of a new–spectral–dimension in optical data storage and processing, is demonstrated for the first time at room temperature in inorganic materials.

The magnetoresistance ρ_xx of a two-dimensional electron gas on the surface of liquid helium below 1 K has been measured up to the extreme quantum limit ℏω_c/kT ⩽ 20, where ω_c is the cyclotron frequency. The resistivity increases almost quadratically with magnetic field, and is compared with a theoretical calculation based on many-electron effects.

The nonlinear spectra of absorption and dispersion near the band edge are calculated for quantum well wires with one subband. The calculations take into account phase space filling, plasma screening and band gap renormalization due to an optically excited electron-hole plasma. Large optical nonlinearities are obtained around the exciton ground state mainly due to state-filling by the optically excited thermal electron-hole plasma, while the plasma screening effects are found to have relatively little influence. For all plasma densities n (including n = 0), the free-carrier transition spectra differ strongly from those calculated with Coulomb interaction.

The nonlinear d.c. conduction in the spin-density-wave state of (TMTSF)₂AsF₆ (TMTSF is tetramethyltetraselenafulvalene) is investigated as a function of temperature (2 to 10 K) and magnetic field (12 T, parallel to the c*-axis). The total nonlinear conductivity follows the variation of the low-field linear conductivity both as a function of temperature and magnetic field in a wide though limited temperature range. The implications on the origin of spin-density-wave damping are discussed.

Using electroreflectance we report the first observation of the Franz-Keldysh oscillations originating from the band gap of a GaAs/Ga_0.67Al_0.33As short-period superlattice. The observed effect enables to measure the reduced effective mass in the direction of the growth axis.

The Derrida model of spin glass with symmetry group Z(Q) for arbitrary Q is considered. It is shown that coding with the use of this model gives a maximum transmission rate allowed by Shannon noisy channel theorem.

The electromagnetic fields in the interior of dielectric gratings are calculated. We find a strong polarization effect on the spatially dependent local fields. It is studied as a function of the photon wavelength and the grating period. The electrodynamic polarization effect strongly modifies the absorption and emission properties of wire gratings.