The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents and of the order parameter and the response function respectively, are calculated to the second order in . Received 9 June 2000 and Received in final form 2 August 2000     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

Crossing of specific heat curves in some correlated fermion systems

Specific heat versus temperature curves for various pressures, or magnetic fields (or some other external control parameter) have been seen to cross at a point or in a very small range of temperatures in many correlated fermion systems. We show that this behavior is related to the possibility of existence of a quantum critical point. Vicinity to a quantum critical point in these systems leads to a crossover from quantum to classical fluctuation regime at some temperature . The temperature at which the curves cross turns out to be near this crossover temperature. We have discussed the case of the normal phase of liquid Helium three and the heavy fermion systems CeAl₃ and UBe₁₃ in detail within the spin fluctuation theory, a theory which inherently contains a low energy scale which can be identified with . When the crossover scale is a homogeneous function of these control parameters there is always crossing at a point. We also mention other theories exhibiting a low energy scale near a quantum critical point and discuss this phenomenon in those theories. Received 25 June 1999     

A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Structure and stability of the anatase TiO2 (101) and (001) surfaces

Well-defined (101) and (001) surfaces of anatase TiO₂ were studied for the first time by secondary-electron imaging and low-energy electron diffraction. Initially, both surfaces show a crystalline structure corresponding to the bulk anatase phase, buried under an atomically thin contamination layer. After mild sputtering with 500 eV Ne⁺ ions, we have observed a surface phase transition from tetragonal anatase to face-centered cubic titanium monoxide TiO. Subsequent annealing at 900 K restores the (1×1) anatase structure at the (101) surface. On the (001) surface, however, a (1×4) reconstruction appears. The unreconstructed structure can be recovered by exposing the surface to oxygen. These observations demonstrate the stability of the anatase surfaces and illustrate the feasibility of preparing and investigating clean surfaces of this technological important form of TiO₂.     

Superconducting and magnetic properties of Nb/Pd 1-xFex/Nb triple layers

The superconducting and magnetic properties of Nb/Pd_1-xFe_x/Nb triple layers with constant Nb layer thickness d_Nb=200 ? and different interlayer thicknesses 3 ?≤ d_PdFe ≤ ? are investigated. The thickness dependence of the magnetization and of the superconducting transition temperature shows that for small iron concentration x the Pd_1-xFe_x layer is likely to be in the paramagnetic state for very thin films whereas ferromagnetic order is established for x ≥ 0.13. The parallel critical field B_c2||(T){B_{c2||}}(T) exhibits a transition from two-dimensional (2D) behavior where the Nb films are coupled across the interlayer, towards a 2D behavior of decoupled Nb films with increasing d_PdFeand/or x. This transition allows a determination of the penetration depth x_F{\xi _F} of Cooper pairs into the Pd_1-xFe_x layer as a function of x. For samples with a ferromagnetic interlayer x_F{\xi _F} is found to be independent of x.     

Finite size scale invariance

We develop a new approach to scale symmetry, which takes into account the possible finite cut-offs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similarity as a limiting case, when the cut-offs are set to infinity (infinite size-system); ii) is consistent with the traditional finite size scaling approach already used in critical phenomena; iii) enables the computation of some of the universal functions appearing in the finite size scaling formulation; iv) allows scale transformations leaving the cut-offs invariant, like in the traditional renormalization approach; v) can be formulated to allow for positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical findings. Received 26 January 1999 and Received in final form 25 October 1999     

Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents. Received 2 May 2000     

Surface tension effects in the zero gravity inflow of a drop into a fluid

As a drop of fluid is deposited on the surface of a miscible fluid (that we call the solvent), it undergoes a strong pulling due to its surface rupture and it acquires a kinetic energy independently of gravity. For the drop and the solvent being of the same fluid we observe a drop injection at an initial velocity which scales as the square root of the surface tension of the drop against air. Once injected, the drop develops a transverse instability giving rise to an expanding ring. Viscosity terminates the process and stops the ring. We show that the final ring height follows a scaling law whereas two asymptotical scaling regimes can be identified for the ring radius. Received 31 August 1999     

Laser capabilities of CuBr mixture excited by RF discharge

Our investigations demonstrated that utilizing copper bromide (CuBr) mixture as a source of Cu atoms in a RF-excited discharge can be a promising alternative to the Cu sputtered system, when the development of Cu ion gas laser is considered. Both spectroscopic and laser investigations showed that the threshold input power for lasing was reduced about 5 times using the CuBr-based system instead of the Cu-sputtered system. Pulsed and CW laser oscillation on Cu⁺ transitions in the near IR spectral region was obtained in RF-excited He-CuBr discharge operated at 13.56 MHz and 27.12 MHz. At input RF power of 800 W, a laser output power of 10 mW at the 780.8 nm Cu ion laser line was achieved. An increase of laser output power by a factor of two, as well as better Cu vapour axial distribution and better discharge stability, was attained when DC discharge was superimposed on the RF discharge. Laser gain on 11 UV Cu ion lines was observed in RF-excited Ne-CuBr discharge. basing on the obtained results, we consider the CuBr laser system excited by RF discharge capable of generating UV laser radiation at relatively low input power. Received 4 January 1999