International Journal of Modern Physics B

The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the Hall conductance is derived and is used for the proof of the integer quantum Hall effect in the realistic situation. Anisotropic quantum Hall gas is investigated based on the Hartree–Fock approximation in the same formalism. Thermodynamic properties, transport properties, and unusual response under external modulations are found. Implications for the integer quantum Hall effect in the finite systems are also studied and a new quantum Hall regime with non-zero longitudinal resistance is shown to exist.

The ground-state and low-energy properties of the two-dimensional J₁-J₂ Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, Europhys. Lett.21, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half — where the effects of quantization are the strongest — the spin-wave expansion turns out to be quantitatively accurate for J₂/J₁≳0.8. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, m^†≃0.3, is in remarkable agreement with recent neutron scattering measurements on Li₂VOSiO₄.

A Monte Carlo simulation technique has been used to investigate the effect of sulphur impurity and ceria support on the surface composition and catalytic activity of Pt–Rh/ceria nanocatalysts. For temperatures in the range of 400–1300 K the surface Pt concentration decreases with increase in sulphur coverage. The Pt concentration at the base of the nanocatalyst in contact with the support increases with metal-support interaction. However, for weak metal-support interaction (V_ms<-0.01 eV) the surface Pt concentration slightly increases with metal-support interaction. Overall, sulphur is found to influence the surface composition much more strongly than the metal-support interaction. The MC-simulated surface composition results have been used to study the energetics of the CO+NO reactions over Pt–Rh/CeO₂ catalysts. It is found that the CO₂ formation rate decreases with increase in sulphur coverage and marginally increases with metal-support interaction up to V_ms=-0.01 eV. All the results qualitatively agree with the experimental results.

In this paper, tunneling effect of Cooper pairs in weak-link superconductor structure with multi-junctions under the condition for overstepping the Josephson approximation is discussed. The equations describing the electric current based on the tunneling effect of Cooper pairs in several kinds of weak-link superconductor structures with multi-junctions are obtained under the condition to overstep the Josephson approximation. For both SISISIS and a four junctions ring, when all junctions are in the zero voltage state, the exact solution of the equations is obtained. It is found that, because of the tunneling effect of the Cooper pairs, an alternating current exists which can be expressed by an elliptic function. For a four junctions ring, the relation between the period of the alternating current and flux is pointed out. At last, the condition for overstepping the Josephson approximation is discussed. The result shows that overstepping the Josephson approximation may be possible when the volumes of superconductors are small enough.

An extended Hubbard model with phonons is considered. q-coherent states relative to the superconducting quantum symmetry of the model are constructed and their properties studied. It is shown that they can have energy expectation lower than eigenstates constructed via conventional processes and that they exhibit ODLRO.

We study the correction to scaling of the rms displacements of random walks in disordered media consisted of connected networks of the lattice percolation in two, three, and four dimensions. The two types of ensemble averages, i.e. an infinite-network average of random walks starting from an infinite network and an all-cluster average starting from any occupied site, are investigated using both the myoptic ants and the blind ants models. We find that the rms displacements exhibit strong nonanalytic corrections in all dimensions. The correction exponent δ defined by the rms displacement of t-step random walks via R_t=At^1/d_w (1+Bt^-δ+Ct^-1+⋯) was found as δ≃0.39, 0.27, and 0.27 for, respectively, two, three, and four dimensions for an infinite-network average, and δ≃0.37, 0.28, and 0.24 for an all-cluster average.

A Mott–Hubbard gap of interacting electrons has potential application to electronic-material engineering. We investigate how a Mott insulator rises, in particular a Hubbard gap changes, when electrons are confined in a structure with hierarchically organized interactions.

Mössbauer investigations have been carried out for the system Li_0.6-0.5xCo_xSb_0.1-Fe_2.3-0.5xO₄ with 0.0≤x≤1.0, x in steps of 0.2. The observed variation of the various Mössbauer parameters like isomershift, quadrupole splitting, nuclear magnetic field and linewidth are explained in terms of cation distribution and superexchange interaction.

The momentum distribution n_k of itinerant electrons in the one-dimensional Falicov–Kimball model is calculated for various ground-state phases. In particular, we examine the periodic phases with period two, three and four (that are ground-states for all Coulomb interactions) as well as the phase separated states (that are ground states for small Coulomb interactions). For all periodic phases examined the momentum distribution is a smooth function of k with no sign of any discontinuity or singular behavior at the Fermi surface k=k_F. An unusual behavior of n_k (a local maximum) is found at k=3k_F for electron concentrations outside half-filling. For the phase separated ground states the momentum distribution n_k exhibits discontinuity at k=k₀<k_F. This behavior is interpreted in terms of a Fermi liquid.

A unified approach is proposed which provides both microscopic and phenomenological description of the first-order phase transition accompanied by the formation of thermodynamically stable bubbles of the new phase. A procedure is proposed for selecting the probable states whose contribution in the thermodynamic behavior of the system is dominant. This technique makes it possible to take into account fluctuation of any scales and to obtain a closed expression for the parameters of the new phase formation, in particular its dimensions, lifetime and time of relaxation towards a thermodynamically stable state. The feasibility of experimental observation the parameters dependence of the new phase bubble on the governing quantities is discussed.

The activation energy of the local dynamics of the polymeric segments is calculated from the spin–lattice relaxation time, measured by NMR method. A new algorithm of analysis of the experimental data is proposed in order to increase the accuracy of the evaluation of this parameter. This method was applied for some polyisoprene-C₇D₈ solutions and for the molten polyisoprene.