International Journal of Modern Physics B

Statistical mechanics of condensed matter systems in physics (fluids and solids) derives macroscopic equilibrium properties of these systems as averages computed from a Hamiltonian that describes the atomistic interactions in the system. While analytic methods for most problems involve uncontrolled approximations, Monte Carlo simulations allow numerically exact treatments, apart from statistical errors and from the systematic problem that finite systems are treated rather than the thermodynamic limit. However, this problem can be overcome by finite size scaling methods, and thus Monte Carlo methods have become a very powerful tool to study even complex phase transitions. Examples given will include unmixing of polymer blends, two-dimensional melting, etc.

We review some recent developments in the study on the peak effect (PE) in critical current, the dip effect (DE) and history effect (HE) in AC susceptibility studied numerically and experimentally. Although a great number of studies on these "hot topics" have been made, their mechanisms are still debating. Therefore we focus here on the results associated with those of our group, including the equivalency of PE and DE, their future caused by different mechanisms.

We study the quantum Hall transition using the density–density correlation function. We show that in the limit ℏ → 0 the electron density moves along the percolating trajectories, undergoing normal diffusion. The localization exponent coincides with its percolation value ν=4/3. The framework provides a natural way to study the renormalization group flow from percolation to quantum Hall transition. We also confirm numerically that the critical conductivity of a classical limit of quantum Hall transition is .

Theoretical study of multi-layered CuO₂ surfaces with localization potential shows that (i) special stable macroscopic quantum states appear when , where χ is the doping level and G is the unit-cell number, and that (ii) the physical phenomena related to ‖c charge motion takes place just as expected in the fictitious situation where whole uniformly doped holes concentrate in one-side surface. In the dielectric measurement of doping-level dependence and film-thickness dependence on c-oriented La_2-χSr_χCuO_4-δ film, we find that (a) anomalous low-frequency polarization is enhanced when a scaling parameter χG is near to , that (b) quasi-static measurement of the polarization property in low doped film shows two typical characteristics explicable by the fictitious charge concentrations, and that (c) ‖c small-voltage conduction measurement on low doped film also shows two types of characteristic which are switched each other triggered by laser irradiation. Since these macroscopic quantum effects with plural levels with very long life time are observable even up to room temperatures, they may be useful in quantum computing application.

In a recent paper¹ we discussed the Bose–Einstein condensation (BEC) in the framework of Tsallis's nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction.

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the nontrivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are non-wetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.