International Journal of Modern Physics B

We review time-dependent current-density-functional theory with the Vignale–Kohn (VK) functional. Historic background and an extensive discussion of the underlying theory is given. In particular, we focus on the application of VK to atoms and (large) molecules in electric fields. Results obtained with VK are shown and the successes and failures of this functional discussed.

In this paper, the classical and quantum chaos characteristic of single electronic motion in the double quantum well with external magnetic field are studied. The system can be regarded as the linear coupling of a harmonic oscillator and a Duffing oscillator. The study shows that because of the interaction of two oscillators, the system demonstrates the characteristic of quasi-periodicity, multi-chaos coexisting attractors, chaos, super-chaos, etc., with different energy. Furthermore, as shown in the corresponding analysis of spectrum distribution statistics, the system in most energy fields demonstrates the coexisting of the integrable and non-integrable characteristic, which means that there is a close corresponding relation in classical and quantum behavior.

Generalized synchronization (GS) of a chaotic oscillator driven by two chaotic signals is investigated in this paper. Both receiver and drivers are the same kind of oscillators with mismatched parameter values. Partial and global GS may appear depending on coupling strengths. An approach based on the conditional entropy analysis is presented to test the partial GS, which is difficult to determine with conventional methods. A trough in conditional entropy spectrum indicates partial GS between the receiver and one of the drivers.

A full quantum mechanical treatment of the problem of three electromagnetic fields is considered. The system consists of three different coupling parameters where the rotating and counter-rotating terms are presented. An exact solution of the wave function in the Schrödinger picture is obtained, and the connection to the coherent states wave function is given. The symmetrical ordered quasi-probability distribution function (W-Wigner function) is calculated via the wave function in the coherent states representation. The Green's function is obtained and employed to find the Bloch density matrix. The expectation value of the energy is also given. In the framework of the vacuum and even coherent states, we have discussed the phenomenon of squeezing. It has been shown that the collapse and revival phenomenon exists at ω₁=ω₂ and is apparent for a long period of time.

The advanced methodology of Green's function method and application of this new methodology have resulted in a set of interesting conclusions concerning thin film properties. It has been concluded that thin films possess high superconductive, thermoisolation and acoustical isolation properties. It is also concluded that physical characteristics of thin films are spatially dependent and that this spatial dependence can be the basis for widening of the nanostructures application field.

The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is addressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero–Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. In a harmonic well of strength ω or on a circle of radius R — both parameters ω and R have to be viewed as long distance regulators — the Calogero spectrum is discrete. It is well known that by confining the anyon model in a 2d harmonic well and projecting it on a particular basis of the harmonic well eigenstates, one obtains the Calogero–Moser model. It is then natural to consider the anyon model on a sphere of radius R and look for a possible dimensional reduction to the Calogero–Sutherland model on a circle of radius R. First, the free one-body case is considered, where a mapping from the 2d sphere to the 1d chiral circle is established by projection on a special class of spherical harmonics. Second, the N-body interacting anyon model is considered: it happens that the standard anyon model on the sphere is not adequate for dimensional reduction. One is thus led to define a new spherical anyon-like model deduced from the Aharonov–Bohm problem on the sphere where each flux line pierces the sphere at one point and exits it at its antipode.

We investigate theoretically manganese oxides where the colossal magnetoresistance (CMR) is observed. We also investigate the similarity between CMR and CeCoIn₅ superconductor. We obtain the Curie temperature T_c using a Kondo lattice model for paramagnetic to ferromagnetic transition. We calculate the isotope exponent of O ion such as α_O for T_c. We investigate the magnetic field dependence on superconducting transition temperature, T_sc, in CeCoIn₅. It is shown that phonon-enhanced spin fluctuations drive this superconductivity once more suggested by us [Phys. Rev. B61, 4289 (2000)]. It is elucidated that the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting states are closely related to the local internal field in order to influence spin fluctuations.

We present a formal derivation of the mean-field expansion for dilute Bose–Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g. the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.