The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with external source which is the time function has been proposed. By using the instanton methods, the macroscopic quantum coherent phenomena and effective capacitance oscillation in the mesoscopic electric circuit have been addressed.

By using multibands BCS theory, we have calculated the superconductivity energy gap and the critical temperature of a thin-film metallic superconductor. The thermodynamic superconducting characteristics such as critical magnetic field, specific heat, as well as the tunneling conductance are investigated for varying film thickness and temperature. We find the oscillation of thermodynamic superconducting properties with the film thickness, including the thermodynamic critical field H-c, the specific heat of normal, superconducting state, and position of the differential tunneling conductance peak. The two universal constants, the nth subband energy gap Delta(n) at temperature T=0 K over k(B)T(c) and the specific heat jump at T-c over normal state specific heat at T-c, are independent of the film thickness. Their values are the same as in the bulk superconductor.

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The effect of scattering in mesoscopic ‘pure’ inductance design circuit, just like in the mesoscopic metallic rings has been address. The quantum characteristics of charge diffusion has also been obtained explicitly. The case in finite temperature has been discussed as well.

The persistent spin current in anisotropic spin ring penetrated by a SU(2) flux is studied by the Schwinger-boson mean field approach.The anisotropy in spin coupling can facilitate the persistent spin current.Ground-state energy and excitation energy gap are also studied.The peak of spin current occurs at the maximum value of the ground-state energy.

Although CdCu3Ti4O12 is isostructural to CaCu3Ti4O12, the room temperature low-frequency dielectric constant of the former compound was reported to be ∼400, only 1/25 of that of the latter material [M.A. Subramanian, et al., J. Solid State Chem. 151 (2000) 323]. In this communication, we report that the dielectric constant of CdCu3Ti4O12 can be remarkably increased by elevating the sintering temperature. The room temperature dielectric constant at 100kHz achieves 9000, almost as much as that of CaCu3Ti4O12, for the sample sintered at 1283K. The appearance of giant dielectric constant in CdCu3Ti4O12 is explained in terms of internal barrier layer capacitance (IBLC) effect with the subgrain boundary as the barrier. Our result supplies an approach in searching for new giant-dielectric-constant materials in the CaCu3Ti4O12 family.

We numerically investigate the transport behavior of a quasi-one-dimensional (1D) square loop device containing the Rashba spin-orbital interaction in the presence of a magnetic flux. The conductance versus the magnetic field shows the Al'tshuler-Aronov-Spivak (AAS) and Aharonov-Bohm (AB) oscillations. We focus on the oscillatory amplitudes, and find that both of them are strongly dependent on the spin precession angle (i.e., the strength of the spin-orbit interaction) and exhibit no periodic oscillations, in good agreement with a recent experiment by Koga [cond-mat/0504743 (unpublished)]. However, our numerical results for the ideal 1D square loop device for the node positions of the amplitudes of the AB and AAS oscillations are found to show some discrepancies with the results for quasi-1D square loops with a finite width. In the presence of disorder and taking the disorder ensemble average, the AB oscillation in the conductance disappears, while the time-reversal symmetric AAS oscillation still remains. Furthermore, the node positions of the AAS oscillatory amplitude remain the same.

This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is addressed. The mesoscopic LC-design is quantized in accord with the charge discreteness. The uncertainty relation for electric charge and current is given. Because the stationary Schrödinger equation is turned to be Mathieu equation in p-representation, the wave function and energy spectrum is formally solved. As further applications, the persistent current is obtained by considering the mesoscopic ring as a pure L-design. The Coulomb blockade phenomenon occurs when applying the theory to the pure C-design. Concerning the time evolution of the states for mesoscopic electric circuit, we are able to study it by the method of characteristics. In order to study the dissipative effect in the circuit, we use density-matrix formulation. In this formulation, several type of “off diagonal” dissipations are expected to be discussed.

. A spin-orbital chain with different Landé g factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé g factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics.

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. The exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. The magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, where the ground state involves one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). The anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points, and remnant weak variation of the magnetization after the last QPT.

By introducing a basis for a novel realization of the SU(4) Lie algebra, we exactly solve a spin-orbital chain with one-ion $L$-$S$ coupling (OILSC) via the Bethe ansatz (BA) approach. In the context of different Landé $g$ factors of the spin and orbital sectors, the OILSC results in rich and novel quantum phase transitions. Some accurate analytical expressions for the critical fields are obtained. Both spin ordering and orbital ordering are found in a gapped singlet phase. The system exhibits many interesting phenomena such as nonvanishing magnetization of the singlet phase, multi-entrance of the singlet in the ground state when the field varies, unsymmetric magnetization in two-component phase and magnetization crossover for different OILSC.

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with external source which is the time function have been proposed. The mesoscopic metallic ring is regarded as a “pure” inductance design, and the dependence of the quasienergy spectrum on a parameter called the electric matching ratio is presented.

We consider the problem of consistence between the Bethe ansatz (BA) wave function and the multiparticle (more than two) scattering in one-dimensional δ-function interacting SU(4) fermions, which the approach of BA does not explicitly take into account. We find the scattering conditions of three and four particles located at the same position and show that the conditions can be fulfilled by the two-particle connection conditions of the BA wave function. So the definition of the BA wave function can be exactly extended to those cases with multiple occupancies. The inconsistence between the BA and multiparticle interacting on a same site in the degenerate Hubbard model, which makes the BA fail for the model, is shown to vanish in the limit of small site spacing. A correspondence relation of the BA equation and SU(4) symmetry of the system is also indicated for the fermions. The degeneracy of state with BA eigenenergy is given. Singlet lies in the case when there are equal numbers of particles in each inner component.

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The mesoscopic metallic ring is regarded as a “pure” inductance design, and the dynamic localization of current has been obtained explicitly.

As well know one-dimensional Luttinger liquid includes many striking properties. In our paper, we study the question of the physical properties of the separated spin-charge Luttinger liquid in an external magnetic field (h). We include more completely interaction such forward scattering (g2 and g4). Charge and spin cannot completely be separated due to the effect of magnetic field. We calculated also the correlation function and manifestly show the action of the interaction parameters.

The spectra of the dielectrical constant and dielectrical loss in three nanostructured α-Fin2 3 samples at different annealed temperatures are measured by using ac LRC method. The relaxation times of polarization and the conductance are calculated by means of the Debye mechanism and the interface effects in two kinds of polarization processes with two different relaxation times are proposed.

The measurements of electric capacities and dielectric loss angles for nanocrystalline γ-Fe2O3, under air and vacuum atmospheres have been conducted by using ac LRC method, and the conductivity and the polarization relaxation time have also been calculated from the frequency spectra of real and imaginary parts of the dielectric constants. The anomalous dielectric behavior implies the existence of two kinds of polarization mechanisms with different relaxation times, which are caused by the defects and the dangling bonds in the interfaces, respectively. The experimental and calculated results indicated that the polarization loss and the conductance loss are dominant in air atmosphere and vacuum, respectively.

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrodinger equation of the mesoscopic electric circuit with external source which is a time function has been proposed. The Josephson-like effects in the mesoscopic electric circuit have been addressed.

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with an external source which is the time function is proposed. The mesoscopic metallic ring is regarded as a `pure' inductance design, and the energy band suppression in mesoscopic metallic ring is addressed exactly.

The quantum theory for mesoscopic electric circuits with charge discreteness is briefly described. The Schrodinger equation of the mesoscopic electric circuit with an external source which is the time function has been proposed. The Bloch wave oscillation and Coulomb blockade in the mesoscopic electric circuit have been addressed. (C) 1998 Elsevier Science B.V.

The importance of discreteness of Cooper pairs tunneling in the mesoscopic Josephson junction is addressed. The Bloch wave oscillation in the mesoscopic Josephson junction is proposed by means of the quantization for the junction in accord with the discreteness of Cooper pair.