International Journal of Modern Physics B

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U_q(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

La_0.5Sr_0.5MnO₃ films on (001) LaAlO₃ were prepared by RF magnetron sputtering using powder target and were studied by SQUID and XPS. The XPS results show the formation of Mn³⁺ and Mn⁴⁺, indicating the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) clusters. SQUID measurement of LSMO on LAO and Si also support an interaction between them at low temperatures, resulting in the shift of hysteresis loops. Large coercivities at low temperature can be attributed to the pinning of both FM and AFM clusters and small coercivities at high temperature to the depinning of both FM and AFM phases, resulting from the thermal motion at higher temperatures which help to overcome the energy barrier and change the magnetic alignments.

Under the dielectric continuum model and Loudon's uniaxial crystal model, by adopting the transfer matrix method, the dispersion properties of the interface optical (IO) and surface optical (SO) phonon modes and their couplings with electrons in multi-layer coupling wurtzite quantum wells (QWs) are deduced and analyzed via the method of electrostatic potential expanding. Numerical calculations on a freestanding symmetrical wurtzite QW and an asymmetrical wurtzite QW have been performed. Results reveal that, in general, there are four branches of IO and two branches of SO phonon modes in the systems. The dispersions of these IO and SO phonon modes are obvious only when the free two-dimensional phonon wave number k_t parallel to the heterostructure interfaces is small. The degenerating behavior for these phonon modes has been clearly observed for small k_t. When k_t is relatively large, with the increase in k_t, the frequencies of the IO and SO phonon modes converge to some definite limiting frequencies in corresponding wurtzite single planar heterostructure. This feature have been analyzed in depth from the mathematical and physical viewpoints. The calculations of electron-phonon coupling function show that, the electrostatic potential distribution of the IO and SO mode in freestanding symmetrical wurtzite QW is either symmetrical or is antisymmetrical; but that in freestanding asymmetrical wurtzite QW is neither symmetrical nor is antisymmetric. The calculation also shows that the SO modes and the short wavelength phonon modes play a more important role in the electron-phonon interaction.

The interrelation between apparent viscosity in steady shear flow and complex viscosity in oscillatory shear flow for magnetorheological (MR) suspensions is investigated. Series of experiments have been conducted using a MR rheometer. An extended Rutgers–Delaware rule is proposed, in which an effective shear rate for oscillatory shear flow is defined as ωΔ_h. Here ωΔ_h is the shift factor dependent on strain amplitude (γ₀), which was found to be similar for different MR suspensions under different magnetic fields. At high strain amplitudes (γ₀≥100%), Δ_h≈γ₀, the Rutgers–Delaware rule is approximately obeyed. At low strain amplitudes (γ₀<100%), the curves of Δ_h fall between the line of the Cox–Merz rule and that of the Rutgers–Delaware rule. The curve of Δ_h at low strain amplitudes depends on the ingredients of the MR suspension. For samples with the same ingredients, a unified curve of Δ_h can be identified in a range of magnetic fields and/or for a range of volume fraction of magnetic particles.

Unlike the Fourier series expansion, the discrete Fourier transform is defined on a finite basis set of harmonic functions. The first approach is widely used in condensed matter to describe the thermodynamic limit of various lattice models, while the latter did not receive sufficient development that would allow to address finite lattices. In the present paper a general expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived for the first time via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Although the final expressions are completely equivalent to Bethe ansatz, the examples allow us to clarify the differences between the two approaches. On the other hand, it is explained why the well known results obtained by Fourier series expansion were incomplete and thus provides a deeper understanding of the approach.

The results of precision heat capacity measurements near the lower consolute point in aqueous solutions of non-ionic surfactants n-dodecyl hexaethylene glycol monoether (C₁₂E₆), C₁₀E₆, and C₁₂E₈, are reported. These surfactants form homogeneous single phase micellar solutions below the lower consolute point, T_c. The pretransitional specific heat in the homogeneous phase below T_c is found to grow with temperature and exhibits a power-law divergence. Analysis of the data obtained for the three systems reveals that the specific heat exponent, α=-α_R/(1-α_R)≅0.5, gives credence to mean field behavior.

We numerically investigated Mott transitions and mixing-demixing transitions in one-dimensional boson-fermion mixtures at a commensurate filling. The mixing-demixing transition occurred in a qualitatively similar manner to incommensurate filling cases. We also found the Mott insulator phase appeared in both the mixing and the demixing states as the fermion-boson interaction or the boson-boson interaction increased. Phase diagrams were obtained in interaction parameter space.