International Journal of Modern Physics B

This article reviews steady-state spin densities and spin currents in materials with strong spin-orbit interactions. These phenomena are intimately related to spin precession due to spin-orbit coupling, which has no equivalent in the steady state of charge distributions. The focus will initially be on effects originating from the band structure. In this case, spin densities arise in an electric field because a component of each spin is conserved during precession. Spin currents arise because a component of each spin is continually precessing. These two phenomena are due to independent contributions to the steady-state density matrix, and scattering between the conserved and precessing spin distributions has important consequences for spin dynamics and spin-related effects in general. In the latter part of the article, extrinsic effects such as skew scattering and side jump will be discussed, and it will be shown that these effects are also modified considerably by spin precession. Theoretical and experimental progress in all areas will be reviewed.

This paper studies the Yang–Lee singularity of the 2-dimensional Ising model on the cylinder via transfer matrix and finite-size scaling techniques. These techniques enable a measurement of the 2-point and 3-point correlations and a comparison of a measurement of a corresponding universal amplitude with a prediction for the amplitude from the (A₄, A₁) minimal conformal field theory.

In the framework of the Bogolyubov approximation and using the Bogolyubov inequalities, we give a simple proof of the coexistence of two non-conventional Bose–Einstein condensates in the case of some superstable Bose system whose atoms have an internal two-level structure, and their energy operators in the second quantized form depend on the number operators only.

The stability boundaries and behaviors of the duration time of synchronization for chaotic Mathieu–Duffing oscillators are investigated. Based on the unidirectional or bidirectional linear state error feedback coupled scheme, the error system is derived. After replacing the chaotic orbit by a regular orbit containing multi-harmonics, we analyze the asymptotic stability of the error system, which leads to a Hill equation. According to Floquet theory and the properties of the Hill equation, the evolution of the discriminant of the Hill equation with respect to the coupling strength is traced to determine the stability boundaries between the synchronization and desynchronization domains. Thus, the critical values of coupling strength are obtained. These critical values are in good agreement with those from numerical simulations. The behaviors of the synchronization time are numerically investigated in the synchronization domain. It is found that the synchronization time reaches an asymptotic minimal value when the oscillators are unidirectionally or bidirectionally coupled, and the two asymptotic minimal values are almost the same. It is also noted that the slowing down behavior of the synchronization time can occur inside the synchronization domain when the coupling is bidirectional.

A study of the thermodynamic properties of Cu in molten Cu–In alloys has been explained using a compound formation model. We use the model to deduce information on thermodynamic properties of the alloy such as the Gibbs free energy of mixing, the enthalpy and entropy of mixing. In this study, we first model the Gibbs free energy in terms of the interaction parameters. Sequel to this, the interaction parameters are utilized to quantify properties such as the concentration–concentration fluctuations in the long wavelength limit, the Warren–Cowley short-range order parameter, and the chemical diffusion. Both positive and negative deviations from Raoultian behavior and concentration-dependent asymmetry in the mixing properties of CuIn₄ liquid alloys were reported. Our analysis suggest that the liquid alloy undergoes a transformation from an ordered (In-rich end) to segregating (Cu-rich end) state. The system also exhibits ideal behavior at the Cu-rich end.

We mainly study the Zeeman effect on electronic structure of carbon nanotori in the presence of magnetic field (B) perpendicular to the tori's plane. As a function of magnetic flux (ϕ), the energy gap (E_g) and density of states (DOS) near the Fermi level are obtained in the case of with and without considering the Zeeman effect. Without spin-B interaction, the ϕ-dependent electronic structure would exhibit the periodical Aharonov–Bohm (AB) oscillation. A magnetic-field-induced semiconductor-metal transition is indicated in the variation of energy gap and DOS of armchair tori. The Zeeman effect on electronic structure is notable at relatively large ϕ (~100ϕ₀, with ϕ₀ = h/e), e.g., more phase transition points may appear in the E_g - B dependence for armchair tori, and the destruction of periodical AB oscillation is distinct due to the Zeeman effect. These results may be observed by scanning tunneling spectroscopy measurement.

We investigate the entanglement transfer in two parallel spin chains by anisotropic Heisenberg XY interaction in an external magnetic field. The perfect entanglement transfer condition is obtained. We find that perfect entanglement transfer can be realized from one spin pair to another spin pair at certain times by adjusting the magnetic field strength and the anisotropy parameter, which suggests its potential usefulness in quantum information process.

The systematics of energetic terms as they are taught in continuum mechanics deviate seriously from the standard doctrine in physics, resulting in a profound misconception. It is demonstrated that the First Law of Thermodynamics has been routinely reinterpreted in a sense that would make it subordinate to Bernoulli's energy conservation law. Proof is given to the effect that the Cauchy stress tensor does not exist. Furthermore, it is shown that the attempt by Gibbs to find a thermodynamic understanding for elastic deformation does not sufficiently account for all the energetic properties of such a process.

The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J₁ and J₂, interlayer coupling constant between the layers J₃ and crystal field interaction Δ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J₂/|J₁|, J₃/q|J₁|) planes for given Δ values and on the (Δ/qJ, J₃/qJ) plane when J₁ = J₂ = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J₁ > 0, J₂ > 0, and for J₃ > 0 or J₃ < 0 on the (kT/J₁, J₃/J₁) planes for given Δ/qJ₁ and J₂/J₁ and on the (Δ/J, kT/J) plane for given J₃/J when J₁ = J₂ = J for the coordination number q = 3. It was found that the system exhibits both first- and second-order phase transitions and tricritical points. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments.

We investigate the inelastic transport properties of quantum dots connected to two leads, based on the combination of a recently developed nonperturbative technique and full counting statistics involving an approximate mapping of a many-body electron–phonon system onto a multichannel scattering system. The full counting statistics is adopted in the calculations of the inelastic transport processes of electrons where the electron–phonon interactions, which are the main source of the inelasticity, are taken into account. For serially coupled double quantum dots, we find that (i) both the current and the noise are suppressed when electron–phonon interaction switches on, and (ii) skewness becomes negative in a certain parameter regime, which is absent in the case without electron–phonon interactions.

We study the herding mechanism for the evolution of cooperation in the snowdrift game. By controlling the herding parameter a, which measures the herding behavior of players, we investigate the cooperative frequency f_c on the payoff r. It is found that, for a small a, large clusters are formed and the system shows an intermediate level cooperation up to a big payoff r. However, as a increases, clusters become smaller, and cooperation decreases faster. When a is large, up to a critical value of about a* = 0.5, most players stay alone, each as a separate cluster, and no cooperation occurs. This phenomenon indicates that an individual favors defection, while group selection favors cooperation.