International Journal of Modern Physics B

In this review we will discuss the experimental and theoretical progresses in studying spin–orbit coupled degenerate atomic gases during the last two years. We shall first review a series of pioneering experiments in generating synthetic gauge potentials and spin–orbit coupling in atomic gases by engineering atom-light interaction. Realization of spin–orbit coupled quantum gases opens a new avenue in cold atom physics, and also brings out a lot of new physical problems. In particular, the interplay between spin–orbit coupling and inter-atomic interaction leads to many intriguing phenomena. By reviewing recent theoretical studies of both interacting bosons and fermions with isotropic Rashba spin–orbit coupling, the key message delivered here is that spin–orbit coupling can enhance the interaction effects, and make the interaction effects much more dramatic even in the weakly interacting regime.

The present paper reviews some general aspects of the stochastic analysis performed by the author in the field of statistical physics, particularly concerning the order formation from unstable states. First, a brief review and some new results are given on the generalization of the Itô-type and Stratonovich-type stochastic integrals. Their physical meaning is also discussed form the viewpoint of symmetry. Secondly, Kubo's stochastic Liouville equation is presented from the viewpoint of separation of procedures, to give a simple derivation of the Fokker–Planck equation. Thirdly, the scaling theory of order formation from the unstable point is re-formulated by introducing here a new order parameter to characterize macroscopic order formation and to clarify the synergetic effect of the initial fluctuation, random noise and nonlinearity. Finally, some discussions are given, particularly concerning applications of the Hida calculus based on the Gelfand triplet space.

We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground states. This is a complicated problem of energy minimization, with three quantum variables under constraints, i.e., the total spin of each species and the total spin of the whole mixture, as well as four parameters, including intraspecies and interspecies spin coupling strengths and the magnetic field. The quantum phase diagram is very rich. Compared with the case without a magnetic field, the ground states are modified by a magnetic field, which also modifies the ground state boundaries or introduces new crossover regimes on the phase diagram. Without interspecies spin coupling, the quantum phase transitions existing in absence of a magnetic field disappear when a magnetic field is applied, which leads to crossover regimes in the phase diagram. Under ferromagnetic interspecies spin coupling, the ground states remain disentangled no matter whether there is a magnetic field. For antiferromagnetic interspecies spin coupling, a magnetic field entangles the ground states in some parameter regimes. When the intraspecies spin couplings are both ferromagnetic, the quantum phase transition between antiferromagnetic and zero interspecies spin couplings survives the magnetic field. When the intraspecies spin couplings are both antiferromagnetic, a magnetic field induces new quantum phase transitions between antiferromagnetic and zero interspecies spin couplings.

Using the method of recursion relations an exact solution of classical Ising models with arbitrary value of spin on the Bethe lattice with arbitrary coordination number is presented. Expressions for the spontaneous magnetization, for the magnetic moments of arbitrary orders, for the susceptibility, for the free energy, and for the specific heat are found as functions of quantities which are determined by the recursion relations. The behavior of the spontaneous magnetization for the Ising model on the Bethe lattice is investigated for systems with spin values up to s = 5 for various coordination numbers and the corresponding critical temperatures are determined. An approximate formula for determining the positions of the critical temperatures for arbitrary high values of the spin variable is found and discussed. It is shown that this formula allows one to determine the full structure of the critical temperatures with very high precision.

We explicate a derivation of a general system of quantum hydrodynamics (QHD) equations for the study of the non-equilibrium processes. Fundamental QHD equations for neutral paramagnetic particles with the own electric dipole moment (EDM) were derived from the many-particle Schrodinger equation. The fact that the influence of spin–spin, dipole–dipole and spin–orbital interaction between particles was taken into account. The problem of definition of spin-waves and polarization waves spectrum in 2D system for the molecules with intrinsic magnetic moments (IMM) and EDM were theoretically investigated and solved for the system of nitric oxide gas in the external electromagnetic fields. The polarization dynamics in system of neutral magnetic and polarized particles is shown to cause formation of a new type of waves as well as changes in the dispersion characteristics of already known waves. Moreover we found the contribution of spin–orbital interaction between gas particles to the elementary excitations and shown that spin–orbital interaction leads to the emergence of magnetization and polarization waves.

In this work, a new method to determine the wall shear stress was developed step by step. To determine the wall shear stress, methods of the suspension rheology are being used for the first time to characterize ER fluids. This work focuses on investigations of the flow behavior of electrorheological suspensions in flow channels with different geometries at different electrical field strengths. Careful interpretation of the results with respect to different gap geometries has shown that the measured flow curves should undergo a combination of corrections. As a result it can be shown that wall slip effects can be measured under application like conditions on a hydraulic test bench.

The rate equation for exchange-driven aggregation of monomers between clusters of size n by power-law exchange rate (~ n^α), where detaching and attaching processes were considered separately, is reduced to Fokker–Planck equation. Its exact solution was found for unbiased aggregation and agreed with asymptotic conclusions of other models. Asymptotic transitions were found from exact solution to Weibull/normal/exponential distribution, and then to power law distribution. Intermediate asymptotic size distributions were found to be functions of exponent α and vary from normal (α = 0) through Weibull (0 < α < 1) to exponential (α =1) ones, that gives the new system for linking these basic statistical distributions. Simulations were performed for the unbiased aggregation model on the basis of the initial rate equation without simplifications used for reduction to Fokker–Planck equation. The exact solution was confirmed, shape and scale parameters of Weibull distribution (for 0 < α < 1) were determined by analysis of cumulative distribution functions and mean cluster sizes, which are of great interest, because they can be measured in experiments and allow to identify details of aggregation kinetics (like α). In practical sense, scaling analysis of evolving series of aggregating cluster distributions can give much more reliable estimations of their parameters than analysis of solitary distributions. It is assumed that some apparent power and fractal laws observed experimentally may be manifestations of such simple migration-driven aggregation kinetics even.

The temperature dependence of spin currents in insulators at the finite temperature near zero Kelvin is theoretically studied. The spin currents are carried by Jordan–Wigner fermions and magnons in one- and three-dimensional insulators. These spin currents are generated by the external magnetic field gradient along the quantization axis and also by the two-particle interaction gradient. In one-dimensional insulators, quantum fluctuations are strong and the spin current carried by Jordan–Wigner fermions shows the stronger dependence on temperatures than the one by magnons.