Zeroth-order phase transitions and Zipf law quantization

From the standpoint of thermodynamic averaging of fission microprocesses, we investigate the origin of radioactive release in an NPP after an accident or after resource depletion. The genesis of the NPP release is interpreted as a new thermodynamic phenomenon, a zeroth-order phase transition. This problem setting results in a problem in probabilistic number theory. We prove the corresponding theorem leading to quantization of the Zipf law for the frequency of a zeroth-order phase transition with different values of the jump of the Gibbs thermodynamic potential. We introduce the notion of hole dimension. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 118–142, January, 2007.     

Pore-Level Modeling of Gas and Condensate Flow in Two- and Three-Dimensional Pore Networks: Pore Size Distribution Effects on the Relative Permeability of Gas and Condensate

We present a mechanistic model of retrograde condensation processes in two- and three-dimensional capillary tube networks under gravitational forces. Condensate filling-emptying cycles in pore segments and gas connection–isolation cycles are included. With the pore-level distribution of gas and condensate in hand, we determine their corresponding relative permeabilities. Details of pore space and displacement are subsumed in pore conductances. Solving for the pressure field in each phase, we find a single effective conductance for each phase as a function of condensate saturation. Along with the effective conductance for the saturated network, the relative permeability for each phase is calculated. Our model porous media are two- and three-dimensional regular networks of pore segments with distributed size and square cross-section. With a Monte Carlo sampling we find the optimum network size to avoid size effects and then we investigate the effect of network dimensionality and pore size distribution on the relative permeabilities of gas and condensate.     

Reflection-Transmission Transition of Bright-Bright Solitons Collision in Two Species Condensates with Repulsive Interspecies Interactions

Considering repulsive interspecies interactions, we study the dynamical properties of bright-bright solitons in two species Bose-Einstein condensates by using a variational approach combined with numerical simulation. It is shown that the interactions between bright-bright solitons vary from repulsive to attractive interactions with the increasing their separating distances, and at equilibrium position the bright-bright solitons are localized. Interestingly, a transition from reflection- to transmission-collision is firstly observed, different from previous results of only reflection collision appearing there. These results will be helpful for the experimental manipulating such solitons.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

Stationary States and Modulational Instability of Coupled Two-Component Bose-Einstein Condensates in a Ring Trap

We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.     

夸克胶子混合真空凝聚和Dyson-Schwinger方程

基于夸克传播子的Dyson-Schwinger方程，计算了夸克胶子混合真空凝聚和夸克真空凝聚. 这些凝聚不仅联系着夸克在真空态中的虚度，而且也表征了真空中夸克分布的空间宽度. 真空凝聚的存在直接反映着QCD真空的非微扰结构. 计算表明：上夸克与下夸克的虚度为λ²_u,d=0.7GeV²，奇异夸克的虚度为λ²_s=1.6GeV². 这些结果与许多用完全不同的方法得到的结果一致.     

Tunneling Dynamics Between Any Two Multi-atomic-molecular Bose-Einstein Condensates

Tunneling dynamics of multi-atomic molecules between any two multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose-Einstein condensates depends not only on the inter-molecular nonlinear interactions and the initial number of molecule in these condensates, but also on the tunneling coupling between them. It is discovered that besides oscillating tunneling current between the multi-atomic molecular condensates, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate molecule on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling.     

Classifying the ground-state phases of spin–orbit coupled spin-2 Bose–Einstein condensate in momentum space

The ground-state phases of two-dimensional spin-2 Bose–Einstein condensate with Rashba spin–orbit coupling are studied. For the equal strengths of the density-density interaction and the spin-exchange interaction, we classify the ground-state phases into four types of stable phases with spin–orbit coupling and spin singlet-pairing interaction in momentum space, i.e., the ring phase, the stripe phase, the triangular phase and the square phase. With increasing the spin–orbit coupling strength, the system undergoes a sequence phase transitions from the ring phase to the stripe phase, and to the square phase for the attractive spin singlet-pairing interaction ($c_2<0$), and the system undergoes a sequence phase transitions from the ring phase to the stripe phase, to the triangular phase, and to the square phase for the repulsive spin singlet-pairing interaction ($c_2>0$).     

玻色-爱因斯坦凝聚体中的怪波操控

利用Darboux变换法, 解析地研究了玻色-爱因斯坦凝聚体(BEC)中的怪波. 结果表明: 当谱参数等于非线性系数时, BEC中形成一种新型的单洞怪波; 而当谱参数小于非线性系数时, BEC中出现双洞怪波. 进一步地, 怪波的出现位置可通过调节周期性势阱的驱动频率和强度来控制. 此外, 随着原子间相互作用的减小, 怪波的最高幅度也随之降低. 相关结果可为预防怪波的危害提供帮助.