Contribution of Disclination Lines to Free Energy of Liquid Crystals in Single-Elastic Constant Approximation

In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.     

Electron gas energy in narrow-gap semiconductors in a magnetic field

The correlation energy of electron gas in narrow-gap semiconductors in a magnetic field was analytically calculated in the random-phase approximation. The results obtained allow calculation of the ground state energy and determination of the electron density corresponding to the energy minimum.     

Two-dimensional electron crystal in magnetic field. Topological phase transitions and stability region.

The phase diagram of a 2-dim. electron system in the magnetic field $\text{H}$ is analyzed. We obtain ab initio the free energy F{U_iκ} of a deformed electron crystal when the long-range Coulomb forces and $\text{H}$ are taken into account. Using F{u_iκ} we find H-dependent interaction between the dislocations and the curve of the topological melting due to the dissociation of dislocation pairs. The topological melting curve for H → ∞ asimptotically approaches to the melting curve of a classical crystal. This result is obtained using Feynman variational technique as well. We examine also the electron liquid crystal phase and the stability region of a 2-dim. crystal at $\text{H}$ ≠ 0. The first-order phase transitions from the crystal and liquid crystal to the isotropic liquid are predicted to take place in a definite region of the phase diagram. We find the increase of the crystal and liquid crystal region on the T-n phase diagram with H increase. The various phenomenological stability criteria are ånaylzed.     

稀释晶场对纳米管上Blume-Capel模型磁化性质的研究

利用有效场理论研究了纳米管上稀释晶场中Blume-Capel模型格点的磁化强度、内能、比热和自由能,得到了系统格点的磁化强度、内能、比热和自由能与温度和稀释晶场的关系.结果表明:稀释晶场取值概率和晶场强度等诸多因素相互竞争,使系统表现出比含恒定晶场作用的Blume-Capel模型更为丰富的磁学特性;稀释晶场会抑制系统格点的磁化强度,导致其基态饱和值小于1;温度较低时,系统格点的磁化强度表现出复杂性;晶场较强时,系统的内能、比热和自由能也呈现出不同的磁学性质.     

Optical probing of a fractionally charged quasihole in an incompressible liquid

In photoluminescence spectroscopy of a low-mobility two-dimensional electron gas subjected to a quantizing magnetic field, we observe an anomaly around nu=1 / 3 at a very low temperature (0.1 K) and an intermediate electron density (0.9 x 10(11) cm(-2)). The anomaly is explained as due to perturbation of the incompressible liquid at the Laughlin state due to close proximity of a localized charged exciton which creates a fractionally charged quasihole in the liquid. The anomaly of approximately 2 meV can be destroyed by applying a small thermal energy of approximately 0.2 meV that is enough to close the quasihole energy gap.     

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pZ=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

接枝聚合物对小分子的选择性吸附研究

文章应用密度泛函理论研究接枝于壁面的方阱链对二元小分子混合物的选择性吸附特性. 系统的Helmholtz剩余自由能泛函被表示为硬球排斥和方阱吸引两部分贡献之和,分别由硬球链流体状态方程和变阱宽方阱链流体状态方程的简单加权密度近似来进行计算. 用此理论方法,分别考察了接枝聚合物的结构性质,以及不同温度下接枝分子层对二元方阱流体的选择性吸附性能. 结果表明:分子刷厚度随接枝密度线性增长而随温度非线性增加,并且在高温下趋于饱和;在较低温度下,接枝聚合物刷能表现出很好的选择性吸附能力,当聚合物刷被加热到高于饱和温度时,该能力将大幅度地减弱. 关键词： 密度泛函理论 接枝聚合物 选择性吸附 方阱链     

Properties of a two-dimensional semimetal in a strong magnetic field

A system of two-dimensional electrons and holes ha s been investigated in a strong magnetic field, when it is sufficient to take into account only the ground Landau level. It has been shown that the interaction of electrons and holes can lead to an ordered state. In this problem, the exchange interaction in electron and hole subsystems is significant. The following two cases have been considered: (a) there are one electron and one hole valleys, and at some magnetic field strength, there exists an ordered state, as in an excitonic insulator; and (b) there exist one electron and two equivalent hole valleys (as in the experiment performed by Kvon et al. [1]), and the hole system has an ordered state of the Stoner ferromagnetic type in a specific range of magnetic field strengths. The spectra of elementary excitations of the Bose and Fermi types have been obtained. The Fermi excitations have a gap in the energy spectrum, whereas the Bose excitations in the ordered states begin with zero (to these excitations there corresponds an electric dipole moment). The self-consistent field approximation has been used, which is exact when the numbers of electrons and holes are equal to each other.     

Band structure and thermodynamic potentials

The behavior of different thermodynamic functions of a system of delocalized electrons in a crystal is considered in the single-band strong coupling approximation depending on the degree of energy band filling and temperature. The chemical potential, grand thermodynamic potential, internal energy, free energy, entropy, and heat capacity are numerically calculated. Dependences of these quantities on the electron concentration at high temperatures are investigated. Their limited energy spectrum leads to the special features in the behavior of these quantities in comparison with the free electron gas.     

Collective modes and the far-infrared absorption of the two-dimensional electron gas in a periodic quantizing magnetic field

We investigate the far-infrared (FIR) absorption of a two-dimensional electron gas in a periodically modulated quantizing magnetic field. The magnetic field varies along only one spatial direction and the external time-dependent electric field is linearly polarized along that axis. The mutual Coulomb interaction of the electrons is treated self-consistently in the ground state and in the absorption calculation within the Hartree approximation. The effects of the magnetic material on top of the heterostructure as a grating coupler is included in the time-dependent incident FIR electric field. We show that, similar to an electric modulation, the absorption can be directly correlated to the underlying electronic energy bands. In addition, the magnetic modulation leads to absorption spectra with a richer structure due to the quite different static response of the electron density to the modulation.     

Coulomb drag in the quantum Hall state: Role of disorder

We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being . We find to be very large, as compared to the zero magnetic field case. We attribute this enhancement to the slow decay of density fluctuations in a strong magnetic field. For a clean system, the linear -dependence of the longitudinal conductivity, characteristic of the state, leads a unique temperature dependence – . Within a semiclassical approximation, disorder leads to a decrease of the transresistivity as compared to the clean case, and a temperature dependence of at low temperatures.     

Ferromagnetism of Electron Gas

We here investigate the density and temperature dependence of polarization using the relativistic formalism for the electron–electron interaction within the Fermi liquid model. The variational method has been used: the free energy has been minimized with respect to the effective mass and the polarization parameter. Then we obtained the equation of state and magnetic susceptibility of the system. The exact results for polarization and magnetic susceptibility have been obtained at zero temperature. It has been shown that for a given temperature (density) there is a critical density (temperature) at which the ferromagnetic phase can appear in an electron gas. The results are in agreement with previous work. Our results show that at nonzero temperatures and in very low and very high densities the ferromagnetism phase cannot exist.     

光学极化子性质对耦合强度和磁场的依赖性

应用线性组合算符和幺正变换方法,研究磁场和耦合强度对光学极化子性质的影响。数值计算表明:当电子接近晶体表面时,光学极化子的振动频率、基态能量和第一激发能仅与磁场有关,且随磁场强度的增强而增大;当电子远离晶体表面时,基态能量和第一激发能与磁场强度和耦合参数均有关,且随磁场强度和耦合参数的增加而增加。     

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy, entropy and specific heat curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.     

磁场中液氦薄膜表面电子涟波子系统的性质

研究了磁场中液氦薄膜表面电子与涟波子强耦合和弱耦合的性质。采用线性组合算符方法导出磁场中液氦薄膜表面电子 涟波子系统的振动频率和基态能量。讨论磁场对表面电子 涟波子系统的振动频率和基态能量的影响。     

最近邻强交换相互作用对spin-1纳米管热力学性质的影响

利用有效场理论研究了纳米管上最近邻强交换相互作用下Blume-Capel模型的内能、比热和自由能,得到了系统的内能、比热和自由能与最近邻强交换相互作用、晶场强度和温度的关系.结果表明:最近邻强交换相互作用、晶场强度和温度等诸多因素相互竞争,使系统表现出比J_1=J_2=J=1时的BC模型更为丰富的热力学性质;系统内能随温度的变化曲线表现出不连续性;比热随温度的变化出现奇异性;一定条件下,基态时的自由能会发生突变.