Order parameter and its critical exponent for some binary mixtures showing induced nematic phase

Refractive index measurements as a function of temperature have been performed for an induced nematic binary system by means of thin prism technique. The temperature dependence of the birefringence (Δn) has been assessed from the measured refractive index data. A direct extrapolation method has been employed to determine the orientational order parameter for the investigated mixtures and the order parameter so obtained has also been compared with the mean field values. The Haller type fitting expression results in a relatively lower value of the order parameter critical exponent (β) compared to the theoretically predicted values. Therefore, a four-parameter power law expression, consistent with the mean field theory as well as the first-order character of the nematic–isotropic (N-I) phase transition have been used to explore the critical behavior of the order parameter near the N-I transition.     

A self-consistent approach for the SmA–SmC* phase transition

By using an analogy with the Maier–Saupe theory of the nematic phase, a mean field theory of the chiral smectic-C (SmC*) phase is constructed. As an order parameter of the SmC* phase, the tilt angle θ is selected, and the feedback effect of θ is introduced into the hindered rotational potential about the molecular long axis. By solving the self-consistent equation for the order parameter θ, the second-order phase transition appears. Also, to describe the SmA–SmC* phase transition under an electric field, a coupling term between a molecular dipole moment and an external electric field is introduced to the potential function. The electroclinic effect in the SmA phase and the hysteresis effect in the SmC* phase, which were described phenomenologically in the past, are found directly from the microscopic theory.     

Metamagnetic model in a field of arbitrary direction

The free energy of a metamagnetic model, in a magnetic field making an angle θ with the direction of uniaxial anisotropy, is calculated in the context of the mean-field approximation. The tricritical temperature decreases as θ increases, and finally vanishes for θ larger than a certain critical angle. In the (H_∥, H_⊥, T) space there is a line of tricritical points which separates two smoothly joining surfaces of first and of second order phase transitions.     

Field-theoretic approach to critical dynamics far from equilibrium

The field-theoretic approach to critical phenomena is extended to deal with critical dynamics far from equilibrium. In particular, the macroscopic evolution equation for the average order parameter is derived in a manner parallel to the derivation of the equation of state. The method is illustrated by deriving the scaled macroscopic equation of motion for the timedependent Ginzburg-Landau model near the critical point for dimensionality near four.     

与光场依赖强度耦合下运动纠缠双原子的周期量子回声

本文将Tavis-Cummings(T-C)模型推广到同时考虑原子运动及与光场依赖强度耦合的情况.运用全量子理论,研究了与光场依赖强度耦合下运动纠缠双原子量子态保真度演化.采用数值计算的方法,探讨了双原子初始纠缠因子θ、光场平均光子数n以及场模结构参量p对双原子量子态保真度演化的影响,解析分析了双原子周期量子回声的形成规律,揭示了其物理实质.结果表明, 在场模结构参量p=1的情况下,无论光强和双原子初始纠缠因子如何取值,双原子均产生周期2π的量子回声;在强相干场n=30条件下,改变p从1到小于800时,Bell态双原子产生2π/p周期量子回声.当p≥800时,无论光场是真空场、弱相干场或强相干场,双原子量子态保真度恒为1,即第一类Bell态原子持续处于保真态;而当双原子初始纠缠因子为3π/4时,无论n、p取何值,双原子量子态保真度保持为1,双原子持续处于第二类Bell态的保真态.其结论表明, 该推广模型具有很好的双原子周期量子回声性质,为纠缠双原子信息高保真输出及噪音环境下量子信息处理的实验实现提供了理论参量和物理载体.     

Determination of bulk values of twist elasticity coefficient in a chiral smectic C* liquid crystal

A method is described for determination of bulk values of a twist elastic coefficient for smectic c-director in chiral smectic liquid crystals with a helical structure. The method was applied to 4-methylbutyloxy phenyl-4-octyloxy-benzoate (C8) in the chiral smectic C* phase. The measurements were performed using optical detection in a small deformation limit. In contrast to the usual methods, initial deformation of the helix (caused by strong surface interactions) was avoided by using homeotropic aligned thick samples. The critical temperature dependence of the measured coefficient was observed. The relation between the measured parameter and the smectic C order parameter is presented.     

The neutron electric dipole moment in the cloudy bag model

An evaluation of the neutron electric dipole moment (NEDM), using the cloudy bag model (CBM) shows that two CP-violating effects (a quark mass term and a pion-quark interaction) have contributions that are about equal in magnitude, but opposite in sign. This cancellation allows the upper limit on the θ parameter to increase by about an order of magnitude.     

Interplay between a homogeneous magnetic field and an antiferromagnetic field in one-dimensional superconductors

Mean-field theory applied to superconductors with one-dimensional band in the presence of both the homogeneous magnetic field H₀ and the antiferromagnetic field H_Q, the second-order phase transition temperature is investigated for the arbitrary angle θ between H₀ and H_Q. It is found that the remarkable superconducting region in the case of θ = 0 is retained only for small θ and that the spatially dependent order parameter coexists with the spatially uniform order parameter except for θ = τ/2.     

Order parameter oscillations in a bounded solid solution and their bifurcations upon cooling

A nonlinear boundary-value problem for the Landau-Khalatnikov equation, which models the time evolution of the order parameter in a binary solution, is considered. A parameter characterizing the closeness of the alloy temperature to the critical temperature is introduced. This parameter depends on the dimensionless diffusivity. A change in this parameter results in successive bifurcations of solutions; so the order parameter corresponds to an oscillating steady-state structure to which almost all nonsteady-state solutions of the boundary-value problem are drawn after a long period of time.     

ESR of γ-irradiated DI-, TRI- and poly-glycin

The effects of γ radiation on glycylglycine, triglycine, and polyglycine have been studied using ESR spectroscopy. The radiation exposures have been performed under vacuum at room temperature. All those irradiated substances show a doublet absorption signal often ascribed to a radical formed on the α carbon of the peptide chain. The magnetic susceptibility has been found to depend on temperature according to the Curie-Weiss law. The radio-sensitivity parameter G_r , the hyperfine splitting constant A_h and the spectroscopic factor g nave been determinated as well as θ which is the temperature corresponding to the Curie temperature of the irradiated substance. The results on C_r , θ and A_h for all peptides studied here agree with the assumption of radiation induced free radicals located at the α carbon of the peptide chain, leading to conclude that the degree of delocalization of the unpaired electron increases for increasing number of glycine units in the peptide. Finally, from negative θ values obtained, a conclusion has been reached on the antiferromagnetic nature of the interaction between unpaired spins.     

A time operator in quantum mechanics

The lower bound on a continuous energy spectrum suffices t⊙ mathematically preclude the construction of a hermitian time operator canonically conjugate to the Hamiltonian. This problem is overcome by enlarging the Hilbert space in such a way as to have either an unbound spectrum or a doubly degenerate positive spectrum. In the enlarged space, the eigenvalue spectrum θ of such an operator ranges from minus to plus infinity and constitutes the conjugate variable of the energy E. On the other hand, the evolution parameter t of the dynamical equations is related to the expectation value of the time operator. Both extensions yield the usual dynamics for state vectors restricted to the physical subspace. Vectors in the complement subspaces describe either negative energy wave packets with forward evolution or positive energy wave packets with backwards evolution. The time energy uncertainty relation is discussed.     

Phase transition to anticlinic texture in free-standing smectic c films

Experimental data on the optical reflectance of free-standing smectic C films were analyzed within the framework of a phenomenological Landau approach. At a certain temperature T _0N (determined from experimental data), which exceeds the known temperature T _c of the volume phase transition from smectic A to smectic C state, a surface phase transition takes place whereby molecules in the surface layer become sloped relative to the normal of the smectic layers. The transition temperatures T _0N ^s,a for N-layer films possessing synclinic (symmetric) and anticlinic (antisymmetric) textures of the order parameter (tilt angle θ) were determined. A comparison of the theoretical and experimental data allowed all parameters of the model to be determined (including critical indices of the correlation length and the surface order parameter). Three possible models of the transition from the state with transverse polarization (perpendicular to the molecular tilt plane) to the state with longitudinal polarization (parallel to this plane) are analyzed. The transition takes place at low (°–°) values of the order parameter θ in the middle layer of the film.     

Polynomial fitting of DT-MRI fiber tracts allows accurate estimation of muscle architectural parameters

Fiber curvature is a functionally significant muscle structural property, but its estimation from diffusion-tensor magnetic resonance imaging fiber tracking data may be confounded by noise. The purpose of this study was to investigate the use of polynomial fitting of fiber tracts for improving the accuracy and precision of fiber curvature (κ) measurements. Simulated image data sets were created in order to provide data with known values for κ and pennation angle (θ). Simulations were designed to test the effects of increasing inherent fiber curvature (3.8, 7.9, 11.8 and 15.3 m(-1)), signal-to-noise ratio (50, 75, 100 and 150) and voxel geometry (13.8- and 27.0-mm(3) voxel volume with isotropic resolution; 13.5-mm(3) volume with an aspect ratio of 4.0) on κ and θ measurements. In the originally reconstructed tracts, θ was estimated accurately under most curvature and all imaging conditions studied; however, the estimates of κ were imprecise and inaccurate. Fitting the tracts to second-order polynomial functions provided accurate and precise estimates of κ for all conditions except very high curvature (κ=15.3 m(-1)), while preserving the accuracy of the θ estimates. Similarly, polynomial fitting of in vivo fiber tracking data reduced the κ values of fitted tracts from those of unfitted tracts and did not change the θ values. Polynomial fitting of fiber tracts allows accurate estimation of physiologically reasonable values of κ, while preserving the accuracy of θ estimation.     

Phase transitions in Edwards-Anderson model by means of information theory

A numeric method to characterize phase transitions is presented, explained and applied to a two-dimensional disordered system that can be thought of as a diluted ferromagnet or an Edwards-Anderson model near the ferromagnetic limit. A computer simulation is implemented to define a time series for order parameters; a file stores the time evolution of each parameter for different dilution concentrations and for a series of temperatures. These files are compressed and they reach a maximum size for temperatures in agreement with critical temperatures for the ferromagnetic/paramagnetic transition obtained by other methods. Site order parameter gives optimum results for this method based on data compression. Data compression procedures are invoked to give a qualitative explanation of this phenomenon. The advantages of this method are discussed by comparing results and procedures with two established methods: the crossing of Binder cumulants and the crossing of time autocorrelation functions. Other possible applications and extensions of this method are also mentioned.     

Structural,electronic, magnetic properties and critical behavior of the equiatomic quaternary Heusler alloy CoFeTiSn

In this article, we study the exchange coupling interactions of the equiatomic quaternary Heusler alloy CoFeTiSn, using the two methods: Monte Carlo simulations and the ab-initio method. In a first step, we use the ab-initio calculations to investigate the structural, the electronic and the magnetic properties of this alloy under the GGA method. The analysis of the energy dependence on the lattice parameter a (Å) of the equiatomic quaternary Heusler alloy CoFeTiSn, is discussed for different atomic configurations. The ferromagnetic configuration is found to be the more stable one, with an optimal lattice parameter value 6.00 Å. On the other hand, the electronic structure results show that the compound CoFeTiSn exhibits a half-metallic character and a spin polarization of 100% at the Fermi-level. The total magnetic moment of this alloy is found to be equal to 2.00 μ_B which follows the Slater Pauling rule. Our results support the half-metallic behavior of the studied material. In order to complete this study, we reported the dependence of the critical transition temperature as a function of the parameter α of the equiatomic quaternary Heusler alloy CoFeTiSn. We showed that the critical temperature increases almost linearly with an increase of the values of the parameter α.     

Angular distribution of the photoelectron spectrum of CO2, COS,CS2, N2O,H2O,and H2S

The photoelectron spectra of the triatomic molecules CO₂, COS, CS₂, N₂O, H₂O, and H₂S have been measured as a function of the angle θ between the direction of the incoming photon and outgoing photoelectron. The photoelectron spectra have been measured with a double-focusing electrostatic electron spectrometer to which has been attached a chamber containing a gas discharge lamp that can be freely rotated. (The photon source used was the 21.22 eV He I resonance line). From the dependence of intensity as a function of θ the angular parameter β was determined for each ionization band observed in the photoelectron spectra. A correlation was noted between the values of β and the molecular orbitals relative to the contributions of oxygen and sulfur atomic orbitals. Individual β values were also obtained for most of the vibrational bands seen in the photoelectron spectra. In most cases the vibrational structure showed little or no change in the angular parameter for a given electronic state. In certain cases, however, such as the fourth ionization band in CS₂, CO₂, and COS, rather sizeable changes in β were observed for the different vibrational bands.     

Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities

A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small.Dedicated to Ilya Prigogine on the occasion of his 70th birthday.     

Magnetic-field-induced quantum criticality in a spin-<Emphasis Type="Italic">S</Emphasis> planar ferromagnet with single-ion anisotropy

The effects of single-ion anisotropy on quantum criticality in a d-dimensional spin-S planar ferromagnet is explored by means of the two-time Green’s function method. We work at the Tyablikov decoupling level for exchange interactions and the Anderson-Callen decoupling level for single-ion anisotropy. In our analysis a longitudinal external magnetic field is used as the non-thermal control parameter and the phase diagram and the quantum critical properties are established for suitable values of the single-ion anisotropy parameter D. We find that the single-ion anisotropy has sensible effects on the structure of the phase diagram close to the quantum critical point. However, for values of the uniaxial crystal-field parameter below a positive threshold, the conventional magnetic-field-induced quantum critical scenario remains unchanged.     

临界中性Gauss-Bonnet-anti-de Sitter黑洞复杂度演化

利用Fan和Liang(Fan Z Y,Liang H Z 2019 Phys.Rev.D 100086016)研究一般高阶导数引力复杂度的方法,对临界中性Gauss-Bonnet-anti-de Sitter(Gauss-Bonnet-anti-de Sitter,AdS)黑洞的复杂度演化进行研究,并且将研究结果和一般中性Gauss-Bonnet-AdS黑洞的结果进行了比较.研究发现,二者的复杂度演化的整体规律是一致的,它们的主要区别在无量纲的临界时间上.对于五维的临界中性Gauss-Bonnet-AdS黑洞,当黑洞视界面为平面或者球面时,不同大小的黑洞的无量纲的临界时间相同,都取到了最小值.当维度超过五维时,不同大小的球对称临界中性Gauss-Bonnet-AdS黑洞的无量纲临界时间的差异明显要比一般的情况小.这些差异很可能和中性Gauss-Bonnet-AdS黑洞的临界性有关.     

Reweighting in nonequilibrium simulations

A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier reweighting schemes, the present approach does not require knowledge of the stationary probability distribution, and so is applicable out of equilibrium. The method is applied to the contact process in two and three dimensions, yielding the critical parameter and spreading exponents to unprecedented precision.