两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Entanglement and quantum phase transition in the Heisenberg-Ising model

We use the quantum renormalization-group(QRG) method to study the entanglement and quantum phase transition(QPT) in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.(N.Y.) 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.     

Finite-size behavior near the critical point of QCD phase-transition

It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.     

Initial data for black holes and black strings in 5D

We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5D spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology for different parameters. The topology varies from S3 to S2 x S1. This phase transition is discontinuous--the topology of the horizon changes abruptly. We explore the behavior around the critical point and present a possible phase diagram.     

Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.     

Ferromagnetic transition in one-dimensional itinerant electron systems

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.     

Critical-point symmetries in boson-fermion systems: the case of shape transitions in odd nuclei in a multiorbit model

We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model [E(5/12)] to describe odd nuclei at the critical point in the transition from the spherical to gamma-unstable behavior. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single-particle orbitals j=1/2, 3/2, 5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the interacting boson-fermion model, with a boson-fermion Hamiltonian that describes the same physical situation.     

磁阱中超冷玻色气体临界行为的观测

超冷玻色气体为研究量子临界现象提供了一个非常干净的实验系统. 弱相互作用下的三维玻色气体的临界行为与⁴He发生超流相变时的临界行为类似, 都属于三维XY型普适类. 从正常流体到超流的量子相变过程中, 系统会经历一个从无序相到长程有序相的转变; 而在相变点附近, 系统参量会表现出一些奇点的特征. 本文从实验上观测到了静磁阱中超冷⁸⁷Rb玻色气体在凝聚体相变温度T_c附近的临界行为. 原子气体从静磁阱中释放, 经过30 ms的自由飞行后, 通过吸收成像得到原子气体的动量分布; 然后从中扣除热原子气体的动量分布, 提取出空间上处于临界区域内的原子气体动量分布, 并对不同温度下的动量分布半高宽进行统计. 统计结果显示: 在非常接近相变温度T_c时, 动量分布的半高宽突然减小, 表现出十分明显的奇点行为.     

Phase transition of charged black holes in massive gravity through new methods

Motivated by providing preliminary steps to understand the conception of quantum gravity, in this paper, we study the phase structure of a semiclassical gravitational system. We investigate the stability conditions and phase transition of charged black holes in massive gravity via canonical ensemble and geometrical thermodynamic approaches. We point out the effects of massive parameter on stability conditions of these black holes and show how massive coefficients affect the phase transition points of these black holes. We also study the effects of boundary topology on thermodynamical behavior of the system. In addition, we give some arguments regarding the role of higher dimensions and highlight the effect of the electric charge in thermodynamical behavior. Then, we extend our study to geometrical thermodynamic approach and show that it can be a successful method for studying the black hole phase transition. At last, by employing the relation between thermodynamical pressure and cosmological constant, critical behavior of the system and the effects of different parameters on critical values are investigated.     

The two-dimensional liquid-vapor coexistence line of methane adsorbed on graphite

We measured the specific heat of two-dimensional films of CH₄ adsorbed on graphite for several coverages and we observed broad peaks at the liquid-vapor transition. The critical temperature is estimated to be 70 ± 1 K, somewhat lower than reported in previous measurements. At intermediate coverages the liquid-vapor boundary is very flat indicating that it could be described by a 2D Ising model. We measured also for some coverages the triple temperature at 56.2 K and the commensurate-incommensurate transition at about 50 K, both in reasonable agreement with previous measurements.     

Large Deviations in the Superstable Weakly Imperfect Bose-Gas

The Superstable Weakly Imperfect Bose-Gas (Sup-WIBG) was originally proposed to solve some inconsistencies of the Bogoliubov theory based on the WIBG. The grand-canonical thermodynamics of the Sup-WIBG has been recently studied in details but only out of the point of the (first order) phase transition. The present paper closes this gap. The key technical tools are the Large Deviations (LD) formalism and in particular the analysis of the Kac distribution function. It turns out that the condensate fraction discontinuity as a function of the chemical potential (that occurs at the phase transition point) disappears if one considers it as a function of the total particle density. We prove that at this point the equilibrium state of the Sup-WIBG is a mixture of two (low- and high-density) pure phases related to two critical particle densities. Non-zero Bose-Einstein condensate starts at the smaller critical density and continuously grows (for a constant chemical potential) until the second critical density. For higher particle densities, the Bose condensate fraction as well as the chemical potential both increase monotonously.     

Quasi-two-dimensional mott transition system Ca2-xSrxRuO4

We have revealed the phase diagram of Ca2-xSrxRuO4: the quasi-two-dimensional Mott transition system that connects the Mott insulator Ca2RuO4 with the spin-triplet superconductor Sr2RuO4. Adjacent to the metal/nonmetal transition at x approximately 0.2, we found an antiferromagnetically correlated metallic region where non-Fermi-liquid behavior in resistivity is observed. Besides this, the critical enhancement of susceptibility toward the region boundary at x(c) approximately 0.5 suggests the crossover of magnetic correlation to a nearly ferromagnetic state, which evolves into the spin-triplet superconductor Sr2RuO4.     

Quantum critical behavior near a density-wave instability in an isotropic fermi liquid

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) approximately Sigma(k) to Sigma(k,omega) approximately Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.     

Phase transition in the 2D random Potts model in the large-q limit

Phase transition in the two-dimensional q-state Potts model with random ferromagnetic couplings is studied in the large-q limit by a combinatorial optimization algorithm and by approximate mappings. We conjecture that the critical behavior of the model is controlled by the isotropic version of the infinite randomness fixed point of the random transverse-field Ising spin chain and the critical exponents are exactly given by beta=(3-sqrt[5])/4, beta(s)=1/2, and nu=1. The specific heat has a logarithmic singularity, but at the transition point there are very strong sample-to-sample fluctuations. Discretized randomness results in discontinuities in the internal energy.     

Resistance noise scaling in a dilute two-dimensional hole system in GaAs

We have measured the resistance noise of a two-dimensional (2D) hole system in a high mobility GaAs quantum well, around the 2D metal-insulator transition (MIT) at zero magnetic field. The normalized noise power S(R)/R(2) increases strongly when the hole density p(s) is decreased, increases slightly with temperature (T) at the largest densities, and decreases strongly with T at low p(s). The noise scales with the resistance, S(R)/R(2) approximately R2.4, as for a second order phase transition such as a percolation transition. The p(s) dependence of the conductivity is consistent with a critical behavior for such a transition, near a density p(*) which is lower than the observed MIT critical density p(c).     

Behavior of the layer compression elastic modulus near,above, and below a smectic C–hexatic I critical point in binary mixtures

We present the first study of the layer compression modulus B carried out near, above and below the Smectic C–Hexatic I critical point in racemic mixtures of methylbutyl phenyl octylbiphenyl-carboxylate (8SI) and the octyloxy biphenyl analog (8OSI), at frequencies ranging from 0.2 Hz to 2 ×103 Hz. The behavior of B as a function of temperature shows a progressive evolution from a first order transition in 8SI to a continuous supercritical behavior in 8OSI. The latter is characterized by an increase in B, which appears above the transition, and which is followed by a leveling off when the temperature is decreased towards the transition. It is proposed that this behavior stems from the relaxation of the hexatic domains which are frozen in the frequency range studied. For the supercritical and near-critical compounds, B exhibits a small dip near the transition temperature, which is visible in the low frequency range only, indicating that the dynamics associated with the critical point is very slow. We also report measurements in the Crystal-J phase of the pure compounds, and show that 8SI behaves mechanically as a hexatic phase and 8OSI as a soft crystal phase.     

Dynamics of nearly spherical vesicles in an external flow

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.     

Diffusion and thermal diffusion of semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition

The approaching glass transition in polystyrene/toluene solutions leads to a sharp decay of both the collective diffusion coefficient D and the thermal diffusion coefficient D(T) at concentrations above 0.2 g/cm(3). The Soret coefficient S(T) = D(T)/D follows power-law scaling from semidilute to concentrated and is not influenced by the slowing down of the dynamics associated with the glass transition. Both D and D(T) are governed by the same friction coefficient. The scaling behavior of S(T) with concentration on approach of the glass transition is compared to the divergence of S(T) near a consolute critical point.     

Directed percolation and the extinction transition on a diffusive substrate

The extinction transition on a 1D heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the fluctuating environment. At the transition point the density decays like t^−0.159, as in directed percolation. However, the scaling function describing the behavior away from the transition and other critical exponents shows significant deviations from the known DP behavior. It is suggested, thus, that the off-transition behavior of the system is governed by local adaptation to favored regions.