Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence（SC） and square of quantum discord（SQD）. The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Phase Relations in TiAl+Nb System

The microstructures and phases of ternary TiAl+Nb alloys containing 50-60 at.-%Al, 0-21 at.-%Nb have been studied using transmission electron microscopy (TEM) and X-ray powder diffraction. The phases present in the alloys and their distribution were found to be a sensitive function of composition. The phase relations between γ-TiAl and γ1 (a new ordered ternary intermetallic compound based on γ-TiAl) were determined. Essentially single γ phase was determined for alloys with relativety low Nb content (≤10 at.-%Nb). the γ1 phase was determined to exist in the composition range containing higher Nb contents (15-21 at.-%Nb). Between γ and γ1 phases, with intermediate Nb contents there is a transitional phase γ1 (a superstructure of γ-TiAl). As for the influence of Al concentration on the phase relations. the γ1 phase was inclined to form in the alloys with relatively high Al contents. The ordering transformation of γ, to γ1 is a continuous ordering process and the transition may be second order.

Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.

The phase relations between the first arrivals of compressional and shear waves, and their signification to full wave logging

This paper describes the three phenomena observed in full wave experiments： 1. the amplitudes （absolute value） of the first compressional and shear arrivals have the same variation rules; 2. the phases of the first compressional and shear arrivals are always opposite to each other; and 3. the amplitude variation periods of the first compressional and shear arrivals are 2π. A full analysis and interpretation points out that these phenomena should appear under the full wave logging condition. Hence,the basis of using phase diffrences to extract useful information from the full wave is found.

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

The current–phase relations of a ring-trapped Bose–Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current–phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current–phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current–phase relation is given by investigating the behavior of soliton solution.

Ni-Ga BINARY PHASE RELATIONS AT 700℃

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A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.

Phase Relations in Si-Al-Y-O-C Systems

The present work investigated the phase relations in SiC-Al2O3-Y2O3-SiO2 (Si-Al-Y-O-C) system. As a continuation of our previous works, the purpose of this study is to understand the high temperature reaction behaviors of SiO2 in the system and its effect on the phase relations of the valuable system of SiC-Al2O3-Y2O3. The phase compositions of six solid-state reacted samples with different components of Y2O3:Al2O3:SiC:SiO2 were analyzed by XRD. The phase relations of the systems were determined. The subsolidus phase diagrams of ternary Al2O3-SiC-SiO2 system and the tentative phase diagram of an extended quaternary Y2O3-Al2O3-SiC-SiO2 system were presented latter involving several coexisting regions of four phases. The high temperature reaction behavior of SiO2 in the system and its effect on the phase relations of system were discussed.

A New Type of Phase Transition Based on the Clausius-Clapeyron Relation Involving a Change in Spatial Dimension

Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transitions from dimension of space, n, to dimension of space, (n - 1), and vice versa, from (n - 1) to n -dimensional space. For the former we can calculate a specific release of latent heat, a decrease in entropy, and a change in volume. For the latter, we derive an expression for the absorption of heat, the increase in entropy, and the difference in volume. Total energy is conserved in this transformation process. We apply this model to black-body radiation in the early universe and find that for a transition from n = 4 to (n - 1) = 3, there is an immense decrease in entropy accompanied by a tremendous change in volume, much like condensation. However, unlike condensation, the volume change is not three-dimensional. The volume changes from V4, a four-dimensional construct, to V3, a three-dimensional entity, which can be considered a subspace of V4. As a specific example of how the equation works, we consider a transition temperature of 3 × 1027 Kelvin, and assume, furthermore, that the latent heat release in three-dimensional space is 1.8 × 1094 Joules. We find that for this transition, the internal energy densities, the entropy densities, and the volumes assume the following values (photons only). In four-dimensional space, we obtain, u4 = 1.15×10125 J? m-4, s4 = 4.81×1097 J? m-4? K-1, and V4 = 2.14×10-31 m4. In three-dimensional space, we have u3 = 6.13×1094 J? m-3, s3 = 2.72×1067 J? m-3? K-1, and V3 = 0.267 m3. The subscripts 3 and 4 refer to three-dimensional and four-dimensional quantities, respectively. We speculate, based on the tremendous change in volume, the explosive release of latent heat, and the magnitudes of the other quantities calculated, that this type of transition might have a connection to inflation. With this work, we prove that space, in and of itself, has an inherent energy content. This is so because giving up space releases latent heat, and buying space costs latent heat, which we can quantify. This is in addition to the energy contained within that space due to radiation. We can determine the specific amount of heat exchanged in transitioning between different spatial dimensions with our generalized Clausius-Clapeyron equation.

Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity

Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

Transformations and phase relations in Nb-Ti-Si ternary system at 1373～1473K

The isothermal sections of the Nb Ti Si ternary system at 1?473?K and 1?373?K were determined by means of diffusion triple technique and electron microprobe analysis. By analyzing the diffusion layers in the diffusion couples, the titanium silicides and niobium silicides forming in this system were identified. The results show that no ternary compounds formed in the Nb Ti Si ternary system at the test temperatures. The phase transformations occurring on cooling from 1?473?K to 1?373?K were discussed.

Relative carrier-envelope phase dependence of resonant propagation of two-colour femtosecond pulses in V-type atomic medium

Using numerical solution of the full Maxwell-Bloch equations, which is obtained by the finite-difference time-domain method and the iterative predictor-orrector method, we investigate the modulation effect of relative carrierenvelope phase （hereinafter referred to as the relative phase） on resonant propagation of two-colour femtosecond ultrashort laser pulses in a V-type three-level atomic medium. It is found that the pulse splitting occurs for a smaller value of relative phase; when the value of relative phase increases to a certain value, only the variation of pulse shape is present and the pulse splitting does not occur any more; moreover, when the value of relative phase is smaller, the pulse group velocity is larger. The relative phase also has an obvious effect on population and spectral property. Different population transfers can be realized by adjusting the value of relative phase. Generally speaking, for the pulses with smaller areas their spectral strengths and frequency ranges decrease obviously with the value of relative phase increasing; for the pulses with larger areas, with value of the relative phase increasing, their spectral strengths decrease remarkably but the relative strengths of the higher frequency components increase significantly, while the spectral frequency range is not varied evidently.

A CONSTITUTIVE RELATION FOR PSEUDO-ELASTIC BEHAVIOUR IN SHAPE MEMORY ALLOYS

A constitutive relation to describe pseudo-elastic deformation in shape memory alloys is pres- ented in this paper. It is capable of describing deformation behaviour of polycrystalline materials under triaxial stress state as well as of monocrystalline materials under one-dimensional condition. Total strain rate is sup- posed to be composed of elastic strain rate and transformation strain rate. Deformation behaviour of Cu-Zn-Sn alloy and Ti-Ni alloy is simulated by use of the proposed constitutive relation. It is shown that simulated results are in a good agreement with experimental data.

STUDY OF CONSTITUTIVE RELATIONS FOR PSEUDO-ELASTICITY AND SHAPE MEMORY BEHAVIOR

Constitutive relations are given for the description of the deformation behavior of shape memory materials. The deformation is the superposition of the elastic, the thermal and the phase transformation deformation caused by the transformation from one to the other among the high temperature phase, the low temperature phase and the stress induced phase. The phase transformation is controlled by the driving force, i.e., the Gibbs energy difference between the phases.

Seismicity research in the subregions of Chinese mainland using strain accumulating and releasing model based on G-R relation

According to the deficiency of the strain accumulating and releasing curves and the previous models, the strain-accumulating rate of the strain accumulating and releasing model has been deduced based on the G-R relation and the empirical formula between energy release and earthquake magnitude, where the strain-accumulating rate is relative independent of the strain-releasing rate. Five typical areas in Chinese mainland are selected on the basis of the hypothesis on active tectonic block, and small earthquakes from 1970 are imported to calculate the annual strain-accumulating rates considering the completeness of historical seismic data. Having introduced the strain-accumulating rates into the amended model, present strain phases are got. According to the present stages in their own cycles, the future earthquake tendency of each sub-region is discussed.

Effects of relative phase on transient evolution in an open resonant ladder-type atomic system

In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion （GWI） always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion （refractive index） without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.

Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves

Free surface elevation time series of breaking water waves were measured in a laboratory flume. This was done in order to analyze changes in wave characteristics as the waves propagated from deep water to the shore. A pair of parallel- wire capacitive wave gages was used to simultaneously measure free surface elevations at different positions along the flume. One gage was kept fixed near the wave generator to provide a reference while the other was moved in steps of 0.1 m in the vicinity of the break point. Data from these two wave gages measured at the same time constitute station-to-station free surface elevation time series. Fast Fourier Transform (FFT) based cross-correlation techniques were employed to determine the time lag between each pair of the time series. The time lag was used to compute the phase shift between the reference wave gage and that at various points along the flume. Phase differences between two points spaced 0.1 m apart were used to calculate local mean wave phase velocity for a point that lies in the middle. Results show that moving from deep water to shallow water, the measured mean phase velocity decreases almost linearly from about 1.75 m/s to about 1.50 m/s at the break point. Just after the break point, wave phase velocity abruptly increases to a maximum value of 1.87 m/s observed at a position 30 cm downstream of the break point. Thereafter, the phase velocity decreases, reaching a minimum of about 1.30 m/s.

Relative phase-dependent two-electron emission dynamics with two-color circularly polarized laser fields

With the semiclassical ensemble model, we explore the relative phase-dependent nonsequential double ionization (NSDI) of Mg by counter-rotating two-color circularly polarized (TCCP) laser pulses. The yield of Mg2+ sensitively depends on the relative phase Δφ and the intensity of TCCP laser fields. At Δφ=1.5π, the yield of Mg2+ exhibits a pronounced peak in the 0.05 PW/cm2 laser field. This behavior results from the increase of the initial transverse velocity compensating for the drift velocity with the decreasing angle by analyzing the angular distributions of the electron pairs in four relative phases. By changing the relative phases, we find that the recollision excitation with subsequent ionization and the recollision-impact ionization mechanisms can be controlled with TCCP laser fields.

Tuning Martensitic Phase Transition by Non-Magnetic Atom Vacancy in MnCoGe Alloys and Related Giant Magnetocaloric Effect

The effects of non-magnetic atom vacancy on structural, martensitic phase transitions and the corresponding magnetocMoric effect in MnCoGel-x alloys are investigated using x-ray diffraction and magnetic measurements. The introduction of non-magnetic atom vacancy leads to the decrease of the martensitic transition temperature and realizes a temperature window where magnetic and martensitic phase transitions can be tuned together. Moreover, the giant magnetocaloric effect accompanied with the coupled magnetic-structural transition is ob- tained. It is observed that the peak values of magnetic entropy change of MnCoGeo.97 are about -13.9, -35.1 and -47.4J.kg-1K-1 for △H = 2, 5, 7T, respectively.