Geometric Phase in a Time-Dependent System with Laguerre Polynomial State

By using of the invariant theory, we have studied the geometric phase in a time-dependent system with Laguerre polynomial state, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Phase transitions in a hydrogen-rich compound：tetramethylsilane

High-pressure behavior of tetramethylsilane is investigated by synchrotron powder X-ray diffraction and Raman scattering at pressures up to 30 GPa and room temperature. Our results reveal the analogous phase transitions, though slight hysteresis for the certain phases. A new phase is found to appear at 4.2 GPa due to the disappeared Raman mode. These findings offer the possibility to understand the evolution of the H-H bonding with pressure in such hydrogen-rich compounds.     

Phase transitions in the Falicov–Kimball model away from half-filling

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ _c , changes to a different ordered phase and at the temperature, that can be several times higher than τ _c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.     

Geometric Phase in a Time-Dependent System with Higgs Algebra Structure

By using of the invariant theory, we have studied the geometric phase in a time-dependent system with Higgs algebra structure, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution. The disappearing condition of the geometric phase is given.     

Phase transitions in self-dual generalizations of the Baxter–Wu model

We study two types of generalized Baxter–Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down-triangles, and the second generalization is to a q-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter–Wu model, the phase transitions appear to be discontinuous.     

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U _ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T _c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U _ff .     

Phase transitions in shape memory alloys: A non-isothermal Ginzburg–Landau model

We propose a model to describe non-isothermal transitions from the austenite to the martensite phase occurring in shape memory materials. The phenomenon is set in the context of the Ginzburg–Landau theory of phase transitions, postulating a free energy depending on the temperature, the stress and the order parameter. In the one-dimensional case, when only two martensitic variants are involved and stress and deformation have a fixed direction, our choice of free energy allows us to deduce a phase diagram describing the main features of a typical SMA. The Ginzburg–Landau equation ruling the evolution of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive equation relating stress, strain and order parameter. The consistency of the model with the second law of Thermodynamics in the form of the Clausius–Duhem inequality is proved. Finally a possible generalization to a three-dimensional model is proposed, by introducing a tensor-valued order parameter.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

Phase transitions in low-dimensional ψ 4 systems

The phase transition in a planar array of weakly coupled Ginzburg–Landau chains with real order parameter is studied, using an original variant of the two-level approximation. The results are extended to the quantum phase transition in a chain of quantum double well oscillators, coupled with an elastic interaction, using the matrix transfer method.     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

Renormalizability of a quark–gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark–gluon model with soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.     

Phase diagram of a simple model of Eu p Sr1−p S

A random site Ising model on the checkerboard square lattice with first neighbor interactionsJ in all first neighbor bonds and second neighbor interactionsJ in red squares is considered as a simple model of the dilute spin glass of Eu _p Sr_1–p S. The phase boundary between the paramagnetic and ferromagnetic phases, and that between the paramagnetic and spin glass phases are calculated. The obtained phase diagram is qualitatively similar to the experimental result by Maletta and Convert.     

Confront holographic QCD with Regge trajectories of vectors and axial-vectors

By matching the predictions of the Dp–Dq soft-wall model in type II superstring theory with the spectra of vector and axial-vector mesons, we show the dependence of the Regge trajectories parameters on the metric parameters of the model. From the experimental results of Regge parameters for vector mesons, it is found that the D3 background brane with both q=5 and q=7 probe brane and D4 background brane with q=4 probe brane are close to the realistic holographic QCD. We also discuss how to realize chiral symmetry breaking in the vacuum and asymptotic chiral symmetry restoration in high excitation states. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking, and a small negative z ⁴ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.     

The 4s24p3−4s4p4 transitions in Br III

The spectrum of bromine was photographed in the 500–1500 Å region on a 3-m normal incidence spectrograph using a triggered spark source. The new observations have led to the rejection of two out of the five levels of the ground state configuration and four out of seven levels of the 4s4p⁴ configuration. Twenty-four lines have been classified in this spectrum.     

Quantum Phase Transition Like Phenomenon in a Two-Qubit Yang-Baxter System

The quantum phase transition for the “q-deformed” Yang-baxter Hamiltonian has been discussed. The calculation shows when the deformed parameter q approaches 1, there exists a quantum critical point for spectral parameter θ. In this Yang-Baxter system, quantum entanglement and the geometric phase can characterize quantum phase transition.     

Phase transitions in h-thiourea under electric‐field

Abstract

Dielectric constant, spontaneous polarization and pyroelectric response measurements were performed on thin samples (e < 100 μm) of H-thiourea as a function of temperature and applied electric field. Along with previous data obtained by optical birefringence, X-ray and neutron diffraction techniques, the results put in evidence three features in the modulated region between the ferroelectric state and the paraelectric one. The tricritical point is determined for E_tr ? 2075 V/mm and T_tr ? 192 K.     

Inverse transitions in the Ghatak–Sherrington model with bimodal random fields

The present work studies the Ghatak–Sherrington (GS) model in the presence of a longitudinal magnetic random field (RF) _hi$h_i$ following a bimodal distribution. The model considers a random bond interaction _Ji,j$J_{i,j}$ which follows a Gaussian distribution with mean _J0/N$J_0/N$ and variance J²/N$J^2/N$. This allows us to introduce the bond disorder strength parameter J/_J0$J/J_0$ to probe the combined effects of disorder coming from the random bond and the discrete RF over unusual phase transitions known as inverse transitions (ITs). The results within a mean field approximation indicate that these two types of disorder have completely distinct roles for the ITs. They indicate that bond disorder creates the necessary conditions for the presence of inverse freezing, or even inverse melting, depending on the bond disorder strength, while the RF tends to enforce mechanisms that destroy the ITs.     

Nucleon electromagnetic form factors in a quark–gluon core model

We study the nucleon electromagnetic form factors in a quark–gluon core model framework, which can be viewed as an extension of the Isgur–Karl model of baryons. Using this picture we derive nucleon electromagnetic dipole form factors at low Q ² and the deviation from the dipole form at high Q ², that are consistent with the existing experimental data.