Properties of hot and dense nuclear matter in a mixed phase

The QCD phase transition is treated within a statistical model taking into account the coexistence of interacting quark-gluon and hadron phases. Being in agreement with the recent lattice QCD data, this statistical mixed phase model predicts that the “softest point” of the equation of state, resulting in the longest-lived fireball effect, is atε _{sp ≈ 0.35}GeV/fm³. It is shown that this “softest point” is washed out at the baryon densities higher than the normal nuclear density. The approach is extended to include strangeness. Attention is drawn to the study of signatures for forming the mixed quark-hadron phase of nuclear matter in the collision energy rangeE _lab ≈ 2–10 GeV/A.     

Electronic structures of Si(1 1 1) in the 7×7↔“1×1” phase transition studied by surface second-harmonic generation

Surface second-harmonic generation (SHG) of Si(1 1 1)-7×7 shows an increase in intensity for the surface-state transition (56%) and the strain-induced E₀′ interband transition (32%) in response to the phase transition to “1×1” taking place around 1100 K. The SHG surface-state transition in “1×1” is assigned as the redshifted S₃→U₁ transition in 7×7 from the observation of no discernible changes in the resonant characteristics. From the symmetry and atomic geometry of the electronic states responsible for SHG, the intensity jump is related to the dissolution of the stacking fault in the “1×1” phase.     

Phase diagram of the system of solid solutions Pb1−X(Li½La½)X(Zr1-YTiY)O3 in the vicinity of the FE-AFE phase stability boundary. II. phase transitions and induced states

Results of the study of phase transitions in the system of solid solutions Pb_1-X(Li_½La_½)_X(Zr_1-YTi_Y)O₃ (PLLZT) at x = 0, 1 under the effect of an electric field are presented. It is shown that there are three regions of Ti-concentration on the “;composition-temperature”; phase diagram. The region of Ti-content from ～ 12 to ～ 19% is the most interesting. In this region the succession of phase transitions depends on the prehistory of the specimens: in the absence of an external electric field only the AFE-PE transition takes place, but after the action of the field, the succession of phase transitions FE-AFE-PE arises. Full “;temperature-field”; phase diagrams are constructed.     

New features of a smectic-A-crystal-B phase transition in a homologous series of liquid crystals

The components L _j of the Lorentz tensor and the polarizability density of molecules G in the smectic-A and crystalline-B phases have been determined for homologues of the series of alkyl-p-(4-alkoxybenzylideneamino-)cinnamates. The quantity L _j (G) in both phases is a linear (quadratic) function of the orientational order parameter of molecules S, which is invariant (noninvariant) with respect to the A-B transition, which is manifested in the form of jumps δL _j and δG and enhancement of the G(S) dependence. An increase in the length of terminal molecular chains and weakening of interlayer correlation of molecules are accompanied by strengthening of the A-B transition of the first order and G(S) dependences in both phases together with an increase in δL _j and δG. Change δG and dependence G(S) in the B phase are related to change in the conformation (flattening) of aromatic molecular cores.     

Overall railway noise impact in the U.K.

As part of a British Rail (BR) “Environmental and Social Impact” study in 1975, an attempt at assessing the relative noise impact of rail and road transport was made; 24 hour L_eq in dB(A) units was adopted for the noise measure, as this appeared to give good correlation with “dissatisfaction” and permitted simple estimation of levels from traffic and location data. Five train types were defined, two classes of line, three regions of population density and three standard topographies. The base L_eq value for each traffic mix, line and population region could be established from BR survey data, and the propagation from topography and population (house) densities, to give the population subjected to each L_eq. The percentage “dissatisfied” at each L_eq was then applied to arrive at the total population “dissatisfied”, which was found to be 106 000. A similar approach applied to motorways and principal “A” roads gave 4480 000 “dissatisfied”.     

Magnetic field dependence of the thermoelectric power of n - type gallium arsenide in the extreme quantum limit

The effect of the quantization of the electron energy levels in a strong transverse magnetic field H on the low-temperature thermoelectric power (TEP) S of a high-purity isotropic semiconductor ($\text{n}$ - type gallium arsenide GaAs) is investigated theoretically. The “electron-diffusion” (S_e) and “phonon-drag” (S_p) components of S( = S_e + S_p) are calculated in the extreme quantum limit, when all the electrons in the conduction band are concentrated in the lowest Landau level. The transition to nondegeneracy, which takes place when the bottom of the lowest Landau level is driven through the Fermi level, has a large effect on the variations of S_e and S_p with magnetic field. The results are illustrated with numerical calculations for $\text{n}$ - type GaAs at 4.2 K with 1.2 × 10¹⁶ cm^-3 electrons.     

(Non)-Abelian gauge field theories of the Fermi gas. Neutron-quark stars

It is indicated that the ground state of Fermi systems with (non)-Abelian gauge interactions has a well defined quantum theory devoid of infrared divergences and mass singularities. This is exploited to develop a systematic quantum theory of the quark gas. The equation of state of the quark gas is evaluated up to second order in the Gell-Mann-Low charge α_S(μ). The analysis based on neutron matter models suggests that the matter in the neutron stars can be in the quark phase provided the color interaction is “moderately” strong i.e. α_S (3 GeV) ? 0.3.     

Application of epidemic models to phase transitions

The Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) models describe the spread of epidemics in a society. In the typical case, the ratio of the susceptible individuals fall from a value S ₀ close to 1 to a final value S_f , while the ratio of recovered individuals rise from 0 to R_f?=?1???S_f . The sharp passage from the level zero to the level R_f allows also the modeling of phase transitions by the number of “recovered” individuals R(t) of the SIR or SEIR model. In this article, we model the sol–gel transition for polyacrylamide–sodium alginate (SA) composite with different concentrations of SA as SIR and SEIR dynamical systems by solving the corresponding differential equations numerically and we show that the phase transitions of “classical” and “percolation” types are represented, respectively, by the SEIR and SIR models.     

Theory of an Fm3m→I4/m structural phase transition in an Rb2KScF6 crystal

An Rb₂KScF₆ crystal having an elpasolite structure undergoes a sequence of Fm3m→I4/m→P12₁/n1 structural phase transitions where the transition to the tetragonal phase is associated with “rotation” of the ScF₆ octahedron. An effective Hamiltonian is constructed to describe the Fm3m→I4/m transition using the approximation of a local mode for which we selected a “soft mode” whose eigenvector corresponds to the rotation of the octahedron. The effective Hamiltonian also includes the relationship between the local mode and the homogeneous elastic strains. The parameters of the effective Hamiltonian were determined using the generalized Gordon-Kim model of an ionic crystal which allows for the deformability and polarizability of the ions. The thermodynamic properties of a system with this model Hamiltonian were investigated using the Monte Carlo method. The calculated phase transition temperature of 250 K is almost the same as the experimental value (252 K). The tetragonal phase remains stable as far as T=0 K and a second transition (to the monoclinic phase) cannot be obtained using this effective Hamiltonian. This suggests that if the transition to the tetragonal phase is mainly associated with “rotations” of the octahedrons, in order to describe the phase transition to the monoclinic phase the effective Hamiltonian must allow for additional degrees of freedom mainly associated with the motion of rubidium ions.     

TDPAC measurements in pure and Fe-doped In 2 O 3

We try to envision that there might be a dark-matter world and neutrinos, especially the right-handed ones, might be coupled directly with dark-matter particles in the dark-matter world. The candidate model would be the extended Standard Model based on SU _c (3) × SU _L (2) × U(1) × SU _f (3) × SU _R (2), with the search of the detailed version through the aid of the two working rules, “Dirac similarity principle” and “minimum Higgs hypothesis”.     

Etude comparative des structures des alumines β stoechiometrique et non stoechiometrique: Transition de phase dans l'alumine β stoechiometrique (II)

The usual preparation methods of β alumina lead to a non stoichiometric compound $\text{(β“N.S.”)}$ of formula 11Al₂O₃?(1 + x) B₂O with x ≈-0.3; a metastable phase with a composition close to stoichiometry $\text{(β“S”}\text{and}\text{x ? 0)}$ can however also be obtained. X-Ray diffuse scattering studies of this stoichiometric form of silver β alumina reveals a sharp order—disorder phase transition at about 307 K. The low temperature ordered state of the silver ions is found to correspond to a 3D hexagonal superstructure with the lattice constants $\text{a}\text{3}\text{, a}\text{3}\text{, c}$. Above the transition temperature 3D short range order is observed up to about 315 K, where a cross over occurs towards a higher temperature 2D short range state, similar to that previously observed at low temperature in $\text{β}{}_{\mathrm{<mtext>Ag</mtext>}}\text{“N.S.”}$. Above 500 K the conducting silver ions are found to be in a 2D quasi liquid state. A similar type of order—disorder phase transition seems to occur in stoichiometric sodium β alumina at lower temperature. It is concluded that the very particular behaviour namely the absence of phase transition in the usual forms of β alumina is a direct consequence of non stoichiometry.     

Magnetic states of the surface and bulk of ferrites near a phase transition at the Curie temperature

Investigations of the magnetic state of a surface layer ~200 nm thick and of the bulk in macroscopic ferrite crystals of the type Ba-M (BaFe₁₂O₁₉) are performed in the phase transition region around the Curie temperature (T _c). The method of simultaneous gamma, x-ray, and electron Mössbauer spectroscopy, which made it possible to compare directly the phase states of the surface and bulk of the sample, is used for the measurements. It is observed experimentally that in BaFe₁₂O₁₉ the transition of a surface layer ~200 nm thick to the paramagnetic state occurs at temperatures below T _c. It is established that the transition temperature T _c(L) of a thin layer localized at depth L from the surface of the crystal increases with distance from the surface and reaches the value T _c at the lower boundary of the “critical” surface layer. Therefore, near T _c a nonuniform state in which the crystal is magnetically ordered in the bulk but disordered at the surface is observed. A phase diagram of the states of the surface and of the bulk of macroscopic magnets near the Curie (or Néel) point is proposed on the basis of all the experimental results obtained in the present work as well as previously published results.     

Thermal phase transition of RbMnFe(CN)6 observed by X-ray emission and absorption spectroscopy

The thermal phase transition of RbMnFe(CN)₆ has been observed by Mn and Fe 3p-1s X-ray emission spectroscopy (XES) and 1s X-ray absorption spectroscopy (XAS). The thermal variations of the spin states and the valences of Mn and Fe were determined to be Mn²⁺(S=5/2)-NC-Fe³⁺(S=1/2) for the high-temperature (HT) phase and Mn³⁺(S=2)-NC-Fe²⁺(S=0) for the low-temperature (LT) phase. These transitions are thus caused by charge transfer between Mn and Fe. The temperature dependences of Mn and Fe 3p-1s XES and 1s XAS were observed as the composition of the spectra of the HT and LT phases. The ratios of the HT component in each spectrum show good agreement with the thermal transition curves observed with magnetic susceptibility measurements.     

The Condensation Phase Transition in Random Graph Coloring

Based on a non-rigorous formalism called the “cavity method”, physicists have put forward intriguing predictions on phase transitions in diluted mean-field models, in which the geometry of interactions is induced by a sparse random graph or hypergraph. One example of such a model is the graph coloring problem on the Erd?s–Renyi random graph G(n, d/n), which can be viewed as the zero temperature case of the Potts antiferromagnet. The cavity method predicts that in addition to the k-colorability phase transition studied intensively in combinatorics, there exists a second phase transition called the condensation phase transition (Krzakala et al. in Proc Natl Acad Sci 104:10318–10323, 2007). In fact, there is a conjecture as to the precise location of this phase transition in terms of a certain distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k₀.     

The adsorption of PH3 on the Si(111)-(7 × 7) surface: an example of autocatalytic dissociative chemisorption

The dissociative chemisorption of phosphine, PH₃, on the Si(111)-(7 × 7) surface has been examined employing supersonic molecular beam techniques. The initial probability of reaction, S_R,0, has been found to be sensitive to substrate temperature, T_s, where S_R,0 increases sharply by approximately a factor of 4–5 as T_s is increased above 800°C, which corresponds well with the (7 × 7) ↔ “(1 × 1)” phase transition. The reaction probability, S_R, measured as a function of dose for PH₃ reacting on Si(111)-(7 × 7) at T_s < 800°C, exhibits a dramatic increase as the surface is exposed to the PH₃ molecular beam. This unique autocatalytic behavior is consistent with a mechanism in which submonolayer coverages of P(a) are capable of lifting the (7 × 7) reconstruction thus giving rise to a more reactive “(1 × 1)-like” phase. The reaction probability of Si₂H₆ on Si(111)-(7 × 7) is also observed to pass through a maximum with increasing P(a) coverages, and can be explained by considering similar changes in surface structure and reactivity.     

High-resolution X-ray emission Lα1 and Lβ2 Spectra of Hf, Ta, W, Re, and Os

The shape and relative intensities S _α=I(α_1s )/I(α_1s ), S _β=I(β_1s )/I(β₂) of the short-wavelength X-ray Lα₁ and Lβ₂ satellites arising from the radiative decay of the states corresponding to L ₃ M _4,5 configurations were investigated experimentally for Hf, Ta, W, Re, and Os. It was established that, in the case of W, the values S _α=2.5%, S _β=4.2% are five to seven times larger than those for Hf and Ta, and by (30–60)% smaller than those for Re and Os. On the basis of the obtained values of S _α,S _β, as well as the observed two-component structure of the Lα₁ and Lβ₂ satellites, it is concluded that the Coster-Kronig L ₁-L ₃ M ₅ transitions (CK) are allowed by the energy conservation law even for tungsten, and, starting with this element, they represent a major channel of generation of the states of LL ₃ M ₅ configuration. Possible features of such a process for the W atom are discussed in comparison with those for Re and Os.     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

Reunion Probability of N Vicious Walkers: Typical and Large Fluctuations for Large N

We consider three different models of N non-intersecting Brownian motions on a line segment [0,L] with absorbing (model A), periodic (model B) and reflecting (model C) boundary conditions. In these three cases we study a properly normalized reunion probability, which, in model A, can also be interpreted as the maximal height of N non-intersecting Brownian excursions (called “watermelons” with a wall) on the unit time interval. We provide a detailed derivation of the exact formula for these reunion probabilities for finite N using a Fermionic path integral technique. We then analyze the asymptotic behavior of this reunion probability for large N using two complementary techniques: (i) a saddle point analysis of the underlying Coulomb gas and (ii) orthogonal polynomial method. These two methods are complementary in the sense that they work in two different regimes, respectively for $L\ll O(\sqrt{N})$ and $L\geq O(\sqrt{N})$ . A striking feature of the large N limit of the reunion probability in the three models is that it exhibits a third-order phase transition when the system size L crosses a critical value $L=L_{c}(N)\sim\sqrt{N}$ . This transition is akin to the Douglas-Kazakov transition in two-dimensional continuum Yang-Mills theory. While the central part of the reunion probability, for L～L _c (N), is described in terms of the Tracy-Widom distributions (associated to GOE and GUE depending on the model), the emphasis of the present study is on the large deviations of these reunion probabilities, both in the right [L?L _c (N)] and the left [L?L _c (N)] tails. In particular, for model B, we find that the matching between the different regimes corresponding to typical L～L _c (N) and atypical fluctuations in the right tail L?L _c (N) is rather unconventional, compared to the usual behavior found for the distribution of the largest eigenvalue of GUE random matrices. This paper is an extended version of (Schehr et al. in Phys. Rev. Lett. 101:150601, 2008) and (Forrester et al. in Nucl. Phys. B 844:500–526, 2011).     

Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation 〈S ₀ S _r 〉 decreases asymptotically asr ^?1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this “superfrustration” on the free energy and on the ground state properties is also discussed.     

On the physics of λφ4 in aℝ2×S 1 space

The physics of λφ⁴ quantum field theory in a space with a closed dimension (?²×S ¹) is studied on the basis of a varitional approach, which supports the existence of two interacting phases of the minkowskian λφ⁴ on nonperturbative grounds. As the lengthL of the closed dimension decreases (1/L becomes the relevant scale), triviality restoration is encountered in the “precarious” phase, as well as symmetry restoration in the “autonomous” phase. The close relation to the finite temperature formalism allows to uncover a temperature symmetry restoration of theT=0 spontaneously broken phase.