Quantum potts gauge-matter systems at finite temperature

A systematic large-N expansion for gauge-matter Potts systems at finite temperature is presented. This allows us to explore the interior of the phase diagrams, taking into account all terms in the hamiltonian. Calculations are carried out in 3 + 1 and 2 + 1 dimensions and the expansion parameter is $\text{1/N}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$, where d is the number of space dimensions. For singly charged matter the Higgs-confinement phase is analytically connected to a high-temperature plasma phase. When the matter fields are multiply charged, both Higgs and confinement phases undergo a finite-temperature phase transition. The free charge phase may or may not undergo a phase transition depending on the number of space-time dimensions. Implications for other models, both abelian and non-abelian are discussed. We also comment on applications to quantum spin systems.     

Study by brillouin scattering of the C33 constant of thiourea submitted to an electric field

The C₃₃ constant is discontinuous for the lock-in transition at T₁ = 169 K. The variation ΔT₁ of the temperature of transition is a linear function of the applied electric field E and we find $\text{d}\text{T}{}_1\text{d}\text{E}\text{=0.82 deg.cm kV}{}^{\mathrm{?1}}$.Above a mean field E = 10 kV cm^?1 the transition observed for a first heating spreads on several degrees because damages appear in the incommensurate phase and the electric field becomes inhomogeneous.The results obtained at low fields are in very good accordance with the value of $\text{d}\text{T}{}_1\text{d}\text{E}$ calculated from the Clapeyron formula.Taking into account of the incommensurability of the phase above T₁, it can be shown that

$\text{dT}{}_1\text{dE}\text{=}\text{C}\text{2πP}{}_{\mathrm{o}}\text{3}\text{3}\text{?}\text{2}$

The knowledge of the spontaneous polarisation P₀ gives for the Curie constant C = 2.1 × 10³ K in qualitative agreement with the value deduced from measurements of the dielectric constant in the ferroelectric direction.     

A mechanism for quark confinement

Euclidean field configurations carrying half integral topological charge, merons, can, unlike ordinary instantons, confine quarks at moderate coupling g. Logarithmic interactions between merons prevent isolated ones from existing for small g. However, in four dimensional QCD a crude calculation indicates a phase transition to a quark confining plasma at an effective coupling $\text{g}{}^2\text{4π}{}^2\text{≈}\text{1}\text{4}$.     

Hydrodynamics of an n-component phonon system

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations $\text{O}$(n). For n ≥ 2 a continuous symmetry is broken for T<T_c, where T_c is the transition temperature. We derive the hydrodynamic equations for the generators of this group, the $\text{1}\text{2}\text{n (n ? 1)}$ angular-momentum variables. Besides the usual hydrodynamics of a phonon system, there are $\text{1}\text{2}\text{n (n ? 1)}$ additional independent diffusive modes for T > T_c. In the ordered phase we find 2 (n ? 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T < T_c require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent $\text{z =}\text{1}\text{2}\text{d}$. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent $\text{z}\text{?}\text{= φ/2ν}$, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.     

Elastic properties of one dimensional compounds

We have investigated the elastic properties of several one-dimensional compounds using a vibrating reed technique. A model calculation shows that a vanishing Young's modulus will occur for elastic one-dimensionality. TTF-TCNQ exhibits a small modulus which decreases with increasing temperature extrapolating to zero at T ≈ 500–700K. The uniaxial stress dependence of the metal-insulator transition temperature is calculated to be $\text{¦}\text{d}\text{T}{}_{\mathrm{c}}\text{/}\text{d}\text{σ¦ ～ (10 ± 5)}\text{K/bar}$. KCP shows a much higher modulus and a phase transformation at ～ 35 K.     

On the arithmetic of phase locking: Coupled neurons as a lattice on R2

Using methods from the geometry of numbers, we derive an explicit, global solution for the phase-locking behavior of a simple integrate-and-fire model of coupled neurons. The solution gives the ratios of phase locking (rotation numbers) attained as functions of the parameters of natural frequency and bidirectional coupling. The ordering of the ratios is related to Farey-type series and to simple continued fractions. A transition between two ratios, say $\text{a}\text{b}$ to $\text{c}\text{d}$, is possible if, and only if, ad?bc=±1. Empirically, similar ordering is evident in published data from various neuron analogues. We compare and contrast the present results with those from models based on Caianiello's equation and on more general mappings on the torus.     

On the theory of collective motion in nuclei. I. Classical theory

From the assumption that the collective Hamiltonian be invariant under the orthogonal group O(A ? 1, $\text{R}$) it is concluded that classical collective dynamics can be formulated on a symplectic manifold. This manifold is shown to be a coset space of the symplectic group $\text{L}$h(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the dequantization of closed-shell collective dynamics and is described in terms of six complex s- and d-quasiparticles. In the limit A ? 1 it is shown that a transformation leads to interacting s- and d-bosons with the symmetry group $\text{u}$ (6) in the collective phase space.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

Model independent analysis of the structure in pp scattering

An empirical study of the structure at $\text{t≈?1.1}\text{in}\text{d}\text{σ}\text{d}\text{t}$ (pp → pp), in terms of two exponential amplitudes plus interference, gives the following results. The steeper exponential shows standard Regge shrinkage, corresponding to a trajectory α ≈1+0.3 t. The other exponential slope stays constant; the overall energy dependence of this amplitude is approximately s^?1 for 10–30 GeV, leveling off possibly to a constant at ISR. The relative phase is about 2.1 rad at the lower momenta, becoming 2.5 at ISR. These results suggest a simple physical picture, in which a relatively unstructured shrinking Regge amplitude interferes with an even-signature non-Regge background. This interpretation predicts that the interference minimum in $\text{d}\text{σ}\text{d}\text{t}$ is deepest at an intermediate momentum near 175 GeV where measurements will soon be made at NAL.     

N2 Monolayers on graphite: Specific heat and vapor pressure measurements — thermodynamics of size effects and steric factors

Calorimetric and vapor pressure measurements of N₂ monolayers on Grafoil have been made in the regions recently explored by neutron scattering. The phase transition at T = 48 K involves approximately symmetric specific heat anomalies of 2&#x0303; K FWHM, and the peak position shifts about 1 K from $\text{1}\text{3}$ to $\text{2}\text{3}$ of one monolayer. In spite of the peak width and temperature shift the transition is intrinsically first order, due to melting of the √3 registered structure into a disordered phase in the presence of 2D vapor. The shift and broadening are shown to be a consequence of size effects primarily due to large edge-to-area ratios of the ordered phase domains. A formula relating the domain size to the shift in transition temperature gives r = 50' A for the mean radius of the domains. At film densities above $\text{2}\text{3}$ monolayer the peak broadens and shifts to a higher temperature until a critical region is reached near T= 85 K. The combined heat capacity and vapor pressure data indicate that there is no two phase region at coverages near monolayer completion and that the transition near T = 85 K is higher than first order. Effects of molecular orientation and surface-normal vibration appear in certain regions of temperature and density. A phase diagram is constructed which is consistent with both calorimetric and neutron scattering results.     

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.     

Photoelectron diffraction effects in XPS angular distributions from GaAs(110) and Ge(110) single crystals

Angular distribution measurements of XPS intensities have been made for various spectral lines from GaAs(110) and Ge(110) single-crystal surfaces. Observed angular distribution curves (ADC's) showed steep intensity variations and sharp peaks due to X-ray photoelectron diffraction (XPED) phenomena. The effects of the type of transition process (photoelectron or Auger), electron kinetic energy and crystal structure on the XPED patterns were examined. Considerably different ADC patterns were observed for high-energy photoelectrons and Auger electrons and for low-energy photoelectrons. ADC's for Ga 3d, As 3d and Ge 3d showed almost the same patterns for scans of the type [110] → [100] → [1$\text{1}$0], but they showed substantially different patterns for [110] → [11$\text{1}$] → [00$\text{1}$] scans. These features correspond well with the structural characteristics of GaAs and Ge crystals. A discussion of the applicability of XPS angular distribution measurements to the geometric analysis of crystal surfaces is presented.     

A neutron scattering study on the incommensurate-commensurate ϵ → ζ phase transition of the perovskite-type layer compound PAMC: A lock-in phase transition with a flipping modulation vector

An elastic neutron scattering experiment between 80 and 120 K has further elucidated the ?- and ζ-phases of PAMC and the ? → ζ phase transition. The temperature dependence of the incommensurate modulation vector $\text{q}\text{= (}\text{1}\text{3}\text{+ δ)}\text{b}{}^1$ of the ?-phase has been determined near the phase transition. At the phase transition the modulation vector locks-in at δ = 0, but below the transition it flips into the $\text{(}\text{b}{}^1\text{?}\text{c}{}^1\text{)}$ direction. The symmetry of ζ-PAMC is monoclinic and the A-centering of the normal δ-phase is partially recovered. Multiple and reversible twinning occurs. Pronounced discontinuities appear at the phase transition in the lattice parameters and reflection intensities.     

Electron drag of dislocations in thin metal plates

The electron force dragging dislocations in a thin metal plate of thickness d has been calculated and the dependence of the drag force F on the parameter $\text{d}\text{l}$ (l is the electron free path length) determined for the cases $\text{d}\text{l ? 1}$ and $\text{d}\text{l ? 1}$. With d ? l, the drag force depends upon the nature of electron scattering on the plate surface. The drag force dependence on the sample size has also been considered for a d.c. magnetic field H parallel to the plate faces. In the case of diffuse scattering the second derivative of F(H) reveals a square root singularity at the value of the magnetic field where the electron orbit diameter is equal to the plate thickness.     

Dynamics of FREI with/without cool flame interaction

The interactions between cool flames and flames with repetitive extinction and ignition (FREI) of stoichiometric n-heptane/air mixture were studied using a micro flow reactor with a controlled temperature profile from 373 to 1300 K. Two different flame dynamics with and without cool flames were observed in reactors with inner diameters $d_{\text{inner}}$ of 1 and 2 mm. Cool flames and FREI are spatially separated at $d_{\text{inner}}=$ 1 mm, whereas interactions between cool flames and FREI are observed at $d_{\text{inner}}=$ 2 mm. At $d_{\text{inner}}=$ 1 mm, the brightness intensity from cool flames depends on the inlet velocity ($u_{\text{inlet}}$). Approximately above $u_{\text{inlet}}=$ 10 cm/s, the brightness intensity from cool flames decreases with increasing inlet velocity, despite a large amount of mixture input. This is because before low temperature ignition occurs under higher inlet velocity conditions, the mixture archives temperature where negative temperature coefficient is dominant. Reaction front propagation speed of FREI decreases monotonically due to heat loss because the extinction points of FREI are located in higher temperatures than the cool flame region. At $d_{\text{inner}}=$ 2 mm, the acceleration of the reaction front in the cool flame region is confirmed experimentally, as predicted in our previous two-dimensional numerical simulations. Additionally, the instantaneous reaction front speed after autoignition is analyzed at $d_{\text{inner}}=$ 1 mm. The instantaneous reaction front speed decreases as the time from extinction to ignition $t_{\text{ex}\_\text{ig}}$ becomes longer because a moderate mixing zone of reactants and products is formed.     

Some implications of the observed decay ψ → f + γ

Describing the ψ → f+γ decay via an intermediate one-photon state avoids difficulties encountered in strong OZI- violating transitions. The ψ → γ →f+γ transition is enhanced an order of magnitude because amplitudes for the u$\text{u}$ and d$\text{d}$ components of the f are proportional to squares of quark charges and add constructively. A rough dynamical estimate agrees with the experimental decay rate. Branching ratios for f+γ,A₂+γ and f′ + γ decays are shown to be very different for electromagnetic and strong transitions and can test models. Tests of the Han-Nambu model and contributions from the weak neutral current are discussed.     

Rising dσdt probes pp diffraction mechanisms

The s-dependence of $\text{d}\text{σ}\text{d}\text{t}$ at fixed t reveals important features of the underlying mechanism. In particular, it can clarify the origin of the structure near t = ?1.2 in high-energy pp elastic scattering. If this structure comes from destructive interference between two terms of different energy dependence (e.g. between single and double pomeron exchanges), the plot of ln $\text{d}\text{σ}\text{d}\text{t}$versus ln s in the interference region will show an inflexion or dip; $\text{d}\text{σ}\text{d}\text{t}$ may even rise with increasing s through a limited interval. Other mechanisms have no such feature. We give illustrations and stress the interest of measurements in the NAL and ISR momentum range.     

Jet analysis in lepton-hadron scattering from QCD

For deep inelastic lepton-hadron scattering we deduce from QCD perturbation theory the cross sections $\text{d}\text{σ}\text{d}\text{T}$ and $\text{d}\text{σ}\text{d}\text{S}$ in terms of the collective jet variables thrust T and spherocity S. We find that the shape of these cross sections depends mainly on the total hadronic energy W. While present data are consistent with the cross sections calculated they do not yet prove or disprove the presence of three-jet contributions. We predict that these contributions will be clearly visible for W ? 12 to 15 GeV.