Phase diagrams and cluster expansions for low temperature models

Low temperature phase diagrams of two-dimensional quantum field models are constructed. Let lie in an (r?1)-dimensional space of perturbations of a polynomial withr degenerate minima. Perform a scaling and assume λ«1. We constructk distinct states on \(\left( {\begin{array}{*{20}c} r \\ k \\ \end{array} } \right)\) hypersurfaces of codimensionk?1 in the space of perturbations. An expansion is used to exhibit exponential clustering of the Schwinger functions of each of these states. At the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima. We draw on ideas of Pirogov and Sinai [24] for this problem.     

Motions of vortex patches

An evolution equation describing the motion of vortrex patches is established. The existence of steady solutions of this equation is proved. These solutions arem-fold symmetric regions of constant vorticity ω₀ and are uniformly rotating with angular velocity Ω in the range $$\tilde \Omega _{m - 1}< \tilde \Omega \leqslant \tilde \Omega _m (\tilde \Omega = \Omega /\omega _0 ,m \geqslant 2)$$ where \(\tilde \Omega _m = (m - 1)/2m\) . We call this class, ofm-fold symmetric rotating regionsD, the class of them-waves of Kelvin. Any may be regarded as a simply connected region which is a stationary configuration of the Euler equations in two dimensions. If then any magnification, rotation or reflection is also in with the same angular velocity Ω ofD. The angular velocity \(\Omega _m = \tilde \Omega _m \omega _0 \) corresponds only to the circle solution, which is a trivial member of every class ,m?2. The class corresponds to the rotating ellipses of Kirchoff. Other properties of the class are established.     

g-Factors of high-spin states in93Ru and95Rh

The g-factors and half lives of three isomers in the N=49 nucleus⁹³Ru and the N=50 nucleus⁹⁵Rh were measured using the PAD method. The results are: . The g-factors are discussed within the shell model and with respect to M1 core polarization and mesonic effects.     

Feynman's path integral

Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, letC be the space of pathsq:T?? → configuration space of the system, letC be the topological dual ofC; then Feynman's integral for a particle of massm in a potentialV can be written where $$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$ and wheredw is a pseudomeasure whose Fourier transform is defined by for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.     

Nuclear quadrupolar relaxation and the dynamics of pairs of atoms in liquids

We have developed a model calculation for the electrical field gradient correlation function on a probe atom in the liquid, c_EFG(t)=20(0)V₂₀(t)>. In this model, symmetry of the liquid is introduced explicitly and the distribution function for therelative coordinate r_i(t) between the probe atom and particle i is calculated using Smoluchowski's diffusion equation with a mean force potential Φ(r)=k_BT In g(r). The results for c_EFG(t) can be characterized by two correlation times, , the shorter one being responsible for the small values of R_Q in pure liquid metals, the longer one producing the increase of R_Q in alloys. Also good agreement is found with recent results for c_efg(t) from molecular dynamics studies.     

The dielectric constant of liquid metals

The dielectric constant of a liquid metal is calculated with the temperature Green's functions technique in the frequency rangeω _P Ω?ξ ₀ andΩ ξ ₀, whereξ ₀ is the resistivity relaxation frequency, andω _P the plasma frequency. The electron scattering is described in the Born approximation using the empirical dynamical structure factor ofVan Hove and a screened electron-ion pseudopotential. At low frequencies (?Ω ?_F=Fermi energy) the result can be identified with Drude's classical formula introducing an effective number of electrons per ion. For?Ω～?_F, however, the result differs in form.     

Der Zerfall des84Rb und die Fluoreszenzausbeute von Krypton

The electron capture decay and the positron decay of⁸⁴Rb were investigated using NaJ (Tl)-detectors and a Ge (Li)-detector. Measurements of all intensities and of some informative double and triple coincidences were performed. From coincidence measurements betweenK-X-radiation and the following γ-radiation we got theK-fluorescence yield of Krypton Ω_itK=0.653 ± 0.004. Taking in consideration former measurements¹ one concludes a continuous behaviour of Ω_itK(Z) forZ=36, 37 and 38 within an uncertainty of 1%. For the branching ratios of the decay of⁸⁴Rb we obtained The half-life of⁸⁴Rb was determined to beT _1/2=(34.5 ± 0.2) d.     

g-factors of rotational states in 176Hf, 177Hf,and 180Hf

g-factors of rotational states in ¹⁷⁶Hf and ¹⁸⁰Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78 · 10¹⁰y ¹⁷⁶Lu and the 5.5 h isomer ^180mHf were used which populate the ground-state rotational bands of ¹⁷⁶Hf and ¹⁸⁰Hf. The integral rotations of γ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu → Hf)Fe₂ and HfFe₂ were observed. The following results were obtained: The hyperfine field in (Lu → Hf)Fe₂ was calibrated by observing the integral rotation of the 9/2^? first excited state of ¹⁷⁷Hf populated in the decay of 6.7d ¹⁷⁷Lu. The g-factor of this state was redetermined in an external magnetic field as Finally the g-factor of the 2 ₁ ⁺ state of ¹⁷⁶Hf was derived from the measured g(2 ₁ ⁺ ) of ¹⁸⁰Hf by use of the precisely known ratio g(2 ₁ ⁺ , ¹⁷⁶Hf)/g(2₁ ⁺, ¹⁸⁰Hf) [2] as      

On a symmetry topological classification of edge states in crystalline spin-Hall insulators with the time reversal invariance

Symmetry analysis reveals all types of singularities of the edge states in two-dimensional systems with a boundary (2D → 1D systems), which are invariant under time reversal. Symmetry reasons also provide the matching condition for material functions parameterizing the Hamiltonian at various points of the Brillouin zone. The unified parameterization of the Hamiltonian makes it possible to construct the mapping of trajectories closed in the quasimomentum k in the Brillouin zone into the SU(2) topological group. There are only two equivalence classes of Hamiltonians, which are given by the elements of the first fundamental group . The first type of surface states corresponds to a normal insulator and the second type corresponds to a topological spin-Hall insulator. Comparison with the classification based on the Pfaffian method is performed.     

A manifestation of the magnetopolaron effect in reflection and absorption of light by a three-level system in a quantum well

The absorption and reflection of light by a quantum well are investigated in the case of two closely spaced levels of electronic excitations in the well. The dependences of the dimensionless absorptance and reflectance ? on the frequency ω_l of the exciting light are calculated. The overall sequence of processes involving absorption and reemission of photons is taken into account. This is beyond the scope of the perturbation theory for the photon-electron coupling constant. It is shown that the perturbation theory is inapplicable when the reciprocal radiative lifetimes of excitations are comparable to the reciprocal nonradiative lifetimes. In this case, the nontrivial dependences and ?(ω_l) are obtained. The total reflection and the total transparency points are determined. The relationships derived are used to analyze the special case of two excitation levels that are formed in the quantum well in a strong magnetic field H normal to its plane due to the Johnson-Larsen magnetopolaron effect. The reciprocal radiative lifetimes of electron-hole pairs are calculated far from and in the vicinity of the magnetophonon resonance. It is found that these lifetimes are proportional to H in the range far from the resonance and depend strongly on the difference H-H _res in the vicinity of the resonance. The dependences of the coefficients and ? on the magnetic field H at different frequencies of the exciting light are deduced.     

Scaling for a random polymer

LetQ _n ^β be the law of then-step random walk on ?^d obtained by weighting simple random walk with a factore ^?β for every self-intersection (Domb-Joyce model of “soft polymers”). It was proved by Greven and den Hollander (1993) that ind=1 and for every β∈(0, ∞) there exist θ^*(β)∈(0,1) and such that under the lawQ _n ^β asn→∞: $$\begin{array}{l} (i) \theta ^* (\beta ) is the \lim it empirical speed of the random walk; \\ (ii) \mu _\beta ^* is the limit empirical distribution of the local times. \\ \end{array}$$ A representation was given forθ ^*(β) andµ _β ^β in terms of a largest eigenvalue problem for a certain family of ? x ? matrices. In the present paper we use this representation to prove the following scaling result as β?0: $$\begin{array}{l} (i) \beta ^{ - {\textstyle{1 \over 3}}} \theta ^* (\beta ) \to b^* ; \\ (ii) \beta ^{ - {\textstyle{1 \over 3}}} \mu _\beta ^* \left( {\left\lceil { \cdot \beta ^{ - {\textstyle{1 \over 3}}} } \right\rceil } \right) \to ^{L^1 } \eta ^* ( \cdot ) . \\ \end{array}$$ The limitsb ^*∈(0, ∞) and are identified in terms of a Sturm-Liouville problem, which turns out to have several interesting properties. The techniques that are used in the proof are functional analytic and revolve around the notion of epi-convergence of functionals onL ²(?⁺). Our scaling result shows that the speed of soft polymers ind=1 is not right-differentiable at β=0, which precludes expansion techniques that have been used successfully ind≧5 (Hara and Slade (1992a, b)). In simulations the scaling limit is seen for β≦10^?2.     

Microscopic model of the coexistence of superconductivity and ferromagnetism in the hybrid ruthenate-cuprate oxide RuSr2GdCu2O8

A microscopic t-J-I model with competing antiferromagnetic (J) and ferromagnetic (I) exchange interactions is proposed for strongly correlated electrons in RuSr₂GdCu₂O₈. It is assumed that for CuO₂ layers and for RuO₂ layers. A superconducting solution of $d_{x^2 - y^2 }$ symmetry was obtained for the CuO₂ layers while competition between ferromagnetism and p-type triplet superconducting pairing is obtained for RuO₂ layers. It is shown that the RuO₂ layers have a lower carrier concentration in the Hubbard subband formed by coupled ((d _xy -p)-π) orbitals compared with a bulk Sr₂RuO₄ crystal, which leads to stabilization of the ferromagnetic state in the RuO₂ layer.     

Stuck in traffic: Patterns of powder adhesion

The adhesion of fine particles to surfaces is important for applications ranging from drug delivery to fouling of solar cells. In this letter, we show that powder adhesion can occur in unexpected patterns, concentrating particular grain types in some locations and clearing them from others, and we propose a straightforward traffic model that appears to reproduce many of the behaviors seen. The model predicts different patterns depending on inter-particle cohesion, and we find in both experiment and model that adhesion occurs in three distinct stages.      

Some remarks on conformal invariant theories on four-lorentz manifolds

Contrary to the eleven-parameter group consisting of Poincaré-transformations and dilatations, the group of so-called special conformal transformations can act on the Minkowski space only as a local conformal Lie transformation group. We show that the universal covering space of the compactified Minkowski space , together with an appropriate metric \(\tilde g\) on it, form a suitable Lorentz manifold that admits universal covering group of the “conformal group” of as a transitive Lie transformation group. This group respects the causality notion on usually defined on a Lorentz manifold. However, possesses only seven isometries in contrast to the well-known ten isometries on the Minkowski space , which correspond to conservation of energy-momentum and angular-momentum.     

Negative magnetoresistance and hall coefficient of a two-dimensional disordered system

Localization corrections to the longitudinal (δρ) and Hall (δρ_H) resistivities of a two-dimensional disordered system are calculated in all ranges of classical magnetic fields, up to the values at which the mean free path of charge carriers l is less than or of the order of the cyclotron radius R _c. It is shown that the physical reason for the departure of the l dependence of these resistivities from the logarithmic law ∝ ln(l _B /l)) (l _B is the magnetic length) at is the nonlocal process of diffusion in the Cooper channel, rather than the transition to a quasi-ballistic regime. Analytical expressions are obtained that allow one to analyze the interference effect in δρ and δρ_H in quantizing magnetic fields , including the quantum limit. Contrary to popular opinion, the localization corrections to ρ_H are shown to be nonzero. They have a sign opposite to that of the charge carriers and lead to a decrease in the magnitude of the Hall resistivity. Their field dependence has the same features and their relative magnitude is of the same order as in the case of the longitudinal resistivity. The quantum corrections to the Hall resistivity are due to the Larmor precession of the closed paths that electrons follow in the process of their multiple scattering by randomly distributed impurities.     

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.      

Active chiral fluids

Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological microswimmers. Here, we derive constitutive material equations for active fluids which account for the effects of active chiral processes. We identify active contributions to the antisymmetric part of the stress as well as active angular momentum fluxes. We discuss four types of elementary chiral motors and their effects on a surrounding fluid. We show that large-scale chiral flows can result from the collective behavior of such motors even in cases where isolated motors do not create a hydrodynamic far field.