Far infrared surface electromagnetic waves propagation on A3B5 semiconductors

The real and imaginary parts of surface electromagnetic waves (SEW) refraction index n_ef in n-type InSb, GaAs and InP have been measured in FIR region (=85–142 cm^–1). The n_ef measurements allowed to determine plasma frequency _p and plasmon damping . The obtained nonlinear SEW propagation distance L dependence on Te impurity concentration in GaAs (N=10¹⁷–10¹⁹ cm^–3) was explained taking into account the conduction band nonparabolity as well as the presence of isostructural phase transition at N=2×10¹⁰ cm^–3.     

μSR studies in the heavy fermion systems UNi2Al3, UPd2Al3 and U2PtC2

We have performed Muon Spin Relaxation (SR) measurements of several heavy fermion systems: UNi₂Al₃ (single crystal), UPd₂Al₃ (single crystal) and U₂PtC₂ (polycrystal). ZF -SR measurements of UNi₂Al₃ show magnetic order below the Néel temperatureT _N=4.6K, with the muon precession frequency(T 0)=2.5MHz at low temperatures. The local field distribution obtained at low temperatures in UNi₂Al₃ resembles that of the incommensurate spin density wave (SDW) system (TMTSF)₂PF₆, suggesting an incommensurate spin arrangement in UNi₂Al₃. TF -SR measurements give the penetration depth(T 0)=6100Å for UPd₂Al₃ and(T 0)=7000Å for U₂PtC₂ respectively. Since UPd₂Al₃ and U₂PtC₂ are clean superconductors (/l-0), we can combine n _s/m^* with the Sommerfeld constant n _s ^1/3 m^* to calculate the Fermi temperatureT _F ^3/4–1/4, which represents the characteristic energy scale of the superconducting carriers. We obtainT _C/T_F 0.01 for both UPd₂Al₃ and U₂PtC₂, comparable to other exotic superconductors, but quite different from simple metal BCS superconductors, whereT _C/T_F 0.01.     

A Comparative study of p-Em and C12-Em interactions at 4·5 GeV/c per nucleon

In this paper we present a comparative study of inelastic interactions of C¹²-Em and p-Em at 4·5 GeV/c per nucleon. The multiplicity distributions and their correlations have been studied. The results show a strong correlation of n _s onn _h in the case of C¹²-Em but not in the case of p-Em. It is also shown that the n _s increases with the increase of the projectile mass. The angular distribution of the target fragments in C¹²-Em shows a massive forward collimation. Comparison is also made in the pseudorapidity distribution of both C¹²-Em and p-Em, the result shows many interesting features.     

Anisotropic fiber with cylindrical polar axes

The newly proposed anisotropic fiber structures with cylindrical polar principal axes appear to be an interesting novel class of special lightguides. In this paper, some interesting results relating to such fibers are derived which, to the knowledge of this author, have not yet been reported in the literature. It is found that, ifn _c0 ( )^1/2>n _zc0( _r )^1/2, TE₀₁ will be the fundament mode with a range of single-mode operation given by 2.61n _zc0 (2 _r )^1/2 /a<2.61n _c0(2 )^1/2. On the other hand, ifn _zc0 ( _r )^1/2>n _c0( )^1/2, then TM₀₁ becomes the fundamental mode whose single-mode operation range is 2.61n _c0 (2 )^1/2 /a<2.61n _zc0(2 _r )^1/2.     

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L ² , inverse temperature > _c and overall magnetization conditioned to take the value m L ² –2m v _L , where _c ^–1 is the critical temperature, m =m () is the spontaneous magnetization and v _L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v _L ^3/2 L ^–2 tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value _c and a function such that the following holds: For < _c , there are no droplets beyond log L scale, while for > _c , there is a single, Wulff-shaped droplet containing a fraction _c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, and are related via a universal equation that apparently is independent of the details of the system.     

Linking numbers of closed manifolds at random in ℝ n,inductances and contacts

We give here new results of topology and integral geometry concerning the Gauss linking number I of closed manifolds inn-dimensional space. The rigid manifolds have arbitrary shapes and dimensions, and are statistically at random positions in ⁿ . Generalizing Pohl's work, for two closed manifoldsC ₁ ^r ,C ₂ ^s , of respective dimensionsr ands, with 0rn–1, andr+s+1=n, we consider the kinematic linking integralI=<I ²(x,O)d ⁿ x>, of the square linking number I ofC ₁ ^r andC ₂ ^s , over the group of Euclidean motions of one manifold (translationsx, rotationsO). Introducing a new tensorial method, and using group theory, we show quite generally thatI=num. fact. , where is a length variable and whereA , (=1, 2) are characteristic functions associated with the manifoldC only. We study functionsA and of a manifoldC ^r , of dimensionr, in all cases 0rn–1.A always exists.A(0) givesC's area, whereas equals the interior volume of a hypersurfaceC. is found to exist and not to vanish only if 2 dimC+1=n andn=3+4q=3, 7, 11 ...A and are explicitly calculated for segments andr-spheresS ^r . As an application the topological excluded volume of a gas of nonlinked spheresS ^r moving in ^2r+1 is calculated. We generalize toN manifoldsC , =1, ...,N, linked successively to each other and forming a ring. The cyclic product of their linking numbers is integrated over the group of motions of the manifolds. It is shown to factorize completely in Fourier space, with special algebraic rules, over the set of 2N characteristic functionsA , , associated with theC 's. The same algebra of characteristic functions is shown to describe a larger class of topology and electromagnetism properties: a new theorem is given for a family of Euclidean group integrals involving the random linking numbers, mutual inductances and contact distributions ofN manifolds.     

Interface formation and a structural phase transition for the spherical model of ferromagnetism

A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L ^{d –d} × ^d ( ^d 2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For _j 0, jd-d, no seams are present except at infinity, whereas if _j = 1/2, impurity saturation occurs. For 0 < _j < 1/2 the physical domain _phys =D ^{d –d} × ^d (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T ₀). Below that temperature (T>T ₀), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition.     

Convergence of Nelson fiffusions

Let _t, _t ⁿ ,n1, be solutions of Schrödinger equations with potentials form-bounded by –1/2 and initial data inH ¹( ^d ). LetP, P ⁿ ,n1, be the probability measures on the path space =C(₊, ^d ) given by the corresponding Nelson diffusions. We show that if { _t ⁿ } _n1 converges to _t inH ¹( ^d ), uniformly int over compact intervals, then converges to in total variation t0. Moreover, if the potentials are in the Kato classK _d , we show that the above result follows fromH ¹-convergence of initial data, andK _d -convergence of potentials.     

Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Existence of solutions for Schrödinger evolution equations

We study the existence, uniqueness and regularity of the solution of the initial value problem for the time dependent Schrödinger equationiu/t=(–1/2)u+V(t,x)u,u(0)=u ₀. We provide sufficient conditions onV(t,x) such that the equation generates a unique unitary propagatorU(t,s) and such thatU(t,s)u ₀C ¹(,L ²) C ⁰(H ²( ⁿ )) foru ₀H ²( ⁿ ). The conditions are general enough to accommodate moving singularities of type x^–2+(n4) or x^–n/2+(n3).     

Mutual Action of Optical Activity and Electro-Optic Effect and Its Influence on the Electro-Optic Q-switch

In this paper, we have studied the mutual action of the optical activity and the electro-optic effect, and its influence on the electro-optic Q-switch. The birefringence (g₃₃/n₀)(/n₀)² resulting from the mutual action is calculated. In the polarization light interferometric experiment setup, the outgoing light intensity expression is given by I = A²₀ cos² (/)(g₃₃/n₀)l – ] + (/)[(–2) + (g₃₃/n₀)(/n₀)²]l, for the optically active crystal on which the voltage is applied.We discuss the influence on the turn-off and turn-on states of the Q-switch caused by the mutual action term (g₃₃/n₀) /n₀)², and the advantage and disadvantage of the two work-manners of the Q-switch (i.e., step-up manner and step-down manner). The synthetic properties of La₃Ga₅SiQ₁₄ electro-optic Q-switch are described in comparison to KD₂PO₄ and LiNbO₃ Q-switches.     

Moduli spaces of curves and representation theory

We establish a canonical isomorphism between the second cohomology of the Lie algebra of regular differential operators on ^x of degree 1, and the second singular cohomology of the moduli space of quintuples (C, p, z, L, []), whereC is a smooth genusg Riemann surface,p a point onC, z a local parameter atp, L a degreeg–1 line bundle onC, and [] a class of local trivializations ofL atp which differ by a non-zero factor. The construction uses an interplay between various infinite-dimensional manifolds based on the topological spaceH of germs of holomorphic functions in a neighborhood of 0 in ^x and related topological spaces. The basic tool is a canonical map from to the infinite-dimensional Grassmannian of subspaces ofH, which is the orbit of the subspaceH _– of holomorphic functions on ^x vanishing at , under the group AutH. As an application, we give a Lie-algebraic proof of the Mumford formula: _n =(6n ²–6n+1)₁, where _n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg, whose fiber overC is the space of differentials of degreen onC.     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x =lim _L (L)/L and the first four magnetization moment ratios V _2n = ²ⁿ / ^{2 n} . As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*_2n . We confirm these predictions by a high-precision Monte Carlo simulation.     

A theorem on the first heteroclinic tangency in two-dimensional maps. Orientation-preserving cases

Using the properties of the Jordan curve, the following theorem on the heteroclinic tangency in orientation-preserving two-dimensional maps is proved: LetT :R ² R ² be a one-parameter family ofC ¹ diffeomorphisms andJ=DetDT be such that 0<J1 or 1J<. LetW _u ⁿ be the unstable manifold of a hyperbolicn-cycle andW _s ^m the stable manifold of a hyperbolicm-cycle. Suppose that for< _c ,W _u ⁿ andW _s ^m have no common points, and that for> _c ,W _u ⁿ andW s/m have a transversal heteroclinic point. Then at= _c ,W _u ⁿ andW _s ^m are in the first asymptotic heteroclinic tangency except for the following three cases: (1)n=m; both cycles are without reflection. (2)m=2n; then- andm-cycles are with and without reflection, respectively; (3)n=2m; then- andm-cycles are without and with reflection, respectively.     

Concrete quantum logics with covering properties

LetL be a concrete (=set-representable) quantum logic. Letn be a natural number (or, more generally, a cardinal). We say thatL admits intrinsic coverings of the ordern, and writeL C _n , if for any pairA, BL we can find a collection {C _i iI}, where cardI<n andC _i L for anyiI, such thatA B= _il C _i . Thus, in a certain sense, ifLC _n , then the rate of noncompatibility of an arbitrary pairA,BL is less than a given numbern. In this paper we first consider general and combinatorial properties of logics ofC _n and exhibit typical examples. In particular, for a givenn we construct examples ofL C _n+1\C _n . Further, we discuss the relation of the classesC _n to other classes of logics important within the quantum theories (e.g., we discover the interesting relation to the class of logics which have an abundance of Jauch-Piron states). We then consider conditions on which a class of concrete logics reduce to Boolean algebras. We conclude with some open questions.     

Survival probability in one dimension for theA+B→B reaction with hard-core repulsion

We study the effect of hard-core repulsion (known as the bus effect) betweenB particles on the reaction-diffusion systemA+BB in the continuous-time random walk model in one dimension with theA particles stationary. We show rigorously that the survival probability of theA particles is asymptotically bounded asC ₁lim _t{[–logS(t)]/t ^0.5}C ₂, whereC ₁ andC ₂ are constants. We also do simulations to confirm our results.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).