Influence of a strong longitudinal static electric field on free carrier faraday effect in an n-type InSb at room temperature at submillimeter wave frequencies

The expression for free carrier Faraday rotation and for ellipticity , as the function of the applied parallel static electric field and static magnetic field for a given value of wave angular frequency and electron concentration N₀, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as , where , , and . Here m^* and e denote the effective mass and charge of electron, respectively. _g is the forbidden bandgap of semiconductor. v₀ is the carrier drift velocity, which is a non-linear function of E₀ in high field condition. A possibility of a simple way of determining the non-linear v₀ vs E₀ characteristics of semiconductors by the measurement of Faraday rotation is also discussed.     

Squarks and gluinos at a TeV e + e − collider: testing the identity of Yukawa and gauge couplings in SUSY-QCD

Supersymmetry predicts the identity of Yukawa and gauge couplings in the QCD sector: . We examine whether the  Yukawa coupling can be determined, by methods complementary to LHC, by analyzing squark–gluino final states at a TeV e ⁺ e ⁻ collider.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

NMRON studies of MnBr2 \cdot 4H2O in applied magnetic fields

NMRON studies for the ⁵⁴Mn transitions in antiferromagnetic MnBr₂ 4H₂O, in the millikelvin regime, are presented and discussed. New values are given for (i) the sum of the effective molecular exchange and magnetic anisotropy fields acting on the Mn²⁺ ions, =2.23(2) T, and (ii) the magnetic dipole hyperfine splitting, A=-201.99(1) MHz, electric quadrupole hyperfine splitting P=0.049(8) MHz and pseudoquadrupole splitting =1.63(2) MHz for the ⁵⁴Mn nuclei.     

Search for stop production in R-parity-violating supersymmetry at HERA

A search for stop production in R-parity-violating supersymmetry has been performed in e⁺p interactions with the ZEUS detector at HERA, using an integrated luminosity of 65 pb^-1. At HERA, the R-parity-violating coupling λ’ allows resonant squark production, . Since the lowest-mass squark state in most supersymmetry models is the light stop, , this search concentrated on production of , followed either by a direct R-parity-violating decay, or by the gauge decay to . No evidence for stop production was found and limits were set on λ’₁₃₁ as a function of the stop mass in the framework of the minimal supersymmetric standard model. The results have also been interpreted in terms of constraints on the parameters of the minimal supergravity model.     

On the Schrödinger equation and the eigenvalue problem

If _k is thek ^th eigenvalue for the Dirichlet boundary problem on a bounded domain in ⁿ , H. Weyl's asymptotic formula asserts that , hence . We prove that for any domain and for all . A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on ⁿ (n3) in terms of is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1     

Gauge-invariant on-shellZ 2 in QED,QCD and the effective field theory of a static quark

We calculate theon-shell fermion wave-function renormalization constantZ ₂ of a general gauge theory, to two loops, inD dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ ₂/da ₀=i(2)^–D e ₀ ² d ^D k/k ⁴=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension _F of the fermion field in minimally subtracted QCD, withN _L light-quark flavours, differs from the corresponding anomalous dimension of the effective field theory of a static quark by the gauge-invariant amount

Über die Einteilchensingularitäten in Relativistischen Quantenfeldtheorien

By subtraction of products of three-point functions the four-point functions in relativistic quantum field theory are decomposed into two parts, in one of which there does not occur any mass-shell-singularity in the variables (; 1, 4). All these singularities are given explicitly by the kernels of the products of the three-point functions. — Necessary and sufficient conditions for the non-triviality of unitaryS-matrices or some of their elements are proved in terms of statements on the occurence of mass-shell-singularities in the vacuum expectation values of field operators. The strongest result we have gained is: If is equal to zero for someN>3, then all transition amplitudesT _2n vanish for everyn.     

Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

Quantized IR properties reconfirmed in the CO and SiO surface oscillators present in the surface layer of A bamboo stem

From analysis of diffusion diagrams of CO stretching band (25002180 cm^–1), bending band (800200 cm^–1) and SiO stretching band (1100700 cm^–1) measured in a skin surface layer of a bamboo stem (silicate cellulose), azimuthal directions where oscillators oriented were shown as ('=-90) _N=a·N-b, with a=28.3, 2×28, 22.7, b=25, 47.5, 10. And N=1,2.....14, N=1, .....6. N=1,2.....16. The optical activity (reflection integral) was shown for the CO stret. band as M_i(N)=a·N+b, with a=21.8, b=42 and N =1,2.....9. And for the bending band as M_i(N)=a·N² +b·N–c, with a=1.87×10¹, b=3.73×10³, c=7.06×10² with N=1,2.....9. Six stepnized fine series in CO weak reflection bands were confirmed as, and with N=1,2.....22. Mean values of the vibrational quantized states of the A, B and C-series in the SiO stretching weak band with R1.0% were shown as, (meV) with .     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

Zeros of partition functions via correlation inequalities

We show analyticity of the pressure for some classical ferromagnetic systems in the region ¦Im ¦ < Re of the external field. The proof, via correlation inequalities, is simpler than existing proofs for the Lee and Yang region {Re 0} and applies, without any approximation procedure, to more general continuous spin variables, e.g., distributed as , where _2n is an arbitrary real number and the other parameters are positive. It also applies directly to plane rotators in the region ¦Im ¦ ¦Re ¦ (Euclidean norms), but the proof will be given in a subsequent article, together with new inequalities between truncated correlation functions.     

Pair-produced heavy particle topologies: MSSM neutralino properties at the LHC from gluino/squark cascade decays

Processes of the form pp → anything → X_iX_j → + + notE are studied via a technique that may be viewed as an adaptation of time-honoured Dalitz plot analyses. X_i and X_j are new heavy states (with i, j =1, . . .,n), which may be identical or distinct; and and are necessarily distinct standard model (SM) fermion pairs whose invariant masses can be measured. A Dalitz-like plot of said invariant masses, versus , exhibits a topology connected to the masses and specific decay chains of X_i and X_j. Aside from relatively minor details, observed patterns consist of a collection of box and wedge shapes. This collection is model-dependent: comparison of the observed pattern to the possibilities for a specific model yields information on which new particle pair combinations are actually being produced, information beyond that extractable from conventional one-dimensional invariant mass distributions. The technique is illustrated via application to the minimal supersymmetric standard model (MSSM) process pp → → e⁺e^- + μ⁺μ^- notE. Here the heavy states are neutralinos (i = 2,3,4) - note that is excluded - which are produced in gluino/squark ( / ) cascade decay chains. Even with fairly modest expectations for the LHC performance during the first few years, this method still provides substantial insight into the neutralino mass spectrum and couplings if gluino/squark masses are relatively low (≃ 400 GeV). Arrival of the final proofs: 29 November 2005     

Measurement of CP violation in stop cascade decays at the LHC

We study the potential observation at the LHC of CP-violating effects in stop production and subsequent cascade decays, , , , within the Minimal Supersymmetric Standard Model. We study T-odd asymmetries based on triple products between the different decay products. There may be a large CP asymmetry at the parton level, but there is a significant dilution at the hadronic level after integrating over the parton distribution functions. Consequently, even for scenarios where large CP intrinsic asymmetries are expected, the measurable asymmetry is rather small. High luminosity and precise measurements of masses, branching ratios and CP asymmetries may enable measurements of the CP-violating parameters in cascade decays at the LHC.     

Eigenvalue Asymptotics for the Schrödinger Operator with a δ-Interaction on a Punctured Surface

Given n2, we put r=min . Let be a compact, C ^r -smooth surface in ⁿ which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L ²( ⁿ ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.     

Measurement of inclusive jet cross sections in photoproduction at HERA

Inclusive jet cross sections are measured in photoproduction at HERA using the H1 detector. The data sample of events in the kinematic range of photon virtualities and photon-proton centre-of-mass energies represents an integrated luminosity of . Jets are defined using the inclusive algorithm. Single- and multi-differential cross sections are measured as functions of jet transverse energy E_T ^jet and pseudorapidity in the domain and . The cross sections are found to be in good agreement with next-to-leading order perturbative QCD calculations corrected for fragmentation and underlying event effects. The cross section differential in E_T ^jet, which varies by six orders of magnitude over the measured range, is compared with similar distributions from colliders at equal and higher energies.Received: 24 February 2003, Revised: 26 May 2003, Published online: 11 July 2003     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .     

A study of charm and anti-charm production in beauty decays with the OPAL detector at LEP

The branching ratio of beauty hadrons to final states containing two charm hadrons, Br(b , has been measured using an inclusive method in hadronic Z⁰ decays with the OPAL detector at LEP. The impact parameter significance of tracks opposite tagged b-jets is used to differentiate b decays from other decays. The result is where det. is the systematic uncertainty due to the modelling of the detector, and is the systematic uncertainty due to the modelling of the underlying physics. Using this result, the average number of charm plus anti-charm quarks produced in a beauty quark decay, n_c, is found to be 1.12 ^{+ 0.11}_-0.10.Received: 11 July 2003, Published online: 18 May 2004