Fermion masses

In this paper, we show that 2m _e m /(m _e ² +m ² = (g _V/g _A) _e ² . From this expression, the Weinberg mixing parameter is shown to be 0·2254 or 0·2746. Assuming that the electron and muon neutrino masses are degenerate, we find thatm _v = (g _V/g _A) _e ² . (m _e m )/M _WL, where M_WL is the mass of the standard W^± boson. The neutrino mass turns out to be 6·5 eV. The -neutrino mass is found to be about 81 MeV. The masses of c, t, s and b quarks are found to be respectively 1·7 GeV, 21·2 GeV, 0·57 GeV and 2·18 GeV by assumingm _d=m _u= 0·3 GeV. All these masses agree with other estimates except the b quark which has about half of its expected value.     

Finite transformations of SU(4)

The problem of determining the representation matrices of SU(4) is investigated. A convenient set of parameters is first introduced by writing the general element of the group as a product of exponential functions of the generators, and the generators are expressed as differential operators involving these parameters. Special matrix elements of finite transformations with a SU(3) singlet as the initial state are then obtained by solving the eigenvalue equation of the quadratic Casimir operator of SU(4). The solution has the form of a product of elementary functions and threed _mm ^j functions of SU(2) and is free from summation over intermediate states. By expanding one of thed _mm ^j functions in an appropriate series a sum rule for the special matrix elements of the permutation operator 12343412 is obtained. The discussions are strictly confined to SU(4), but, some of the results given here can be extended to unitary groups of higher dimensions.     

The effective mass of holes in CdSb from reflectivity measurements

From the measured reflectivity near the plasma edge the effective mass of free holes in Ag-doped CdSb was determined. In the studied concentration rangem _b ^* >m _a ^* >m _c ^* is valid. The dependence of the effective mass on the concentration of free holes indicates a strong non-parabolicity of the bands.The authors wish to thank Dr. B. Rheinländer for discussions and information about his results before publication. Mrs. D. Vaková carried out the measurements on UR-10 Zeiss, Mrs. V. Míková prepared the single crystals, Mr. J. Kapar oriented them by X-ray diffraction and Dr. L. Satoura determinedN and. The authors thank them for their help.     

Biharmonic pumping in dye lasers with distributed feedback

Conclusions We have shown that biharmonic pumping can effectively excite traveling population gratings in an active medium when m <(W_o/2 +1/T₁), and temperature gratings if m <(₀x_m)^–1. As the order m increases the population-grating excitation efficiency decreases, while that of the temperature gratings may either increase or decrease. The times taken for the thermal and resonance processes which form the gratings to build up are given by the expressions t=₀x_m, t =T₁/(1 +W₀T₁/2), respectively. In this case distributed feedback is formed by a thermal mechanism if (14) is satisfied, and by resonance mechanism if the opposite inequality is satisfied. The self-excitation threshold over a wide range of parameters depends logarithmically on the amplitude of the grating forming the distributed feedback. Hence, for a comparatively small excess of the threshold, self-excitation of a laser with distributed feedback is possible over a wide spectrum. Thus, for double excess of the self-excitation threshold and T₁ =10^–9 sec, =1, and H =8 lasing over a wide spectrum of 10 cm^–1 is possible.Translated from Zhurnal Prikladnoi Spektroskipii, Vol. 40, No. 2, pp. 195–202, February, 1984.We wish to thank A. A. Afanasev and P. A. Apanasevich for useful discussions.     

Spin and density fluctuations in disordered narrow-band superconductors

A tight-binding theory of strong-coupling superconductivity is formulated on the basis of a random lattice model with local electron-electron and contact-type electronphonon interactions. Functional-derivative technique yields a systematic deduction of the electron self-energy in terms of Coulomb repulsion, density and spin fluctuations. A novel procedure is proposed to average disordered Berk-Schrieffer-type equations. The phonon ( ^ph)-, Coulomb ^C-, and paramagnon ( ^m)-mediated coupling parameters entering the superconductingT _c are calculated for diffusive behaviour in dirty systems or alloys. The critical reduction ofT _c due to ^m differs from the logarithmic singularity for a clean sample.     

Fluctuations in coagulating systems

Time-dependent fluctuations in a system of coagulating particles are studied, using the master equation for the probability distributionsP(m,t) for the occupation numbersm={m _k} (k=1,2,...) of thek-cluster states. Van Kampen's-expansion is used to determine the deterministic (order ⁰) and fluctuating part (order ^–1/2) of the solution. We calculate the time-dependent behavior of the fluctuations in the cluster size distribution. The model under consideration is of special interest since it exhibits a phase transition (gelation). For monodisperse initial states we give explicit expressions for the probability distribution of the fluctuations and for the equal-time and two-time correlation functions also near the phase transition. For general initial conditions we study the fluctuations (1) for large cluster sizes, (2) in the scaling limit (near the critical point), and (3) for large times. Our results show that the deterministic approach to coagulation processes (Smoluchowski theory) is invalid very close to the gelpointt _c and at large times (tt _M), where the distance from the gelpoint and the timet _M depend upon the size of the system.     

Study of the Β decay of6He with allowance for second-class currents and the antineutrino mass

The effects of the rest mass of the electron antineutrino are studied with allowance for the induced tensor form-factor F_c of the second-class current according to the Weinberg classification during the decay of the⁶He nucleus. We calculate the contribution of m and F_c to the electron-antineutron angular correlation coefficient A_e and the degree of longitudinal polarization P_e of the decay electrons. When m is nonzero, the coefficient A_e tends asymptotically to zero both at the beginning and endpoint of the spectrum, whether or not the second-class currents are taken into account. The series of qualitatively new experiments planned for the near future to measure the e- correlation for pure Gamow-Teller transitions (the⁶He nucleus could be a suitable nucleus here) with an accuracy of the order of 1% would allow the available estimate of the form-factor F_c to be improved substantially.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–67. September, 1989.     

A UNIFIED QUANTUM HALL CLOSE-PACKED COMPOSITE BOSON (CPCB) MODEL

Single-wavelength Landau cyclotron orbitals (SWOs) have been used as quantum Hall basis states to reproduce integer quantum Hall plateaus in a two-dimensional (2D) close-packing representation. But at the high magnetic fields B that correspond to fractional Hall plateaus, these SWOs are too small to give close packing. It is conventionally assumed that the fractional quantum Hall states are formed from collective electron excitations (CEEs). However, by invoking the use of multiple-wavelength Landau orbitals (MWOs), we can close-pack the fractional Hall plateaus in the same manner as the integer plateaus. Quantum Hall plateaus are characterized by the filling fractions n _e/n =k/m, where k=1, 2,... (all integers) and m=1, 3,... (all odd integers), and where n _e and n are the 2D electron e and magnetic flux =h/e densities, respectively. A composite particle (CP) is a bound state of an electron and m flux quanta . If m is even or odd, the CP is a composite fermion (CF) or composite boson (CB). In the CEE models, both CF and CB formalisms have been used. In the alternative MWO approach introduced here, the close-packed MWOs on a =k/m plateau each contain m de Broglie wavelengths . Each MWO traps m external flux quanta, produces m diamagnetic induced flux quanta, and carries the filling fraction , which accounts for the extreme accuracy (one part in 10⁸) of the Hall plateau conductance, _H= e ²/h. Since m is odd, these MWOs are CB states, and they form a boson condensate of close-packed composite boson (CPCB) states. The m=1 (m<1) CPCBs tile the integer (fractional) Hall plateaus. The filling fraction index k corresponds to k layers of CPCB orbitals. Plateau formation itself is due to the linear B dependence of the density of CPCB states. The CPCBs are decoupled from the semiconductor substrate, and hence may have large m* effective mass values. THE MWOs near the =1/2 non-plateau region are m=2 CF states.     

Dynamical mass generation

We investigate the possibility of calculating the fermion and the gauge-boson masses within an electroweakSU(2)_L ×U(1)_Y gauge-invariant model without the Higgs fields. Instead of the whole Higgs sector we introduce one Abelian vector boson C with massM renormalizably interacting with leptons and quarks of chiralities L and R with a strengthh. An interplay of all interactions which contribute to the fermion masses results in the fermion mass formulam _f= =M exp[87²/(3y(f _L)y(f _R)h ²)], wherey(f _L,R) are the C hypercharges, and y(f_L). y(f _R) < 0. The intermediate-boson massesm _w andm _z are expressed in terms of the fermion masses via sum rules.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Electric quadrupole moments of radioactive Pt isotopes

Nuclear orientation experiments were performed on¹⁸⁹Pt (I=3/2^–; T_1/2=11 h),¹⁹¹pt (I=3/2^–; T_1/2=2.8 d) and^195mpt=3/2^–; T_1/2=4.0 d) in an Os single crystal at temperatures down to 10 mK. Preliminary results for the quadrupole splitting _o=e²qQ/h are +48 (9), +39 (6), and –87 (12) MHz for¹⁸⁹ptOs,¹⁹¹ptOs, and¹⁹⁵mptOs, respectively. Preliminary results for the quadrupole moments are –0.8 (4), –0.6 (3), and +1.4 (7) b for¹⁸⁹pt,¹⁹¹pt, and¹⁹⁵mpt, respectively. In addition, the quadrupole subresonance structure of¹⁸⁹pt and¹⁹¹pt in Fe was measured with quadrupole-interaction resolved NMR-ON spectroscopy. The results for the magnetic hyperfine splitting _M=¦g_NB_HF/h¦ and _Q are:¹⁸⁹ptFe: _M=277.9 (1) MHz; _Q=+1.39 (5) MHz.¹⁹¹ptFe: _M=320.17 (3) MHZ; _Q=+1.39 (3) MHz. The ratio of the quadrupole moments of¹⁹¹pt and¹⁸⁹pt is deduced to be Q (¹⁹¹Pt/Q^l89pt)=+1.00 (4). The negative quadrupole moments of¹⁸⁹pt and¹⁹¹pt indicate a predominantly oblate shape of the ground states.     

Multimode q-Oscillator Algebras with q2(k+1) = 1 and Their Bargmann–Fock Representations

A countably infinite class of multimode q-oscillator algebrasA _k;m (k = 1, 2, ..., m = 1, 2, ...) is obtained with the aid of the R-matrix method in quantumgroup theory for q ^2(k+1) = 1. The related Fock spaces are given and they showthat the q-particle systems described by A _k;m obey a generalized Pauli exclusionprinciple. The algebras A _k;m are represented on a kind of q-holomorphic functionspaces B(¯) _k;m which are generalizations of the usual Bargmann–Fock spaceswith many Grassmann variables and have Hilbert space structures with the scalarproduct given by an algebraically defined integral. When taking k = 1 or k , all of the above are reduced to the corresponding results for the usual multimodefermion and boson systems, respectively.     

Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education     

Deviation from Reference Planes and Reference Misorientation for Σ3 Boundaries

The purpose of the present work is to study the crystallography of a particular family of interfaces, 3 boundaries in copper, in the context of the relationships between 3 plane indices, their deviation from reference planes, and the deviation from exact 3 matching, v/v_m. The relatively high values of v/v_m recorded were considered to be the result of texture development during annealing and various back twinning and 3ⁿ impingement interactions. The results show that there is a reasonable correlation between the deviation from a reference misorientation (v/v_m) and the deviation from reference interface plane (R). Measurement of v/v_m alone provides an indirect estimate of the plane type and hence energy of the boundary, at least for 3 boundaries, and moreover is more germane to the experimental mode of data collection. The effect of intragrain orientation variations on the interface parameters was also studied, and it was shown that there is a 20% difference between misorientations calculated near the interface compared with displaced from the interface.     

An extension of Kotani's theorem to random generalized Sturm-Liouville operators

We consider the random operator: –d/m (dx)d ⁺/dx+q (x), wherem (dx) andq (x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.     

Periodic and flat irreducible representations ofSU(3) q

We construct all the periodic irreducible representations ofU(SU(3)) _q forq am-root of unity. Their dimensions arek(2m) ² fork=1,...,m (onlyk=1,...,m/2 for evenm). Their interest is that they could be a tool to generalize the chiral Potts model. By truncation of these representations, we construct flat representations ofU(SU(3)) _q , in which all the multiplicities of the weights are set to 1.     

The λϕ 3 4 field theory in a finite volume

The unnormalized doubly cutoff Schwinger functions converge as the ultraviolet cutoff is removed. The limits, the finite volume unnormalized Schwinger functions, are tempered distributions and areC in the coupling constant. They have asymptotic expansions given by perturbation theory. For sufficiently small they can be normalized and then they are the moments of a measure onI (IR³).Supported in part by the National Science Foundation under Grant GP 40354X.     

Parametric excitation of spherical modes in ferromagnetic spheres by perpendicular and parallel pumping

The fine structures of the threshold of subsidiary absorption and parallel pumping, observed on highly polished YIG spheres in 1975 by W. Jantz et al., are discussed with a model which uses instead of plane spin-waves the true modes regarding the shape of the sphere. These spherical modes are magnetostatic modes taking additionally the exchange interaction into account. At the closely spaced resonances of the fine structure of parallel pumping single spherical modes with angular-momentum quantum numberm=0 are excited, whereas at the resonances of subsidiary absorption pairs of spherical modes with big angular-momentum quantum numbers (|m|1000) satisfying the selection rulem+m=1 are excited. The analysis of the fine structure of subsidiary absorption shows that in regimes where the plane wave approximation predicts the excitation of spin-waves with formalk0, modes withk1.5·10⁵ cm^–1 have the lowest threshold. This discrepancy is discussed with the effect of surface pit scattering, which increases the threshold of modes withk < 2/_pit, where _pit is a typical size of the surface pits. Consequently modes withk22/_pit instead ofk0 have the lowest threshold.     

Thepin structure employed as current amplifier

Injection of excess carriers into thei region of a forward biasedpin diode diminishes proportionally its resistivity (primary circuit). Resistivity variations in thei region are used to control higher currents and powers in the secondary circuit. This basic idea is developed quantitatively for a simplified symmetrical model of thepin structure in a stationary regime and then generalized for the asymmetrical case. The frequency characteristics of the electronic device are studied. For demonstration of the theoretical results thepin structure in silicon with known parameters is used.Notation 2d [m] length ofi region - D [m² s^–1] ambipolar diffusion constant - e [C] electron charge - E ₂ [Vm^–1] electric field strength iny direction - i ₁ [Am^–2] current density inx direction - i ₂ [Am^–2] current density iny direction - i _m [Am^–2] current density due to recombination of carriers ini region - i _1ef ,i _2ef [Am^–2] effective values of currentsi ₁,i ₂ - i _ns ,i _ps [Am^–2] saturated current densities from the heavily dopedn, p regions - i intrinsic region - I [A] total current throughp-n junction - I ₁ [A] total current in pin diode - I ₂ [A] current in secondary circuit - k[J grad^–1] Boltzmann's constant - L=(D) [m] ambipolar diffusion length of carriers in middle region - n(x) [m^–3] excess electron concentration in middle region - ¯n [m^–3] average value of electron concentration in middle region - n _i [m^–3] intrinsic electron concentration - n _A [m^–3] acceptor concentration inp region - n _D [m^–3] donor concentration inn region - p(x) [m^–3] excess hole concentration in middle region - q [m²] area of electrodes 3 and 4 - Q [C] charge stored ini region - R [m^–3 s^–1] recombination rate - s [m] width of diode - t [m] thickness of diode - T [K] absolute temperature - U [V] voltage acrossp-n junction - U ₁ [V] voltage acrosspin diode - U ₂ [V] voltage across terminals of secondary circuit - U _m [V] voltage drop acrossi region - V _D [V] voltage drop acrossn — i andp — i junctions at zero load - W ₁ [W] power inpin diode circuit - W ₂ [W] power in secondary circuit - x [m] distance from center of diode - coefficient in current amplification factor - [rad] phase shift of diode current with respect to applied voltage - [s] life time of excess carriers ini region - [m² V^–1 s^–1] carrier mobility ini region in the symmetrical model - _n [m² V^–1 s^–1] electron mobility ini region - _p [m² V^–1 s^–1] hole mobility ini region - [^–1 m^–1] conductivity     

On the indistinguishability of classical particles

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature become small. Thus, microscopic particles like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2)³ are reduced to points in the phase space, the partition functionTr{exp(–) for N identical bosons (fermions) approaches (2)^–3N(N!) ... d³r₁ d³p₁ ... d³r_N d³p_N exp(–H). The two factors, (2)^–3N and (N!)^–1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles.     

Another Look at Just-So Solar Neutrino Oscillations

We take another look at Just-So solar neutrino oscillations, characterizing them by the energy E_/2 at which the distance-varying angle is /2, instead of by the usual m ² . The rising spectrum recently observed by SuperKamiokande is consistent with an E_/2 6–9 MeV and marginally with 48 MeV. The pp neutrinos must then be reduced to one-half the standard solar model prediction, and ⁷Be neutrinos must make up a significant part of the SAGE and GALLEX gallium signal. For E_/2 close to 9 and 48 MeV, the ⁷Be neutrinos will also show a large seasonal variation, emphasizing the importance of direct measurements of the ⁷Be neutrinos.