Remarkable effects of uniaxial stress on stimulated far IR emission from hot holes in germanium in crossed electric and magnetic fields

Stimulated far IR emission due to l-h as well as cyclotron transitions of hot holes in uniaxially stressedp-Ge (P H E) was studied. The results obtained showed the significance of intersub-band hole tunnelling for these mechanisms of generation and may be explained by a change in tunnelling produced by the stress. A considerable expansion of the stimulated light hole cyclotron emission band was observed in a stressed crystal. This expansion allows covering (in one sample) of all generation bands in the light hole cyclotron resonance (CR) masers in unstressedp-Ge, reported so far.     

Wide-range tunable sub-millimetre cyclotron resonance laser

The results of investigation of cyclotron type stimulated emission processes inp-Ge in strong crossedE B fields are presented. Using the optimumE,B field orientation the spectral range of continuous tuning of the emission line frequency was increased substantially. A tunable sub-millimetre laser with the tuning rangev = 25 to 95cm^–1 ( = 105 to 400m), output power 10 to 100mW and emission linewidthv 0.2cm^–1 is described.     

Landau quantization and hot hole stimulated FIR emission in crossed electric and magnetic fields

Theoretical and experimental investigations of the resonant amplification of far-infrared (FIR) radiation by hot holes in germanium in theE B field configuration have shown that stimulated emission is possible not only at the fundamental but also at higher harmonics of the light-hole cyclotron resonance frequency. Single line tunable FIR laser oscillations close to the fundamental and the second cyclotron harmonic are demonstrated and explained within the presented model. In the crossed field configuration a repulsion of light and heavy hole levels is predicted as a result of interaction.     

Far IR cyclotron resonance and luminescence of hot holes inp-Ge

A survey of techniques and experimental results from the investigation of hot hole effects in germaniumvia their absorption and spontaneous emission in the far IR (FIR) range. The results of a cyclotron resonance absorption investigation of hot holes in crossedE andB fields in a wide wavelength range 0.3 to 2 mm at 40 K are presented. The light hole sub-band overpopulation and the absorption pecularities under streaming conditions are investigated. Mechanisms of FIR emission ofp-Ge at liquid helium temperatures are analysed. A new emission mechanism associated with the crystal lattice emission is revealed and an estimation of FIR phonon-assisted absorption is made. The population inversion of h-l transitions is diagnosed by the effect of flare up of FIR luminescence of hot holes in Ge with an applied magnetic fieldB E, and the FIR radiation gain at l-h transitions is estimated. The different factors affecting the flare up and the gain of FIR radiation, such as the crystallographic orientation of the crossedE andB fields, slight nonorthogonality of theE andB fields, the sample heating during the electric field pulse and the uniaxial stress, are discussed.     

High power splitting of the cyclotron resonance induced photoconductivity in n-GaAs

Conclusion In summary our results show that photoconductivity and optical absorption under cyclotron resonance conditions in high purity n-GaAs are more complex than it has been assumed previously. As cyclotron resonance can only be measured with non zero free electron concentration, and because the 2p _– shallow donor level remains below the N=0 Landau level for all magnetic field strengths, a certain population of 2p _– states must be present and thus the interference between both absorption processes is unavoidable as long as 2p _–2p ₊ electric dipole transitions are activated by ionized impuritics. This interference gets most drastically manifest at high intensities causing an apparent splitting of the photoconductivity line. Even at lower intensities however when the dip in the photoconductivity line is not observable, all optical characteristics previously attributed to cyclotron resonance are affected by the shallow donor absorption. The energy separationE _2p+–E _2p– of shallow donors in a magnetic field is exactly equal to w _CR only for isolated impurities in the effective mass approximation. The same electric stray field of ionized impurities which cause the activation of 2p _–2p ₊ absorption may shift the donor energy levels due to stark effect. For magnetic field strengthsB<1 T a field dependent deviation ofE _{2 +}–E _{1p –} from the cyclotron resonance quantum energy was observed [15] amounting up to 8 pc. In this case we expect that the peak positions of photoconductivity and absorption do not spectrally coincide and do not occur at the resonance magnetic field strength of 01 Landau level transitions. Thus effective masses determined by standard cyclotron resonance methods at low magnetic fields may be incorrect by a few percent.     

Negative mass cyclotron resonance maser

Physical principles, design and operation characteristics of a negative mass cyclotron resonance maser inp-type germanium are considered in this paper. The formation of anisotropic inverted distributions of negative effective mass heavy holes in strong electric and magnetic fieldsE H [001], resulting in negative conductivity in the millimetre and submillimetre wavelength ranges, is discussed. The generation is observed at 0.9 to 8mm in low compensated germanium samples with the hole concentration rangeN ₀ 2×10¹² to 2×10¹⁴ cm^–3 at low temperaturesT 25 K in electric fieldsE 40 to 350Vcm^–1. The maser frequency is tuned by the magnetic field corresponding to a cyclotron resonance frequency of carriers with an effective mass ofm _c 0.4m ₀. The spectral width of the emission in single mode operation does not exceed several megahertz. A pulse duration of 1 to 200 s and a repetition rate off _rep 1 to 200 Hz has been obtained limited by sample heating. Possibilities of improving the maser characteristics inp-Ge as well as in other A_III B_v semiconductors and the perspectives of new frequency tuning methods due to the application of uniaxial stress and magnetic field are demonstrated.     

Conditional expectation and commutativity in von Neumann algebras

LetH be a Hilbert space,A the von Neumann algebra of all bounded operators onH,B a von Neumann subalgebra ofA, andw a bounded linear functional onA. The functionalw is said to commute withBA ifw(AB)=w(BA) for allAA. It is shown that the mapBw (BAB) is a complex measure on the orthocomplemented partially ordered set of all orthogonal projections inB for everyAA if and only ifw commutes with all members ofB. For anyAA, the conditional expectation ofA with respect toB andw is defined and it is shown that this expectation exists for an Abelian separableB ifw commutes with all members ofB. Using Gleason's theorem it is shown thatw commutes withB if and only if the density operator ofw commutes withB.     

Andreev levels of SNS-junctions in weak magnetic fields

Spatial quantization of the energy spectrum of quasiparticles, bound by Andreev scattering in the normal layer of SNS junctions, remains observable in weak constant magnetic fieldsH parallel to the phase boundaries. Quasiparticles, especially in the low lying Andreev states, can traverse thick normal regions many thousand times before they are scattered once by interaction withH . This confirms the expectation that quasiparticle transport phenomena in superconducting heterostructures should be little influenced by magnetic fields as long as the cyclotron radius greatly exceeds the average spatial extension of the unperturbed wave functions normal to the phase boundaries.     

Decay of the new isotope127Pr

A new isotope,¹²⁷Pr, has been identified and its decay has been studied using on-line isotope separation of⁹⁴Mo (³⁶Ar,p2n) reaction products. The half-life of the isotope was determined to be 7.7(6) s, and a /X-ray spectrum has been obtained. A partial level scheme is proposed for¹²⁷Ce on the basis of-singles,-gated and-coincidence data.The authors would like to thank the TIARA cyclotron crew for their cooperation in generating an intense³⁶Ar beam as well as in operating the cyclotron. This work was partly supported by the JAERI-University Collaborative Research Project.     

Functional Realization and Nonlinear Induced Representation in the Geometrodifferential Conception of Extended Particles

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables , a physical wave _x () representing the proper characteristics of the particles, and a functional wave X [ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The first study is undertaken in a special instance _x () = (x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed.     

Quantum effects in submillimetre hot hole semiconductor lasers

The hole dynamics and emission processes in degenerate band semiconductors in strong crossedE B fields were studied both theoretically and experimentally. The Luttinger effective mass Hamiltonian was used to study the Landau level energy spectrum in anisotropic valence bands of Ge. The dependence of the energy spectrum onE,H fields orientation is analysed. The role of quantum effects, such as interaction and mixing of light and heavy hole states in the scattering process and Landau level population is studied. The results of experimental studies of stimulated emission spectra for intersub-band and cyclotron transitions as well as their dependence onE,H field orientation are presented, the experimental data being in good agreement with the quantum model calculations.     

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.     

Electrodynamics Under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion in presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S is given by H = a(H – v × D) and E = a(E + v × B), where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S are given by D = E, B = H and J = E. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proven that the electrodynamics proposed explains satisfactorily the Wilson effect.     

Numerical simulation of heavy hole cyclotron resonance NEMAG inp-Ge

The cyclotron resonance of heavy holes in germanium underE ₀B ₀[001] fields is simulated by the numerical Monte-Carlo technique. Linear and non-linear regimes of hot hole interaction with high-frequency transverse electric field E [0 0 1] are considered. A new procedure for the calculation of components of the gyrotropic part of the hot hole differential mobility tensor is proposed. We concentrate mainly on negative transverse effective mass hot holes.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

Theory of ferromagnetic resonance in metallic and insulator films

Simple intuitive explanations of the frequencies and intensitiesI of magnetostatic modes (with negligible exchange energy) and exchange modes (negligible microwave-field demagnetization energy) are given. The effects of explicit boundary conditions on the transverse, time-varying componentm of the magnetization (i.e., the amount of pinning) and the effects of inhomogeneities in the internal fieldH _i and saturation magnetizationM _s are discussed. A bulk inhomogeneity inM _s changes the effective exchange constant, while a bulk inhomogeneity inH _i lowers the fields for resonance of all high-order exchange modes by the same amount. The pinning conditions affect the values of andI of the exchange modes and the mixed exchange-magnetostatic modes, but have little effect on the magnetostatic modes. A surface-imperfection source of pinning and of the inhomogeneities inH _i andM _s is discussed.Part of this work was performed while the author was atNorth American Rockwell Science Center, Thousand Oaks, California.     

Current-induced coupling between conductance channels in membranes

The driven system of conducting channels in a nerve membrane is investigated. A current flow generates a coupling between the channels: the current through a channel is influenced by the presence of other conducting channels via the deformation of the equipotential surfaces within the media adjacent to the membrane. We derive an integral equation for the membrane voltageV(s) (s in the membrane plane) and solve it for different membrane conductance distributions(s) including models for stochastic distributions of conducting channels.V(s) is a nonlinear functional of(s). The system of coupled channels is compared with an Ising model. The system exhibits a multi-channel interaction which can be characterized by two different rangesd _int andD ₁. For a mean channel distanced ₀d _int interaction effects are negligible, and ford ₀D ₁ all channel-voltages are equal and thus represent a mean-field for the channels. Increasing conductivity of the medium decreasesd _int and increasesD ₁. With experimental data on sodium channels in nerve membranes we find:d _intd ₀, i.e. a 50% decrease of the channel-voltages by the interaction, andD ₁10³10⁴ d ₀, which indicates mean-field behaviour of the channels. In a subsequent paper we shall treat the statistics of channels which open and close stochastically under the influence of the local membrane voltage.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

Electron states in quantum-dot and antidot arrays placed in a strong magnetic field

Quantum electronic states in a dot (antidot) array in the presence of a dc magnetic field are studied. A new method of numerical calculation of the electron spectrum and wave functions in a two-dimensional periodic potential and perpendicular magnetic field is proposed. The magnetic-subband energies, density of electron states, and electron density |ψ(x,y)|², as well as the amplitude of the potential, and lattice period and degree of anisotropy for different magnetic fields have been found. The calculations were performed for quantum dots in the In_0.2Ga_0.8As-GaAs and GaAs-Al_0.3Ga_0,7As systems. The rearrangement of the spectrum with variation of magnetic field and with transition from the tight-binding to weak-binding approximation is studied (ω _c is the cyclotron frequency, and V ₀ is the periodic-potential amplitude). The calculations show that the two-dimensional lattices epitaxially grown presently on semiconductor surfaces permit observation of quantum effects associated with rearrangement of the spectrum (electron transport and optical absorption) in magnetic fields H⩽1 MG. Fiz. Tverd. Tela (St. Petersburg) 40, 1134–1139 (June 1998)     

Note on the Wiedemann-Franz law and the Mott rule in two-dimensional systems in strong magnetic fields

Modivated by a contradiction in the literature, the range of validity of the Wiedemann-Franz law and the Mott rule has been reexamined for a 2d electron-impurity system in a strong magnetic field. The condition for these laws to be fulfilled is shown to be thermal energy level broadening rather than thermal energycyclotron energy.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday