Some remarks on variable range hopping—in particular in the quantum Hall regime

An expression for the heat conductivity _xx is derived in the effective medium approximation. Mott type formulas are obtained for _xx and the Peltier coefficient _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like . The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity _xx , the results are fully consistent with the experimental data on _xx and the density of states at the Fermi level. Finally, _xx is estimated which together with _xx and _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients _xx and _xy .Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Four-baryon weak interactions with ΔS = 1 and SU (6) symmetry

Relations are found among the amplitudes for four-baryon processes with S = 1 under the assumption that the Lagrangian for s-wave weak interactions has the transformation properties of a component of the SU(6) 35-plet. In particular, it is found that the amplitudes for the¹S₀ ¹S₀ and³S₁ ³S₁ transitions for the p pn reaction are the same, within a sign.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 70–77, October, 1969.     

Quantum mechanics without the projection postulate

I show that the quantum state can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of determinate quantities (selected by and the boundary conditions) can have values. The probabilities defined by (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate.     

Continuity and relative hamiltonians

Let ( _n ) _n 1 be a norm convergent sequence of normal states on a von Neumann algebraA with _n . Let (k _n ) _n1 be a strongly convergent sequence of self-adjoint elements ofA withk _n k. It is shown that the sequence of perturbed states converges in norm to . A related result holds forC ^*-algebras. A counter-example is provided to show that it is not sufficient to assume weak convergence of ( _n ) _n 1 even whenk _n=k for alln. However, conditions are given which, together with weak convergence, are sufficient. Relative entropy methods are used, and a relative entropy inequality is proved.     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

Study of magnetic after-effect in magnesium manganese ferrites

The magnetic after-effect caused by the diffusion of electrons was studied in detail in MnMg ferrites of the series Mg _x Mn_1.15–x Fe_1.85O₄₊ ; the comparative measurements were also carried out on a sample of MgFe₂O₄₊₍<0). By combining the two methods, (a) investigation of the disaccommodation of initial permeability at different temperatures and (b) measurement of the displacement of the maximum of the temperature dependence tan with the frequency, it was possible to study the relaxation processes whose time constants lay between 0.5 sec and several hours, or between 10^–4 to 10^–7 sec. It was found that the processes taking place at low temperatures and studied by method (a) differ from those observed at high temperatures by method (b), particularly in the lower activation energies and greater dispersion of the time constants. In addition to these two main relaxation processes a weak relaxation superposed over the main disaccommodation was found in ferrites with non-zero content of manganese. An analysis of the intensity of different relaxation effects showed the participation of Mn ions in these relaxation effects and it was found that both main relaxations are probably equivalent as regards the final steady state, to the creation of which they lead; they differ however in the mechanism of electron diffusion by which this state is realized. The main features of the different diffusion mechanisms are discussed.

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, , MnMg Mg _x Mn_1.15–x Fe_1.85O₄₊ . MgFe₂O_{4+ (}<0). ()- , () tg , , 0,5 sec , 10^–4–10^–7 sec. , , () , , (), , , . , . Mn , , , , , ; , , , . .

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In conclusion the author thanks Dr. J. Bro and K. Závta for valuable discussion and F. Vilím for carefully carrying out the measurements.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

РАСПAД170Lu

The spectrum of -radiation of the radioactive isotope¹⁷⁰Lu was studied by means of two Ge(Li) coaxial semiconductor detectors. Around 150-transitions belonging to the decay of¹⁷⁰Lu were found and their relative intensities were determined. Using the relative intensities of the conversional electrons from other works the internal conversional coefficients and the multipolarities of -ray transitions in the¹⁷⁰Yb nucleus were established. Twenty new excited levels of the¹⁷⁰Yb nucleus were introduced.A comparison of the experimental results with the predictions of the superfluid and Davydov models is made. The possible existence of I=O^– excited states in the level scheme of¹⁷⁰Yb is discussed.

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On leave fromFaculty of Mathematics and Physics, Charles University, Behová 7, Praha, Czechoslovakia.

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On leave fromNuclear Research Institute, Czechosl. Acad, Sci., e, Czechoslovakia.     

Invariants of the length spectrum and spectral invariants of planar convex domains

This paper is concerned with a conjecture of Guillemin and Melrose that the length spectrum of a strictly convex bounded domain together with the spectra of the linear Poincaré maps corresponding to the periodic broken geodesics in determine uniquely the billiard ball map up to a symplectic conjugation. We consider continuous deformations of bounded domains _s ,s[0, 1], with smooth boundaries and suppose that ₀ is strictly convex and that the length spectrum does not change along the deformation. We prove that ₀ is strictly convex for anys along the deformation and that for different values of the parameters the corresponding billiard ball maps are symplectically equivalent to each other on the union of the invariant KAM circles. We prove as well that the KAM circles and the restriction of the billiard ball map on them are spectral invariants of the Laplacian with Dirichlet (Neumann) boundary conditions for suitable deformations of strictly convex domains.Supported by Alexander von Humboldt foundation     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Experimental verification of the theory of the successive production of striations in a glow discharge

The properties of the wave of stratification in the plasma of the positive column in a glow discharge in neon are measured. The measurements are compared with the results of the theory of the successive production of striations and good agreement is found.

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In conclusion the author thanks M. Novák for help in measuring and evaluating the experimental results, and F. Kroupa and V. Krejí for carefully reading this paper and for valuable remarks.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Determination of random variations in ionosphere height from phase fluctuations of VLF signals

Conclusions A feature of our problem of restoration of fluctuations in ionosphere height is that the experimental data(t, _k) obtained at a fixed reception point are functions of time, whereas the function ₁(u, y₂) to be restored is a function of the coordinates. If we use the assumption that the irregularities migrate transversely, coordinate y₂ can be exchanged for time t. Restoration with respect to the second coordinate u=x_i–x₀/2 is in effect obtained by using data(t, _k) on some set of carrier frequencies.The resultant solution of the restoration problem is in the form of an expansion of ₁(u, y₂) in known functions determined from the observed data(t, _k). We have evaluated the solution accuracy, which depends on the overall power signal-to-noise ratio at all frequencies used. We have demonstrated that the restoration algorithm contains an optimum number (with respect to accuracy) of coefficients to be evaluated.Khar'kov Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 20, No. 8, pp. 1138–1145, August, 1977.     

Martensitic transformation and change in the lattice periods of methane in the low-temperature region

The study establishes the generality of the fcc-bct martensitic transformation mechanisms in methane and steels in which the martensite phase is in the form of two alternating types of structural domains (a packet of thin twins {110}101). This finding made it possible to decribe the crystallogeometric connection between the - and -phases in methane by the Kurdyumov-Sachs orientation relations and to explain the low-temperature lattice anomalies of -martensite.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 73–78, February, 1989.We thank L. V. Skibina and M. M. Chernik for their useful discussions of the work done in the course of the present investigation.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

gl q (n) and quantum monodromy

A generalized Toda lattice based on gl(n) is considered. The Poisson brackets are expressed in terms of a Lax connection, L=–() and a classical r-matrix, {₁,₂}=[r,₁+₂}. The essential point is that the local lattice transfer matrix is taken to be the ordinary exponential, T=e; this assures the intepretation of the local and the global transfer matrices in terms of monodromy, which is not true of the T-matrix used for the sl(n) Toda lattice. To relate this exponential transfer matrix to the more manageable and traditional factorized form, it is necessary to make specific assumptions about the equal time operator product expansions. The simplest possible assumptions lead to an equivalent, factorized expression for T, in terms of operators in (an extension of) the enveloping algebra of gl(n). Restricted to sl(n), and to multiplicity-free representations, these operators satisfy the commutation relations of sl _q (n), which provides a very simple injection of sl _q (n) into the enveloping algebra of sl(n). A deformed coproduct, similar in form to the familiar coproduct on sl _q (n), turns gl(n) into a deformed Hopf algebra gl _q (n). It contains sl _q (n) as a subalgebra, but not as a sub-Hopf algebra.     

Hydrogen density modes and coherent phasetransition in NbHx

We calculate the eigenmode spectrum of the elastic interaction of hydrogen dissolved in host samples of spheroidal geometry. This spectrum is employed to study the shape-dependent coherent - phasetransition in NbH_x. The results are compared with a recent Neutron radiography measurement.     

НИЗКОЧАСТОТНЫЕ КОЛЕ БАНИЯ ПРЯМОУГОЛЬНЫХ ПЛАСТИНОК ADP

- — . , - NH₄H₂PO₄,- ADP. ; - .