Parity operator and quantization of δ-functions

In the Weyl quantization scheme, the -function at the origin of phase space corresponds to the parity operator. The quantization of a functionf() on phase space is the operator f(/2)W()dM, whereM is the parity andW() the Weyl operator.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

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.     

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     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

On the bimetric theory of gravitation

Rosen's bimetric theory is analyzed anew and is shown to have deficiencies if the space is assumed to be Riemannian. The problems are due mainly to the introduction of the flat metric , and the identification of the stress-energy tensor,T . It is indicated that if the Riemannian interpretation could be avoided the theory still holds promise as a viable theory of gravitation.     

Fractional Quantum Hall Effect and (2 + 1)-Dimensional Quantum Electrodynamics

By investigating the gap equation defining thefull electron propagator in the framework of (2 +1)-dimensional quantum electrodynamics, we derive thefractional quantum Hall effect at the filling factors = 1/2, 1/3, 2/5, 1/9. In particular, thevalue = 1/2 emerges as the lowest order of thedevelopment of this gap equation.     

Assignments of submillimeter emissions in difluoromethane pumped by12C18O2 and12C18O2 lasers

A FT spectrum of ₃, ₉ and ₇ of CH₂F₂ is recorded and assigned between 1030 and 1230 cm^–1. Coincidences with CO₂ lasers are investigated.Submillimeter emissions are unambiguously assigned by a loop procedure including only IR and SMM measurements. In some cases pseudo-loops are added using ground state computed energies. In spite of the large perturbations, an exact model for excited vibrational states is not needed to ascertain SMM assignments.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Far-infrared laser stark spectroscopy of CH3OH and13CH3OH

The high resolution laser Stark spectra of methanol and¹³C-substituted methanol have been studied up to Stark fields of about 60 000V/cm with the HCN and DCN lasers. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations. For methanol, the transitions J _k =7₅ 6₄ A, _t=0; J _k =11₄ 10₃ E _l , _t=0; and J _k =17₃ 16₂ E₂, _t=0 have been identified while the assignments for¹³C-substituted methanol are J _k =14₈ 15₇ A, _t=0; J _k =15₃ 14₂ A⁺, _t=0; J _k =10₇ 9₆ A, _t=0; and J _k =27₉ 27₈ E₁, _t=0. Zero-field frequencies for the assigned transitions are given with improved accuracy over those calculated from available molecular constants, especially for¹³CH₃OH.     

Основные соотношени я длн построения механических селект оров нейтронов

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Speculations on the cluster radius below the percolation threshold

We suggest the average radius of percolation clusters withs sites to vary belowp _c ass ⁰, where ₀ is the exponent for the mean radius of self-avoiding walks. This result gives the desired asymptotic behavior of the correlation function for percolation (connectivity) and is consistent with Leath's Monte Carlo data.     

The scattering of waves by a periodic surface

The paper derives a general formula for the scattering of electromagnetic (or sound) waves from a periodic, perfectly conducting (or perfectly rigid) surface. No restrictions are imposed on the angle of incidence, the size of the surface or the degree of roughness. Except for the basic Kirchhoff approximation, the method is exact. The results confirm, generalise or correct special cases obtained by more complicated methods.

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The progressive-stiffness method applied to XY4 molecules in the light of the theory of characteristic frequencies

It is shown that the success of progressive stiffness when applied to tetrahedral XY₄ molecules is due to the existence of three approximate characteristics. On separating the group of all angular coordinates for the ₄(F₂) vibrations, the noncharacteristic frequency and form coefficients a and _s are approximately equal to zero; on separating the group of all the valence coordinates for the ₃(F₂) vibrations, is approximately zero.     

State-to-state rotational energy transfer in OH (A 2Σ+, υ′=1)

State-to-state rotational energy transfer (RET) coefficients for thermal collisions of OH (A ²⁺, =1) with He, Ar, N₂, CO₂, and H₂O at 300K were determined from time-resolved laser-induced fluorescence (LIF) measurements. The RET coefficients are very similar in both qualitative behaviour and absolute magnitude to those measured previously for OH (A ²⁺, =0).     

Directed compact lattice animals: Exact results

The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we find=0 and =1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirm =1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the result =1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.     

Die Umwandlung der Fackelentladung in die Hochfrequenz-korona

Zusammenfassung Durch künstliche Senkung der Temperatur der Fackelentladung geht diese Entladung in eine Hochfrequenz-Korona über. Wenn die Temperatur der Entladung sinkt, wächst in ihr die elektrische Feldstärke; dadurch werden die Bedingungen des thermodynamischen Gleichgewichts gestört und es beginnt der Übergang von der thermischen zur elektrischen Ionisation. Die Erläuterung wird durch die Spektralanalyse und das Studium der Fackelentladung mittels einer zeitlich zerlegten Photographie ergänzt.

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Abschließend danke ich Herrn Prof. V. Kunzl für seine anregenden Hinweise.     

Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation,anomalous exponents,and depletion zone

An experimental investigation of one-dimensional, diffusion-limited A+BC chemical reactions is reported. The persistence of reactant segregation and the formation of a depletion zone is observed and expressed in terms of the universal time exponents: (motion of the boundary zone), (width of instantaneous product formation zone), (rate of instantaneous local formation of product), (rate of instantaneous global formation of product), etc. There is good agreement with the recently predicted and/or simulated values:=1/2,=1/6,=2/3,=1/2, in contrast to classical predictions (=0,=1/2,=0,=–1/2). Furthermore, classically the segregation would not be preserved and there would be no formation of a depletion zone and no motion (just dissipation) of the reaction zone. We also discuss the relations to electrode oxidation-reduction reactions, i.e., A+CC where C is a catalyst, electrode, or trap.     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.