Method of green's functions in the theory of quantum kinetic equations. II

The kinetic and antikinetic equations are obtained for the single-particle Wigner function in the context of the method of Green's time-temperature functions for an inhomogeneous system of weakly interacting particles situated in a time-dependent electric field. The kinetic equation is derived here from the equation of motion for Green's function, satisfying the causality condition.     

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. In contradistinction to former formulations where the Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum (Fermi-Dirac or Bose-Einstein) statistics of the quasiparticles. Provided that small deviations from the thermodynamical equilibrium only are present, the boundary conditions are linearized, and then their “renormalization” is investigated in case of the elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, suggest that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying the Maxwell-Boltzmann statistics.     

Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields

Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.     

Covariant calculation of effective cross sections in quantum electrodynamics. I

A special representation of the amplitudes of the electron and positron wave functions is used to derive a method for calculating the S-matrix elements. This method is analogous to that proposed in a previous paper by the author, but it gives equations in covariant notation.     

Adiabatic expansions of green's functions in electromagnetic and gravitational fields. Radiative corrections

A solution of Maxwell's equations is constructed that describes a homogeneous electromagnetic field in a curved space-time in the lowest adiabatic approximation in the curvature. The Green's function for Dirac particles in this field is constructed to the same accuracy. It is shown that in the case of a super strong magnetic field the main approximation is the two-dimensional approximation, moreover, the gravitational correction is determined by a single component of the curvature tensor R₁₂₃₀. The mass operator of the electron is calculated in this approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 32–38, February, 1986.     

Instability of layered quantum liquids: 5. Collective modes at low density

We calculate the plasmon dispersion of electron superlattices by taking into account many-body effects via the local-field correction. For small electron density we find a weak roton structure in the dispersion of optical plasmons. Landau damping is strongly enhanced by many-body effects, especially for acoustical plasmons. We compare with experimental results of high-T _c superconductors. Some experiments are suggested.     

Method of Green's functions in the theory of quantum kinetic equations. I

The solution of the dynamic equation is strongly degenerate for systems with an infinite number of degrees of freedom. A causality principle is stated, whereby the particular solution of the dynamic equation, which is at the same time a solution of the kinetic equation, can be selected. The principle is applied here to the multitime formalism of correlation functions. A basis is thus obtained for the method of Green's time-temperature functions in the theory of kinetic equations.The author thanks all those who have discussed the topics in this paper with him, particularly V. L. Bonch-Bruevich, D.A. Kirzhnits, V.M. Fain, E.S. Fradkin, and A. S. Shekhter.     

The partial distribution functions and effective pair potentials of some H-bonded liquids from diffraction data

The partial structures and distribution functions are directly linked to structural model of molecular liquids. The comparative study of partial distribution function of different hydrogen-bonded liquids gives the information that hydrogen-bonding is stronger in alcohols than in water and ammonia. The effective pair potential is directly related to the pair correlation function. The comparative study of such potentials for different hydrogen-bonded liquids gives some characteristic features.     

Equilibrium properties of a multi-component ionic mixture: I. Sum rules for correlation functions

Equilibrium statistical methods are used to derive sum rules for two- and three-particle correlation functions of a multi-component ionic mixture. Some of these rules are general consequences of the electrostatic character of the interaction, whereas others depend on specific thermodynamic properties of the system. The first group of rules follows from the BBGKY hierarchy and a clustering hypothesis for Ursell functions. The sum rules of the second group are obtained by describing the system with the help of a restricted grand-canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant.     

Electron states,effective masses and transverse effective charge of InAs quantum dots

The electron energy levels, direct energy band gaps, electron and hole effective masses as well as the transverse effective charge of InAs spherically shaped quantum dots have been studied as a function of the quantum dot radius considered as varying from 1 to 10 nm. The direct energy band-gap as well as the electron and heavy hole effective masses decrease non-linearly with increasing the quantum dot radius. Nevertheless, the transverse effective charge is found to increase with increasing the quantum dot radius. It is concluded that the quantum confinement has a strong influence on all the studied physical quantities for quantum dot radius below 6 nm. The results of the present contribution show that more opportunities can be offered to tailor desired optoelectronic properties surpassing those presented by bulk InAs materials.     

G. N. Lewis' atom and quantum Monte Carlo studies of liquids

Liquids that involve changes in electronic structure are difficult to simulate using pairwise additive forces. In this paper we use a semiempirical model of the internal structure of atoms in order to simulate simultaneously electronic and nuclear dynamics of fluids. The proposed excitonic phase of mercury is critically examined with these models.     

Instability of layered quantum liquids: 4. Intraplane and interplane correlations

We calculate the local-field correctionsG(q, q _z) f electron superlattices with interlayer distanced in order to describe many-body effects. A generalized Hubbard expression for the local-field correction is derived. The sum-rule version of the self-consistent approach for the local-field correction is developed and used to discuss the effects of exchange and correlation. The RPA-parameterr _s and the ratiod/a ^* determine the many-body effects.a ^* is the effective Bohr radius. The stability region for the Fermi liquid behavior of the layered electron gas is discussed: (i) forda ^* the critical RPA-parameterr _sc1 is determined by exchange andintraplane correlation effects, (ii) forda ^* withr _sc1 correlation effects are small and the instability point is mainly determined by exchange effects, (iii) forda ^* withr _sc<1 exchange andinterplane correlation effects are both important for the instability point. Our results are important for high-T _c superconductors, organic superconductors and semiconductor superlattices.     

Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input-output functions, tuning curves, and response phases

Basilar membrane (BM) velocity was measured at a site 3.5 mm from the basal end of the chinchilla cochlea using the M?ssbauer technique. The threshold of the compound action potential recorded at the round window in response to tone bursts was used as an indicator of the physiological state of the cochlea. The BM input-output functions display a compressive nonlinearity for frequencies around the characteristic frequency (CF, 8 to 8.75 kHz), but are linear for frequencies below 7 and above 10.5 kHz. In preparations with little surgical damage, isovelocity tuning curves at 0.1 mm/s are sharply tuned, have Q10's of about 6, minima as low as 13 dB SPL, tip-to-tail ratios (at 1 kHz) of 56 to 76 dB, and high-frequency slopes of about 300 dB/oct. These mechanical responses are as sharply tuned as frequency-threshold curves of chinchilla auditory nerve fibers with corresponding CF. There is a progressive loss of sensitivity of the mechanical response with time for the frequencies around CF, but not for frequencies on the tail of the tuning curve. In some experiments the nonlinearity was maintained for several hours, in spite of a considerable loss of sensitivity of the BM response. High-frequency plateaus were observed in both isovelocity tuning curves and phase-frequency curves.     

Relativistic kinetic theory of quantum systems: I. Wigner functions for a relativistic spin-12 system

For a dilute and nondegenerate relativistic spin-$\text{1}\text{2}$ system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner functions. The transformation properties of the latter under Lorentz transformations are discussed.     

Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.     

Gauge transformations and quantum mechanics I. Gauge invariant interpretation of quantum mechanics

Quantum mechanical operators are interpreted according to their equations of motion. Operators representing physical quantities which have classical analog are constructed by requiring that the quantum and the classical (i.e., Newtonian) equations of motion have a term by term correspondence. Of special importance to the interpretation of quantum mechanics is the particle's energy operator. In the presence of a time-varying electric fieldE, the particle's energy operator is constructed so that its time derivative is the power operatorJ · E (J being the current operator). This interpretation of operators, such as the particle's energy operator, is gauge invariant despite the possible explicit dependence on electromagnetic potentials of the operators concerned. A gauge invariant interpretation of quantum mechanics is obtained by expanding the wave-function (in an arbitrary gauge) in the orthonormal set of eigenfunctions of the particle's energy operator (in the same gauge) and by interpreting the resulting expansion coefficients as probability amplitudes. This formulation possesses all the traditional gauge freedom and contains no gauge ambiguity. (Here, by gauge invariance we also mean that the dependence on paths in the DeWitt-Mandelstam formalism and on the procedures for path averaging in the Belinfante-Rohrlich-Strocchi formalism does not occur.) In particular, probability amplitudes and transition matrix elements are gauge invariant, and the transition matrix elements between states of different energies are proportional to the corresponding matrix elements of J · E, rather than J_μA_μ. Lamb found experimental evidence that led to the conclusion that “the usual interpretation of probability amplitudes” was gauge dependent and was correct only in the gauge in which the interaction Hamiltonian was of the form of the electric dipole interaction −er · E(0, t), instead of the usual −eA(0, t) ·p/mc. It is shown here that the gauge invariant formulation for bound systems derives the electric dipole interaction in any arbitrary gauge as the result of the long wavelength and lowest order approximation of fields. For a quantum system interacting with a precessing magnetic field, the Güttinger-Schwinger procedure of quantizing the system along the instantaneous magnetic field has been known to yield the correct transition probabilities during the interaction. This quantization procedure follows directly from the gauge invariant formulation. The electric and the magnetic multipole interactions appearing in the gauge invariant formulation directly correspond to terms in the classical Poynting theorem. The gauge invariant magnetic multipole interactions differ from their counterparts in the conventional formalism. For example, the gauge invariant magnetic dipole interaction involves the time derivative of the magnetic field. This result is shown to be consistent with the Poynting theorem. Although the gauge invariant interpretive scheme proposed here is formulated for a nonrelativistic, spinless charged particle, the extension to the Dirac equation is straightforward.     

Ionization energies of liquids from energy distribution,quantum yield and second derivative curves

The energies of the lowest ionization band of eight liquids of low vapor pressure are determined from energy distribution curves (EDC), quantum yield spectra (collected electrons per incident photon as a function of photon energy), and second derivative curves (SDC) of retarding potential curves. Threshold energies from EDCs and quantum yield spectra agree if one takes into account a 0.15 e V shift caused by the spectrometer's rather low resolution and a small difference (0.15 eV or less) resulting from the use of approximate extrapolation methods. Threshold energies from EDCs and SDCs agree to within 0.1 eV after correction for the half-width of the high-energy branch of SDCs. Multiple ionization bands are exhibited by the SDCs of some of the liquids, and the observed splittings agree well with the results from gas-phase UPS spectra. A new spectrometer for the measurement of EDCs of liquids is described. The liquids studied are 6-chloro-1-hexanol, 2-ethyl-1-hexanol, ethylene cyanohydrin, ethylene glycol, 1,5-pentanediol, tetraglyme, triethylene glycol and tetraethylene glycol.     

On quantum group invariant spin chains at roots of unity and two-point correlation functions

We review the recent developement in the investigation of quantum group invariant two-point correlation functions for quantum spin chains. Starting from the algebraic definition of invariant two-point operators which are already known for theXXZ Heisenberg chain, we compute the corresponding correlation function for theXY chain. The uniqueness and the physical relevance of invariant correlation functions is discussed.