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1.
Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical 2 grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.  相似文献   

2.
The averaged retarded electron Green functionG +(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG + (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about F() in quasi-1d conductor KCP is found  相似文献   

3.
Extending earlier work of Littlewood (1987) a theory for the collective mode (Fröhlich mode) response of weakly pinned charge density waves (CDW) is given. Long range Coulomb interaction is incorporated in both a proper definition of the measured ac conductivity CDW() and in the Fukuyama-Lee-Rice treatment of phason dynamics. The frequency and wave number dependent quasi particle resistivity is shown to appear only in the internal phason lines in the perturbation expansion of the impurity averaged phason propagatorD ren. Quantitative results for CDW() are evaluated within the self-consistent Born approximation toD ren in three spatial dimensions taking anisotropy into account. Besides the low frequency relaxation mode we find a significant effect of the longitudinal optical phason LO on the Fröhlich mode pinning frequency when descreening sets in at low temperatures. This is yet another manifestation of selection rule breaking by inhomogeneous pinning and establishes the special role that LO plays in the dynamics of CDW. An explicit analytical formula for CDW() is given and discussed in some detail including the important analyticity properties. Available measurements of the linear ac response in a wide range of frequencies and conductivities are compared with the theory and found to agree with the theoretical predictions supporting the concept of weak pinning in CDW.  相似文献   

4.
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 + 14 3), inverse Raman scattering ( A + 1 + ), and cascading light up-conversion of the type 1 + (i) R (i+1).  相似文献   

5.
The coherent potential approximation (CPA) is applied to the investigation of the off-diagonal disorder effect on the AC conductivity of the disordered binary alloys, due to intraband absorption. The frequency dependence of the conductivity () is numerically calculated for various parameters describing the alloy and various positions of the Fermi level in the band. The anomalous behaviour in the frequency dependence of the conductivity is found. The parameter () — optical relaxation time, used by many researchers, in this case is invalid.  相似文献   

6.
The temperature-frequency dependences of the conductivity (), capacitance (C), and dielectric-loss coefficient () have been measured for metalglass film (composition As30Ge10Si12Te48)-metal structures in an alternating electric field. The glass film was obtained by the method of radiofrequency sputtering in an argon atmosphere, and the top and bottom molybdenum electrodes by thermal evaporation in vacuum. The measurements were made in the frequency range 4·102–2·104 Hz at temperatures 209–299°K. The relaxation component r= of the conductivity for T < 240°K and high frequencies does not depend on the temperature (T) and is proportional to 0.8. At higher temperatures, r() is described by a complicated curve, which has at low frequencies the behavior 2 and goes over to saturation at large values of . In this range of frequencies and for positive temperatures r exp(E/T), where E 0.45 eV. The frequency-temperature dependences of r, C, and ' are interpreted on the basis of Fröhlich's model. The calculated and experimental curves are compared. It is assumed that the loss of relaxation type is due to two processes, one of which is governed by carrier hops between localized states near the Fermi level and is predominant at low temperatures. The other is determined by carrier hops between the same states through the valence band and is predominant at positive temperatures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 35–39, September, 1980.  相似文献   

7.
Third order harmonic mixing voltageE 0 in case of frequency matching, =21=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.  相似文献   

8.
We study the structure factor for a large class of sequences of two elementsa andb such that longer sequences are generated from shorter ones by a simple substitution rulea 1(a, b) andb 2(a, b), where the's are some sequences ofa's andb's. Such sequences include periodic and quasiperiodic systems (e.g., the Fibonacci sequence), as well as systems such as the Thue-Morse sequence, which are neither. We show that there are values of the frequency at which the structure factors of these sequences have peaks that scale withL, the size of the system likeL (). For a given sequence a simple one- or two-dimensional dynamical iterative map of the variable can easily be abstracted from the substitution algorithm. The basin of attraction of a given fixed point or limit cycle of this map is a set of values of at which there are peaks of the structure factor all of which share the same value of. Furthermore, only those values of which are in the basin of attraction of the origin can have()=2. All other peaks will grow less rapidly withL. We show how to construct many sequences which, like the Thue-Morse sequence, have noL 2 peaks. Other qualitative features of the structure factors are presented. Our approach unifies the treatment of a large class of apparently very diverse systems. Implications for the band structure of these systems as well as for the analysis of sequences with more than two elements are discussed.  相似文献   

9.
A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency OSC inherent in the model. In the present investigation a current noise of strengthT N proportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: OSC,T N ,and a crossover frequency OSC. Results are evaluated for the ac conductivity (;E 0,E ) as function of frequency , dc bias electric fieldE 0 and ac signal field strengthE . ForE 0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E 0,E =0) vs.E 0, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT N .The results stress the need for a complete Fokker-Planck treatment sinceT N is not simply related to the line width.  相似文献   

10.
An investigation of the evolution of the free induction signal as a function of /1 is made, where is the nonhomogeneous width of the magnetic resonance line of a double-level spin system and 1 = B 1, where is the gyromagnetic ratio and B 1 is the amplitude of a radio-frequency field. It is shown that two stages can be distinguished in the evolution of the free induction signal on excitation of the spin system by a large-area pulse (1 t 1 >> 1) of length t 1. In the first stage (t t 1), reversible relaxation leads to an oscillatory and exponential dip. With a fixed 1, an increase in practically does not change the frequency of oscillations and the signal amplitude decreases. In the second stage (t > t 1), there is only an exponential decay of the signal at a rate equal to . It is demonstrated that, with nonresonant excitation, the coherent properties of the free induction signal manifest themselves in the formation of a single-pulse echo. The theoretical results are in good agreement with the experimental data obtained in nuclear magnetic resonance for protons in glycerin. The conclusion is drawn that the theorem of coherent transients in double-level systems with a finite nonhomogeneous width of the line is valid.  相似文献   

11.
Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA g B u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.  相似文献   

12.
We employ QCD sum rules to calculate the coupling constant g by studying the three point -correlation function. Our result complements the analysis of this coupling constant utilizing the experimental value of the 00 decay rate studied within the framework of chiral perturbation theory including vector meson and meson intermediate states.  相似文献   

13.
A theory for the conductivity of a three-dimensional regular lattice-gas of charged particles is formulated. The hopping-motion of the particles is described by a masterequation. From the density-response-function at long wave-lengths the dynamic conductivity () is derived. Its high-frequency limit () and the corresponding activation energy are calculated by using the mean-spherical approximation for the corresponding static correlation functions. For systems with weak or intermediate coupling the dynamic part of the conductivity is computed within mode-coupling theory. The results are compared with hopping models based on short-range interactions.  相似文献   

14.
We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesW n, n+1 which are independently distributed according to a probability density(w). For two general classes of(w), we rigorously determine the asymptotic behavior of the relevant single site Green function 0() near=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivity() uniquely to 0(–i), and we conjecture that the resulting asymptotic behavior for() is also exact. The critical exponents associated with the various asymptotic laws depend on(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments.  相似文献   

15.
The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x 2,x 3) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x 2,x 3) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.  相似文献   

16.
Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x2, x3 surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.  相似文献   

17.
For a wide range of crystalline materials and glasses, it has been shown that, at low temperatures, the ac conductivity () is proportional to frequency , corresponding to a loss per cycle that is independent of frequency. This paper explores the features of this constant-loss behavior, showing that it is a truly bulk phenomenon, that it is only slowly dependent on temperature (i.e., not activated) and, in the case of glasses, that it does not give rise to a mixed alkali effect. The pair approximation model with hopping over an asymmetric barrier is fitted to some of the results, but doubts remain as to whether this model is appropriate for systems with low defect concentrations.  相似文献   

18.
Resonant third-order sum-frequency mixing of continuous-wave visible and ultraviolet laser light is investigated in the metal vapors of Sr, Ca, Mg, and Zn. The laser radiation (with the frequencies 1, 2, and 3) is generated by single-mode dye- and argonion lasers. The third-order nonlinear susceptibility is enhanced by tuning the laser frequencies 21 or 1+2 to a two-photon resonance. The wavelength of the generated coherent VUV radiation (with the frequency VUV=31, VUV=21+2 or VUV=1+2+3) is tunable in spectral regions between 133 and 217 nm. For most conversion processes an additional enhancement of the nonlinearity is provided by an autoionizing level or by a highly excited state close to E=VUV. With laser powers of 0.2–3 W the power of the generated sum frequencies is in the range of 5×105–6×1010 photons s–1 (0.5 pW–60 nW).  相似文献   

19.
The wave function of the ground state of the helium atom is derived by the variational-iteration technique with the Hylleraas-Eckart momentum representation of the wave function as a first approximation. This function is used to calculate the ratios of the differential cross sections (n=2)/(n=1) and (2p)/(2s) for helium ionized by an electron impact. The calculation is conducted in the plane-wave impulse approximation for symmetric noncoplanar kinematics of the (e, 2e) process. The results are compared with previous calculations in which variational wave functions of the configurational interaction type were used. Good agreement with the existing experimental data for (n=2)/(n=1) is obtained. The results are generalized to helium ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 45–50, December, 1986.  相似文献   

20.
Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of electric or magnetic type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an antiparticle. Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (, 0, ,l, m), where 0 is the mean of the angular frequencies of the plane waves making up the configuration, is the variance of those frequencies, is a positive constant with dimensions of action, andl, m are angular momentum quantum numbers withl a positive integer andm an integer such that ml. The rest energy of the particle is 0, its spin is m, and its lifetime is of the order of 1/. Its antiparticle has 0 replaced by –0.  相似文献   

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