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1.
Classical and quantum statistical mechanics are compared in the high temperature limit =1/kT0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as 2 for smooth potentials and as for potentials with hard cores.Supported in part by FAPESP. Permanent address: Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil  相似文献   

2.
If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature become small. Thus, microscopic particles like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2)3 are reduced to points in the phase space, the partition functionTr{exp(–) for N identical bosons (fermions) approaches (2)–3N(N!) ... d3r1 d3p1 ... d3rN d3pN exp(–H). The two factors, (2)–3N and (N!)–1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles.  相似文献   

3.
Within the framework of the conditions ; » –1 ( –1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < o, including the jump () for ( – o + ) 0T as well as peaks in the function () at the points s=s (s=1, 2, 3,...). The value (1) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.  相似文献   

4.
The magnetic moment of the23Mg (I =3/2+, T1/2=11.3 s), has been determined as |(23Mg)|=0.5364±0.003 µN by use of -NMR detection with the recoil polarization obtained through a low energy nuclear reaction.  相似文献   

5.
Current/voltage (CV) characteristics of solid solutions Pb1–xSnxTeln (with D. 22x3. 24 and 0.2NIn1.0 atomic percent) were studied at He temperatures, in presence of background at 300K. Also the photoconductivity of these materials was measured in conditions of background screening and illumination at wavelengths 100µm and 2mm.CV-characteristics are interpreted within a model of two-electron capturing by Jahn-Teller centers. Photoconductivity in millimeter and submillimeter wavebands, having relaxation times less than 10–5 sec, is related with heating of electronic gas in process of electromagnetic power absorption by the free carriers.  相似文献   

6.
Tetragonal (GdxNd1–x)1+ Fe4B4 alloys have been investigated for 0.2x1 by Mössbauer spectroscopy, using the 86.5 keV155Gd resonance. The Gd quadrupolar interaction e2qQ=12.67(5) mm/s for x=1, nearly independent of x, is the largest observed to date in metallic compounds of Gd. A crystal field term A 2 0 =–2450±50 K/a 0 2 is inferred. This quadrupolar interaction shows some dispersion increasing when x decreases, reflecting the quasi incommensurate nature of the (Gd,Nd) and Fe+B sublattices in the (GdxNd1–x)Fe4B4 structure (=0.109 for x=0 and =0.139 for x=1). The hyperfine field is perpendicular to the c axis for x0, but no unique direction is obtained for x=0.  相似文献   

7.
A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x 1)–(T, x 2). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 –1 cm–1, at least up to (4.2 K,x)1350 –1 cm–1 and forT60 K. But it is absent, if (4.2 K,x)180 –1 cm–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx c 0.14. On the other hand, the presence of a term proportional toT 1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.  相似文献   

8.
The oxidation state of Fe and Ti ions implanted in yttria stabilized zirconia (YSZ) was studied by XPS (X-ray photoelectron spectroscopy) in combination with depth profiling using Ar+ sputtering. In the as-implanted state of the sample Fe was found to be present as Fe3+, Fe2+ and as metallic Fe0. This is in agreement with earlier conversion electron Mössbauer Spectroscopy measurements. For Ti-implanted YSZ in the as-implanted state the majority of the Ti is present as Ti4+, Ti3+, and Ti2+ ions, while a part of the Zr cations is present in the divalent oxidation state (Zr2+). After oxidation in air, the Fe and Ti ions are present only in the valence three and four oxidation states, respectively.  相似文献   

9.
LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , N , N the modular operators to (, ), (N, ), resp (N , ). Assume now -it N it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups it , N ir , N is ,t, r, s generate a unitary representation of the group S1(2, )/Z 2 of positive energy.Another result is related to two half-sided modular inclusions (1 , ) and (2 , ). Under proper conditions the three modular groups it , 1 ir , 2 is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.  相似文献   

10.
By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.  相似文献   

11.
For a -dimensional system of particles with the two-body potentialq(r)+ v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.  相似文献   

12.
Interphase boundaries between 3C SiC grains and two different -Si3N4 morphologies in Si3N4–SiC composites have been studied by transmission electron microscopy. In general, boundaries between small -Si3N4 intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas boundaries between large -Si3N4 grains and adjacent SiC grains were invariably covered with thin intergranular films. Orientation relationships approximating to [110] 3C SiC [0001] -Si3N4 and (001) 3C SiC (10 0) -Si3N4 were found to dominate between 3C SiC grains and the intragranular -Si3N4 precipitates, but there was no evidence of any favoured orientation relationship between the large -Si3N4 grains and adjacent SiC grains. The rationale for special orientation relationships arising when there is no intergranular film present at 3C SiC–-Si3N4 interfaces is explored geometrically using the near-coincidence site lattice model, with the significant result that the dominant orientation relationships between 3C SiC grains and the intragranular -Si3N4 precipitates have low misfits relative to all other possible orientation relationships between 3C SiC and -Si3N4.  相似文献   

13.
For potentialsV=V(x)=O(|x|–2–) for |x|,x3 we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+Vz 2)–1 has an analytic continuation from + to {kOImk|<b} as an operator from b ={f=e b|x| g|gL 2(3)} to b . Based on this, we define for potentialsW=o(e –2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)  相似文献   

14.
A polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e for every self-intersection and e /(2d) for every self-contact to the probability of an n-step simple random walk on d , where , >0 are parameters. It is known that for d=1 and > the chain collapses down to finitely many sites, while for d=1 and < it spreads out ballistically. Here we study for d=1 the critical case = corresponding to the collapse transition and show that the end-to-end distance runs on the scale n = (log n)–1/4. We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size n times a constant. Moreover, we derive the asymptotics of the partition function.  相似文献   

15.
The entire sodium ion content of sodium alumina (Na1.67Mg0.67Al10.33O17) can be replaced with a variety of lanthanide ions by simple diffusion reactions at moderate temperatures (500–700°C). Lanthanide alumina crystals are hard, clear, chemically stable, and have well-defined crystal structures. The fluorescence spectrum of Nd3+ in alumina is similar to that in YAG. The lifetime of the4 F 3/2 state of Nd3+ in completely-exchanged alumina (350s at 1021 Nd3+ cm–3) is about 45% longer than in YAG (240s at 1020Nd3+ cm–3). The lanthanide aluminas may be of considerable interest as new phosphor and laser host materials.  相似文献   

16.
The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.
, . , . , , . , . .
  相似文献   

17.
In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.  相似文献   

18.
The microstructure of fiber-like SiC/Si3N4 composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si3N4 composite particulate consisted of a-SiC core and a -Si3N4 outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si3N4 composite particulate, a crystal relationship of (111)-SiC | (102) -Si3N4 and (111)-SiC (114) -Si3N4 was identified; in the other type of the SiC/Si3N4 composite particulate, a crystal relationship of (111)-SiC (001) -Si3N4, and (111)-SiC (101) -Si3N4 was observed.  相似文献   

19.
The paramagnetic state (+e) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: Si = 1.45(3) s, Te = 12.5(8) s at 290 K, Te = 12(2) s at 250 K.  相似文献   

20.
Duality invariance of the Dirac-Schwinger charge-symmetric theory for electromagnetism leads one to consider the complex-valued amplitudes 1 and 2 for the separation between the magnetic monopole and quarks in the logarithmic charge plane. It is observed that the orthogonality relation on the latter amplitudes, Re( 1 * 2)=0, is equivalent to the equation (ln 9 –1)(ln 2)=(1/2) 2, which is indeed satisfied by the experimental value fora to within 0.027%. In addition to fixing the unit of electric charge at a primary physical value, the orientation of 1, 2 may also prescribe the Cabibbo angle to have the theoretical value 12.4438.  相似文献   

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