摘要:

AbstractFrom the notion of equivalence relation and classes induced by them, the sets of points related by reversible processes restricted suitably are shown to be disjoint. By definition, each of thr above sets is arcwise‐connected and so connected by HAUSDORFF'S theorem. Adiabatic processes are defined to be those in which, changes of states of a system are entirely by changing the deformation coordinates. First and second laws of thermodynamics are introduced just after CARATHÉODORY. Then by arguments of abstract mathematics every points in an r. a. set in an (n+ 1)‐dimensional space has been shown to gave a neighbourhood homeomorphics to an‐dimensional sphere, i. e., an r. a. set is ann‐dimensional manifold having one‐to‐one correspondence with the deformation space. Thus, the existance of reversible adiabatic surfaces has been

ISSN:0003-3804    

DOI:10.1002/andp.19694770702

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractSpherically symmetric vacuum solutions of TREDER'S gravitation theory are investigated and the problem of the gravitational collapse in this theory is discussed. It is shown that the surfacer=a+bof the solution\documentclass{article}\pagestyle{empty}\begin{document}$ ds^2 \, = \, - \,\left({\frac{{r - a - b}}{{r - a}}} \right)^2 \,dt^2 \, + \,\frac{{r^2 }}{{(r - a)^2 }}dt^2 \, + \,r^2 \,(d\Theta ^2 \, + \,\sin ^2 \,\Theta d\varphi ^2) $\end{document}is an impermeable physical barrier.

ISSN:0003-3804    

DOI:10.1002/andp.19694770703

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractExtending the method developed in a previous paper [1] the correlation functions both for electric field strength and intensity are calculated. In the latter case the result is obtained quite easily by solving a differential equation. In the first case, on the contrary, a detailed knowledge of the photon creation operatorb+is necessary, especially of the different temporal behaviour with respect to phase and amplitude. In the main, the results are in agreement with those published by other authors. Of special interest is the result that the damping constant for intensity correlations tends to the value corresponding to the case of thermal radiation, in the region far from threshold.In addition, the ansatzb+= (ro+ ϱ) exp{iχ(t)} (roc‐number) introduced by HAKEN is discussed from a quantum mechanical point of v

ISSN:0003-3804    

DOI:10.1002/andp.19694770704

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractWe construct the energy‐momentum tensor of a pole‐dipole‐like mass distribution in a RIEMANNian space‐time and derive the appropriate equations of motion, the manifest covariance being achieved by means of the bilocal vector of geodetic parallel displacement. In a theory with a second flat background metric the equations of motion are also formulated covariantly in terms of surface integrals. The paper concludes with a brief discussion of the equations of motion of the spin p

ISSN:0003-3804    

DOI:10.1002/andp.19694770705

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractA spinning three‐leg propagating along and being orthogonal to a time‐like world line in a RIEMANNian space‐time is associated with a pole‐dipole‐like mass distribution. This is demonstrated by variation of the appropriate action functional with respect to the metric. The interaction with the metrical field automatically guarantees the stationarity of the action functional against variations of the kinematic variables, hence the equations of motion follow from the field

ISSN:0003-3804    

DOI:10.1002/andp.19694770706

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractThe “diagonal” weighting function Φ(α) of the density matrix expressed in the coherent states is examined being decomposed in the base of the Laguerre polynomials. A criterion of the convergence inL2‐space is obtained. This decomposition is also studied as a generalized function. The equivalence of the FOCK and SUDARSHAN representations of the density matrix is proved using present formulae. Some theorems from the moment theory are applied and general assumptions are given under which the Φ‐representation is an ordinary non‐negative function or a generalized function whose support is composed of a finite number of points. The results are demonstrated on the examples of the thermal and coherent fields, their superposition and on the Fock state of the field. The decomposition of the Φ‐function in terms of the LAGUERRE polynomials is useful for approximative determination of the Φ‐function from a finite

ISSN:0003-3804    

DOI:10.1002/andp.19694770707

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractFollowing the method of MORITA the calculation of the partition function for quantum plasmas is reduced to the corresponding classical problem. The free energy of low density quantum plasmas is represented by a cluster expansion. The cluster integrals of second and third order are given in form of integrals over the two particle or three particle SLATER sum respectively. The first corrections added to DEBYE'S limiting law of the free energy for low density plasmas are expressed by the limit of an integral over the binary SLATER sum. Two explicit expressions for the binary SLATER sum are given in terms of the energy eigenfunctions or the momentum eigenfunctions respectively.

ISSN:0003-3804    

DOI:10.1002/andp.19694770708

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractIn part I of this paper the cluster integral of second order for quantum plasmas was given by a definite integral over the SLATER sum of two particles. Here this integral is calculated exactly, using the method of perturbation theory with respect to the interaction parametere2for the orderse2kwithk≦ 3, and the method of scattering phase shifts for the orderse2kwithk≧ 4. The cluster integral of second order is expressed by quantum virial functions and exchange virial functions. These functions are expressed in form of integrals over the complex energy plane. From these integrals TAYLOR expansions and asymptotic representations of the virial functions are derived. In the case of lower temperatures, the semiclassical formulae derived by LARKIN and the author are obtained, using the first terms of the asymptotic representat

ISSN:0003-3804    

DOI:10.1002/andp.19694770709

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractThe theoretical results of the macroscopic motion of a plasma are reported being produced by a nonlinear interaction with laser radiation. Consequences are discussed for a radiation confinement of laser produced plasmas.

ISSN:0003-3804    

DOI:10.1002/andp.19694770710

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

ISSN:0003-3804    

DOI:10.1002/andp.19694770701

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY