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1.
We study the physical content of the Snider quantum transport equation and the origin of a puzzling feature of this equation, which implies contradictory values for the one-particle density operator. We discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability, a condition which puts a limit on the validity of the Snider equation. In order to improve its range of application, we propose a reinterpretation of the equation as a mixed equation relating the real one-particle distribution function (on the left-hand side of the equation) to the free distribution (on the right-hand side), which we have introduced in a recent contribution. In its original form, the Snider equation is valid only when used to generate Boltzmann-type equations where collisions are treated as point processes in space and time (no range, no duration); in this approximation, virial corrections are not included, so that the real and free distributions coincide. If the equation is used beyond this approximation to generate nonlocal and density corrections, we conclude that the results are not necessarily correct.  相似文献   

2.
Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.  相似文献   

3.
The post-NEWTON ian approximation of the gravo-dynamics of planetary motions is given by a LAGRANG ian . For ε = 1/8, β = 3/2 und γ = ?1/2 this LAGRANG ian is the well-know function for EINSTEIN 's geodesic motion in an isotropic SCHWARZSCHILD metric. The perihel motion is given by TISSERAND 's formula   相似文献   

4.
In this article a particular solution of Heun equation is derived by making use of the Nikiforov‐Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods‐Saxon potentials).

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5.
In this note we give two new simple derivations of the good-cut equation, the equation which governs (complex) self-dual asymptotically flat gravitational fields. One of these derivations is remarkably simple, involving only a few lines. Our main point of interest, however, is in the second derivation. Though it is slightly more complicated, this method of derivation is almost certainly generalizable to cover real asymptotically flat space-times and thus lead to a generalization of the good-cut equation.  相似文献   

6.
A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77 critical.  相似文献   

7.
Van Hove's partial density matrix, E (t), in his generalized master equation is interpreted as a Wigner representation of two-time dyad for energy E and time t. This interpretation enables us to integrate the energyE in Van Hove's master equation. The resultant equation is of non-Markov type on two time parameters. Starting with this master equation, the derivation of quantum kinetic equations, including the second-order approximation in the density expansion, is discussed. The scaling of the quantum kinetic equation is examined in detail for a system in which particles interact through the delta shell potential. It is shown that the quantum kinetic equation, including three-particle scattering, may exist for the physical situations of low-energy scattering,high-energy scattering, and for resonance scattering for time scales of the system sufficiently separated. In deriving the quantum kinetic equation, a factorization theorem form-particle distribution functions is proved to arbitrary order in perturbation expansion.  相似文献   

8.
9.
Statistics of random world lines in a fixed electromagnetic field are considered. The equation for a vectorj i is obtained. This vector describes the density of random world lines in a pure ensemble. It is shown that in the two-dimensional space-time this equation coincides with the Dirac equation to within the terms of the order of magnitude of (/L)2 ( is Compton's wavelength,L is a typical length of the system).  相似文献   

10.
p-adic 4-theory and its discrete hierarchical version arerelated by integral functional equation. Simple renormalization procedure,using the solution of this functional equation, is discussed in themassless case.  相似文献   

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