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1.
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
2.
R. Lang 《Communications in Mathematical Physics》1979,65(2):129-149
We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR
1. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R
–1, and all ergodic initial distributions with an intensityI()R
–1 converge weakly ast to the extreme equilibrium state with the same intensity. 相似文献
3.
Existence and uniqueness results are established for solutions to the Becker-Döring cluster equations. The density is shown to be a conserved quantity. Under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined. Denoting the set of equilibrium solutions byc
(), 0
s
, the principal result is that if the initial density 0
s
then the solution converges strongly toc
(o), while if 0 >
s
the solution converges weak* toc
(s). In the latter case the excess density 0–
s
corresponds to the formation of larger and larger clusters, i.e. condensation. The main tools for studying the asymptotic behaviour are the use of a Lyapunov function with desirable continuity properties, obtained from a known Lyapunov function by the addition of a special multiple of the density, and a maximum principle for solutions. 相似文献
4.
Vladimír Syneček 《Czechoslovak Journal of Physics》1954,4(4):472-476
On the basis of the non-negativity for electron density in a crystal (r), the existence of inequalities and equalities between the coefficients of the Fourier expansion of the function (r) (r+t) is shown, which limits the choice of phases of the structure factors. 相似文献
5.
Charles Radin 《Communications in Mathematical Physics》1971,23(3):189-198
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
6.
We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ=
x
y
. Both functions showt
–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt
–2 andt
–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters. 相似文献
7.
Dynamical properties of valence-fluctuating systems are studied at absolute zero of temperature. The self-consistent perturbation theory developed for rare-earth impurity systems is used with some refinement. The theory takes account of the orthogonality catastrophe caused by hybridization of 4f and conduction electrons. Extensive numerical results are reported for the 4f-electron density of states 4f
() and the dynamical magnetic susceptibility (). The results cover both the intermediate-valence and nearly integral-valence regimes of a model Ce impurity system. The present theory gives reasonable overall feature of dynamics including a sharp peak in 4f
(0) in the Kondo regime. However, the low-frequency limit of dynamical quantities is not consistent with the Fermi-liquid property. It is shown that interpolation of the present results and those by the Fermi-liquid theory is possible. Hence accurate dynamical information is obtained over a wide excitation-frequency range. 相似文献
8.
We establish an analogue of Weyl's classical theorem for the asymptotics of eigenvalues of Laplacians on a finitely ramified (i.e., p.c.f.) self-similar fractalK, such as, for example, the Sierpinski gasket. We consider both Dirichlet and Neumann boundary conditions, as well as Laplacians associated with Bernoulli-type (multifractal) measures onK. From a physical point of view, we study the density of states for diffusions or for wave propagation in fractal media. More precisely, let (x) be the number of eigenvalues less thanx. Then we show that (x) is of the order ofx
d
S/2 asx+, where the spectral exponentd
S
is computed in terms of the geometric as well as analytic structures ofK. Further, we give an effective condition that guarantees the existence of the limit ofx
–d
S/2(x) asx+; this condition is, in some sense, generic. In addition, we define in terms of the above spectral exponents and calculate explicitly the spectral dimension ofK.The research of Michel L. Lapidus was partially supported by the National Science Foundation under Grant DMS-8904389 (transferred to the University of California as grant DMS-9196085) and Grant DMS-9207098, as well as by Yale University 相似文献
9.
Experimental data on
0 meson polarization in
–
p reaction at 5 GeV/c are presented. Change in
0 meson polarization for mesons produced at smallP
2
and atP
2
0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed for
0 meson production in¯pp reactions.The authors are indebted to Ján Piút, Richard Lednický, V. S. Rumiancev and N. K. Koutsidi for discussions and critical comments. 相似文献
10.
The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where
(,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form
where i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly. 相似文献
11.
We consider classical acoustic waves in a medium described by a position dependent mass density (x). We assume that (x) is a reandom perturbation of a periodic function 0(x) and that the periodic acoustic operator
has a gap in the spectrum. We prove the existence of localized waves, i.e., finite energy solutions of the acoustic equations with the property that almost all of the wave's energy remains in a fixed bounded region of space at all times, with probability one. Localization of acoustic waves is a consequence of Anderson localization for the self-adjoint operators
onL
2(
d
). We prove that, in the random medium described by (x), the random operatorA exhibits Anderson localization inside the gap in the spectrum ofA
0. This is shown even in situations when the gap is totally filled by the spectrum of the random opertor; we can prescribe random environments that ensure localization in almost the whole gap.This author was supported by the U.S. Air Force Grant F49620-94-1-0172.This author was supported in part by the NSF Grants DMS-9208029 and DMS-9500720. 相似文献
12.
Simba A. Mutangadura 《Communications in Mathematical Physics》1990,132(3):581-592
Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on . 相似文献
13.
Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ±i, – and giving rise to homoclinic chaos when the Shil'nikov condition < is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius—Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variablex are explicitly derived. 相似文献
14.
A realistic pion form factor model respecting the usual fundamental principles supplemented by reasonable assumptions is constructed by means of conformai mapping having some specific uniformization properties. The model includes the contributions of higher rho-resonances without any conflict with analyticity, provides a certain flexibility for the asymptotic behaviour and depends just on the physical parameters. The best fit of all existing data is achieved with(770),'(1600) and the asymptoticst
–3/2. The predicted values of the pion charge radius, P-wave isovector scattering length, as well as theI=J = 1 scattering amplitude at the experimental measurable region coincide with the world averaged data.Dedicated to the 30th anniversary of the Joint Institute of Nuclear Research.The authors are indebted to Prof. V. A. Meshcheryakov, Dr. S. B. Gerasimov and Dr. D. Krupa for many stimulating and illuminating discussions. 相似文献
15.
We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+
v
K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda
0() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy. 相似文献
16.
It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx
3=(x
1), where the surface profile function (x
1) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x
1)(x
1)/2(x
1)=W (|x
1–x
1|) has the Lorentzian formW(|x
1|)=a
2/(x
1
2
+a
2) we find that d=0.9080a; when it has the Gaussian formW(|x
1|)=exp(–x
1
2
/a
2), we find that d=1.2837a; and when it has the nonmonotonic formW(|x
1|)=sin(x
1/a)/(x
1/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) [the Fourier transform ofW(|x
1|)] decays to zero with increasing |Q|. We also obtain the functionP(itx
1), which is defined in such a way that, ifx
1=0 is a zero of (x
1),P(x
1)dx
1 is the probability that the nearest zero of (x
1) for positivex
1 lies betweenx
1 andx
1+dx
1. 相似文献
17.
The behaviour of products of local fields for lightlike distances is investigated. If a light cone expansion ofA(x)A(y) exists, then already the four point function carries the singularity arising in the expansion for (x–y)20. For a special class of field theories, discussed by S. Schlieder and E. Seiler, it is shown that the light cone expansion is possible.
Notation.
the Schwartz space of strongly decreasing testfunctions over
n
A=scalar field operator, which fulfils the Wightman axioms [we freely writeA(x),x 4 andA(g),g
].
=Hilbert space. =vacuum state.
is the linear hull of the vectors
(With respect to the definition of operators with complex argument cf.[6]!)
By (x
2) (x
2) we denote a sequence of functions
which converges to (x
2) as 0. 相似文献
18.
Z. Haba 《Letters in Mathematical Physics》1996,37(2):223-231
Let
t
be an analytic solution of the Schrödinger equation with the initial condition . Let
t
be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then
t
(x)
t
(x)1 (
t
(x)), where
t
(x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations. 相似文献
19.
A. Z. Dubničková S. Dubnička B. I. Khasin P. Mäsiar 《Czechoslovak Journal of Physics》1987,37(7):815-829
The analysis of all existing pion form factor data by a model respecting the fundamental principles, including (770), (1250) and (1600) contributions without inelastic effects and depending just on the physical parameters is carried out. The comparison of the obtained results with a previous analysis performed by means of a model with only (770) and (1600) contributions and inelastic effects confirmes the conclusions of Novosibirsk experimental group that the (1250) contribution and inelastic effects in e+e–+– are indistinguishable. However, theoretically predicted behaviours of the P-wave isovector phase shift and the inelasticity from both models and their comparison with existing data unambiguously favour the model with (770), (1600) and inelastic contributions.We are indebted to Dr. D. Krupa who called our attention to the concise (in comparison with our original diagrammatized presentation) and transparent algebraic proof, given in the text by (30)–(33). One of us (A. Z. D.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics in Trieste. 相似文献
20.
D. C. Srivastava 《General Relativity and Gravitation》1986,18(11):1159-1180
In this note, a spherically symmetric charged perfect fluid executing shear-free motion has been investigated under the assumption of validity of an equation of state. Mashoon and Partovi [4] have studied this problem and have established several theorems giving the properties of such fluid distributions. We find that there is one more solution which is new. It is characterized by three parameters, one of which is the charge parameter. In the limit of vanishing charge the metric goes over to the Wyman metric [2]. It has been shown that the solution does not match with the Reissner-Nordström solution at a boundary and hence it is not suitable to represent a bounded system. We have also discussed the possibility of this solution representing the physical universe. We have found that the solution after a proper choice of constants may satisfy the physical requirements3p,d/dp 1 but will violate the condition /1 wherep, , and represent, respectively, the pressure, matter density, and charge density of the fluid. Therefore, the charged Wyman solution is unsuitable to represent the physical universe. Thus we conclude that for a charged perfect fluid distribution executing shear-free motion the field equations do not admit any physically meaningful solution if we assume the validity of an equation of state.This paper was partially presented at the 12th meeting of Indian Association for General Relativity and Gravitation and the symposium on Applications of General Relativity to Astrophysics and Cosmology held at Puna, India, November 9–12, 1983. 相似文献