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1.
From a vector space V equipped with a Yang-Baxter operator R one may form the r-symmetric algebra S
R
V= TV/ v w– R( v w), which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebra M
R
V= T(End( V))/ f g– R( f g) R
-1. In the case when R satisfies a Hecke-type identity R
2=(1– q) R+ q, we construct a differential calculus
R
V for S
R
V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino when R is essentially the R-matrix of GL
q
( n). Elements of
R
V may be regarded as differential forms on the quantum vector space S
R
V. We show that
R
V is M
R
V-covariant in the sense that there is a coaction *:
R
V M
R
V
R
V with *d=(1 d) * extending the natural coaction : S
R
V M
R
V S
R
V. 相似文献
2.
In recent articles we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models were treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential, etc.). This model has the advantage of allowing us to determine the geometry of the universe by thermodynamic stability arguments. In this paper, in search for evidence for the definition of gravitational temperature, we will investigate a massless conformal scalar field in an Einstein universe in detail. We will argue that the gravitational temperature of the Einstein universe is given as T
g=1/2 ) ( c/k) (1/ R
0), where R 0 is the radius of the Einstein universe. This is in accord with our definition of gravitational temperature in Friedmann thermodynamics and determines the dimensionless constant as 1/2 . We discuss the limitations of the model we are using. We also suggest a method to generalize our gravitational temperature to arbitrary space-times granted that they are sufficiently smooth.Based on three essays awarded honorable mention in the years 1987, 1988 and 1989 by the Gravity Research Foundation—Ed. 相似文献
3.
An information-theoretic notion of entropy is proposed for a system of N interacting particles which assesses an observer's limited knowledge of the state of the system, assuming that he or she can measure with arbitrary precision all one-particle observables and correlations involving some number p of the particles but is completely ignorant of the form of any higher-order correlations involving more than p particles. The idea is to define a generic measure of entropy S[
] = –Tr
log
for an arbitrary density matrix or distribution function
, and then, given the true N-particle , to define a reduced
R
P
which reflects the observer's partial knowledge. The result, at any time t, is a chain of inequalities S[
R
1
] S[
R
2
]... S[
R
N
] S[ ], with true equality S[
R
p
]= S[
R
p+1
] if and only if the true factorizes exactly into a product of contributions involving all possible p-particle groupings. It follows further than (1) if, at some initial time t
0, the true factorizes in this way, then S[
R
p
(] S[
R
p
( t
0)] for all finite times t>t
0, with equality if and only if the factorization is restored, and (2) the initial response of the system must be to increase its p-particle entropy. 相似文献
4.
We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold ( M, g
0). We use relations between different Lorentzian structures unequivalent to g
0 and topological properties of M given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related to g
0 by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+ p+ e. 相似文献
5.
Let H
l
be the Hamiltonian in a P() 2 theory with sharp space cutoff in the interval (– l/2, l/2). Let E
l
=inf( H
l
), ( l)=– E
l
/ l, and let l be the vacuum for H
l
. discuss properties of ( l) and
l
. In particular, as l, there are finite constants <0 and such that ( l) , (( l)– ) l, and hence ( l)= + / l+ o( l
–1). Moreover exp(– c
1
l)
l
1exp(– c
2
l) for c
1, c
2 positive constants, where
l
1 is the L
1( Q, d0) norm of 1 with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations of H
l
in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow. 相似文献
6.
The impurity contribution to the resistivity in zero field ( T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to the c-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in ( T) as well as ( T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima at T
m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity poly( T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing ( T) as a function of universal quantities T/T
K and RKKY/ T
K
, where RKKY is the RKKY-interaction strength and T
K the Kondo temperature. With respect to the two lattice directions studied, the behavior of ( T and ( T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday 相似文献
7.
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 that OP1, 1O and such that if P┴ R, Q┴ R, then PQP+RQ+R for all P, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state on B(), the bounded linear operators on . 相似文献
8.
We present exact calculations of reliability polynomials R( G, p) for lattice strips G of fixed widths L
y
4 and arbitrarily great length L
x
with various boundary conditions. We introduce the notion of a reliability per vertex, r({ G}, p)=lim |V|R( G, p) 1/|V| where | V| denotes the number of vertices in G and { G} denotes the formal limit lim |V|G. We calculate this exactly for various families of graphs. We also study the zeros of R( G, p) in the complex p plane and determine exactly the asymptotic accumulation set of these zeros
, across which r({ G}) is nonanalytic. 相似文献
9.
The exact analytic result is obtained for the Fourier transform of the generating function F( R, s)=
n=0
s
n
P( R, n), where P( R, n) is the probability density for the end-to-end distance R in n steps of a random walk with persistence. The moments R
2( n), R
4( n), and R
6( n) are calculated and approximate results for P( R, n) and R
–1( n) are given. 相似文献
10.
We investigate the fluctuations in N
(R), the number of lattice points nZ
2 inside a circle of radius R centered at a fixed point [0, 1) 2. Assuming that R is smoothly (e.g., uniformly) distributed on a segment 0 RT, we prove that the random variable
has a limit distribution as T (independent of the distribution of R), which is absolutely continuous with respect to Lebesgue measure. The density p
(x) is an entire function of x which decays, for real x, faster than exp(–| x| 4–). We also obtain a lower bound on the distribution function
which shows that P
(–x) and 1– P
(x) decay when x not faster than exp(– x
4+). Numerical studies show that the profile of the density p
(x) can be very different for different . For instance, it can be both unimodal and bimodal. We show that
, and the variance
depends continuously on . However, the partial derivatives of D
are infinite at every rational point Q
2, so D
is analytic nowhere. 相似文献
11.
The generally covariant Lagrangian density G = + 2 K matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentials g
ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form
kl
i
=
kl
i
for the coefficients
kl
i
of the affine connections is postulated a priori. Alternatively, we can interpret the Lagrangian G as a functional of , g ik, and the coefficients
kl
i
. Then the
kl
i
are determined by the Palatini equations. From these equations and from the symmetry
kl
i
=
lk
i
for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10 –81erg cm 3 相似文献
12.
We consider percolation on the sites of a graph G, e.g., a regular d-dimensional lattice. All sites of G are occupied (vacant) with probability p (respectively, q=1–p), independently of each other. W denotes the cluster of occupied sites containing a fixed site (which will usually be taken to be the origin) and W the cardinality of W. The percolation probability is the probability that # W=, i.e., (p)=P
p{# W=}. Some critical values of p,p
H and p
T, are defined, respectively, as the smallest value of p for which (p)> 0, and for which the expectation of # W is infinite. Formally, p
H=inf { p(p)>0} and p
T=inf{ p E
p{# W}=}. We show for fairly general graphs Gthat if p
T, thenP
P{#W n} decreases exponentially inn. For the special casesG =G
0= the simple quadratic lattice andG
1= the graph which corresponds to bond-percolation on 2, we obtain upper and lower bounds for(p) of the formC¦p¦-P
H¦, and bounds forEp{#W} of the formC¦p–p
H¦–. We also investigate smoothness properties of (p)=E
p{number of clusters per site} =E
p {(#W)–1; (#W) 1}. This function was introduced by Sykes and Essam, who assumed that (·) has exactly one singularity, namely, atp=p
H. For the graphsG
0 andG
1, (i.e., site or bond percolation on 2) we show that (p) is analytic atp p
H and has two continuous derivatives atp=p
H. The emphasis is on rigorous proofs.Research supported by the NSF through a grant to Cornell University. 相似文献
13.
The well-established relation between Potts models with v spin values and random-cluster models (with intracluster bonding favored over intercluster bonding by a factor v) is explored, but with the random-cluster model replaced by a much generalized polymer model, implying a corresponding generalization of the Potts model. The analysis is carried out in terms a given defined function R(), an entropy/free-energy density for the polymer model in the case v=1, expressed as a function of the density of units. The aim of the analysis is to determine the analog R
v
() of R() for general nonnegative v in terms of R(), and thence to determine the critical value of density vg at which gelation occurs. This critical value is independent of v up to a value v
P, the Potts-critical value. What is principally required of R() is that it should show a certain given concave/convex behavior, although differentiability and another regularizing condition are required for complete conclusions. Under these conditions the unique evaluation of R
v
() in terms of R() is given in a form known to hold for integral v but not previously extended. The analysis is carried out in terms of the Legendre transforms of these functions, in terms of which the phenomena of criticality (gelation) and Potts criticality appear very transparently and v
P is easily determined. The value of v
P is 2 under mild conditions on R. Special interest attaches to the function R
0(), which is shown to be the greatest concave minorant of R(). The naturalness of the approach is demonstrated by explicit treatment of the first-shell model. 相似文献
14.
Let the Lie groups G and H act on the manifold P in such a way that P fibres as a principal G-bundle over P/G and as an H-bundle over P/H. We find that every pair (,) where is an H-invariant connection form in PP/G and is a G-invariant connection form in PP/H corresponds uniquely to a connection form in PP/(H×G) and a cross-section of a vector bundle with base P/(H×G). 相似文献
15.
We motivate the definition of the Einstein 3-form G
by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L
1-form, defined via G
= L
*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L
1-form is discussed, generalized, and put into proper perspective. 相似文献
16.
We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density – e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N
, the number of mobile particles of charge e. As expected, the distribution of N
has, for large , a Gaussian form with a variance which grows only as ^| |, where | | is the length of the perimeter of . The properties of this system depend only on the coupling parameter = kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^( ) decreases to an asymptotic value ^() ^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length
L=2 ^/ associated with charge fluctuations behaves very differently from that of the Debye length,
D1/
, which it approaches as 0. The pair correlation function of the OCP is also studied. 相似文献
17.
Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperature T
R
is found in exactly two dimensions only. The free energy F, the correlation length and the interface roughness h
2 are found to behave—ln Fln h
2( T
R
– T) –1 for temperatures T approaching T
R
from below. The linear relaxation rate of the order parameter is found to be proportional to
–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference above T
R
, shows a metastable regime below T
R
with a spinodal limit of metastability
c
, beyond which oscillatory growth starts. The critical behavior of
c
is found to be ln
c
–( T
R
– T) –1+ O(ln ( T
R
– T)). 相似文献
18.
Muon catalyzed fusion of deuterium and tritium (CF) yields the same energy gain per reaction as fusion with magnetic or inertial confinement (17.6 MeV). The crucial points of Cf are, however, very different, namely (a) the energy cost W
() for production of one – and (b) the number n of reactions a single muon can catalyze on the average. (b) is ultimately limited by the effective sticking probability
f : n1/
f. With standard methods one has W
()5 GeV,
f=0.5%. Hence a standard CF reactor can never reach a net energy gain. To solve this problem, ways discussed since about a decade are to increase the efficiency by both (i) energy multiplication using a fissionable blanket and (ii) breeding. A new way to increase the safety of fission devices mostly due to Yu. Petrov is outlined. On the other hand there is a hope to lower W
() slightly and
f drastically, the latter by artificial reactivation. New theoretical results for beam cooling in an omegatron type driven integrated CF reactor, important for W
() and, in particular,
f, is presented. 相似文献
19.
The beam asymmetry B has been measured for the reaction d pn in the energy range E
= 0·4 ÷ 0·8 GeV and angles
p
cm
= 45 ÷ 95° and for d 0d at energies E
=0·5, 0·6, 0·7 GeV and angle
cm
= 130°. The results obtained are compared to existing theoretical predictions which take into account the possible contribution of dibaryon resonances.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985. 相似文献
20.
An attempt has been made here to study the MHD effects on the slow motion of a viscous, incompressible and conducting fluid between two parallel porous infinite plane walls in presence of a transverse magnetic field varying periodically with time. The problem has been investigated firstly for the case of non-conducting walls and finally for the case of conducting walls.Notation biV
velocity vector
-
U
0
prescribed velocity
- biH
magnetic field vector
-
t
time
-
density
-
coefficient of viscosity
-
coefficient of kinematic viscosity
-
conductivity of the medium
-
magnetic permeability
-
magnetic viscosity
-
w
conductivity of the wall
-
l
thickness of the wall
-
L
a constant characterising the thickness of the fluid slab
-
electric conductance ratio, =
w
l/(L)
-
frequency of the H
0 variations
-
P
a constant, –1/ p/x=P
- ( x, y, z)
cartesion co-ordinates
-
Y
dimensionless cartesian co-ordinate corresponding to y
-
M
Hartmann number
-
R
Reynolds number
-
R
m
magnetic Reynolds number
-
R
c
Reynolds number for cross-flow
-
S
magnetic pressure number
-
P
dimensionless pressure gradient
-
¯t
dimsnsionless time
-
Ps
a parameter 相似文献
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