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1.
A. Angeletti 《Letters in Mathematical Physics》1980,4(6):495-504
Let (x) be the Dirac's delta,q(x)L
1
(R)L
2
(R) be a real valued function, and , R; we will consider the following class of one-dimensional formal Schrödinger operators on
. It is known that to the formal operator
may be associated a selfadjoint operatorH(,) onL
2(R). Ifq is of finite range, for >0 and || is small enough, we prove thatH(,) has an antibound state; that is the resolvent ofH(,) has a pole on the negative real axis on the second Riemann sheet.Work done while the author was supported by an undergraduate fellowship of the (Italian) National Research Council (CNR). 相似文献
2.
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
3.
J. De Cannière 《Communications in Mathematical Physics》1982,84(2):187-205
Let be a state on aC*-dynamical system
. For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of
associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O. 相似文献
4.
G. Date T. R. Govindarajan P. Sankaran R. Shankar 《Communications in Mathematical Physics》1990,132(2):293-313
We compute the homotopy groups
0 and
1 of the classical configuration space of anO(3) invariant field theory on
×, where
is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications. 相似文献
5.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
6.
Stella A. L. Xie X. C. Einstein T. L. Bartelt N. C. 《Zeitschrift für Physik B Condensed Matter》1987,67(3):357-361
The controversial 2-d, 3-state chiral Potts model is studied using transfer matrix finite size scaling. at =0, we find dq
N/dN
–4/5, whereq is the wavevector, the chiral field, andN the strip width (N=4–10). The result is consistent with den Nijs's crossover exponent =1/6. With surface fields on the infinite free boundaries, exponents associated with bulk magnetizationy
H, surface magnetizationy
H, and surface susceptibility are computed vs. ; results are similar for
or to the infinite direction. Preliminary results are given for the bulk specific heat critical amplitudes, to test the universality of amplitude ratios. The interface wetting line is located for 01/4 using simple transfer matrix calculations of surface tensions in the solid-on-solid approximation. Overhangs or bubbles seem relatively unimportant at all temperatures. 相似文献
7.
The effective conductivity
* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on
d
, where the cells or bonds are randomly assigned the conductivities
1 and
2 (
1,
2ne0) with probabilitiesp
1 andp
2=1–p
1. A rigorous basis for the very old and widely used low volume fraction expansion of
* is established, by proving that
* is an analytic function ofp
2 in a suitable domain containing [0, 1]. In the case of the bond lattice ind=2, rigorous fourth-order upper and lower bounds on
* valid for allp
2,
1, and
2 are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability. 相似文献
8.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献
9.
We study the Leibniz homology of the Poisson algebra of polynomial functions over (2n
,) where is the standard symplectic structure. We identify it with certain highest-weight vectors of some
2n
(
)-modules and obtain some explicit result in low degree. 相似文献
10.
A. Möbius 《Zeitschrift für Physik B Condensed Matter》1990,79(2):265-273
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
11.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
12.
We compute analytically the probability distribution function
() of the dissipation field =()2 of a passive scalar advected by a d-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor–Kraichnan regime). The tail of the distribution is a stretched exponential: for , ln
()–(d
2
)1/3. 相似文献
13.
The elastic and radiative
+
p scattering are studied in the framework of an effective Lagrangian model for the
++ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole (
++) and background contributions (
0, , , and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the
++ obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative
+
p scattering is
nuclear magnetons. 相似文献
14.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
15.
We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=-1H, which differs fromK, but turns out to be 5 close to it. Special attention is devoted to numerical integration for scattering problems. 相似文献
16.
L'ubomír Hrivnák 《Czechoslovak Journal of Physics》1959,9(6):685-691
An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e2/r [1+exp (–qr].
s- , –e2/r [1+exp (–qr].相似文献
17.
M. Šícha V. Veselý J. Studnička J. Prostějovský M. Novák 《Czechoslovak Journal of Physics》1962,12(12):919-929
Zusammenfassung Es wurde ein Verfahren zur Erregung von stationären Schichten, der Schichtungswelle und der laufenden Schichten in der Gleichstromentladung ausgearbeitet, das auf der Einwirkung eines Hochfrequenzfeldes auf einen kurzen Abschnitt der positiven Säule beruht. Dieses Verfahren wurde zum Studium aller drei angeführten Schichtungsarten in Neon benützt, insbesondere jedoch zum Studium des Zusammenhanges zwischen den laufenden und den stationären Schichten.Bei stationären Schichten wurden zweifache Strukturen festgestellt und es wurde deren Abhängigkeit vom Entladungsstrom und von der Größe des erregenden Hochfrequenzfeldes verfolgt.Bei der Schichtungswelle wurde die Stelle deren Entstehung ermittelt und es wurde nachgewiesen, daß das Hochfrequenzfeld diese Welle lokal an der Stelle dessen Einwirkung auf die positive Säule hervorruft.Bei den laufenden Schichten wurde deren Resonanzfrequenz in Abhängigkeit vom Entladungsstrom und die Abhängigkeit der Wellenlänge der Schichten von der Frequenz untersucht.Es wurde festgestellt, daß der extrapolierte Wert der Wellenlänge für die Nullfrequenz erheblich niedriger ist als die Länge der stationären Schichten. Weiter wurde eine Übereinstimmung der Frequenz der laufenden Schichten in der Schichtungswelle mit der Resonanzfrequenz der künstlich hervorgerufenen laufenden Schichten festgestellt.
, , . , . . , . . , . , .相似文献
18.
Let (, d) be a first-order differential *-calculus on a *-algebra
. We say that a pair (, F) of a *-representation of
on a dense domain
of a Hilbert space and a symmetric operator F on
gives a commutator representation of if there exists a linear mapping : L(
) such that (adb) = (a)i[F, (b) ], a, b
. Among others, it is shown that each left-covariant *-calculus of a compact quantum group Hopf *-algebra
has a faithful commutator representation. For a class of bicovariant *-calculi on
, there is a commutator representation such that F is the image of a central element of the quantum tangent space. If
is the Hopf *-algebra of the compact form of one of the quantum groups SL
q
(n+1), O
q
(n), Sp
q
(2n) with real trancendental q, then this commutator representation is faithful. 相似文献
19.
Shou Xian She 《Optical and Quantum Electronics》1991,23(8):1045-1054
We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis. 相似文献
20.
J. Bendisch 《Journal of statistical physics》1991,62(1-2):435-442
Following an approach of Toulouse, ground states in random 2D Ising ±J spin glasses (without external magnetic field), on square lattices, and with concentrations 0p0.5 of antiferromagnetic bonds are studied by means of minimal matchings of frustrated plaquettes. Lete(p) be the ground-state energy per spin in the thermodynamic limit. Then the well-known equatione(p)=–2+(p)f(p) holds, wheref(p) is the concentration of frustrated plaquettes and(p) is the average connection length between paired frustrated plaquettes in minimal matchings. Introducing
(p) as the probability that a frustrated plaquette is matched to another frustrated plaquette by a connection of length (in a minimal matching), the average length(p) can be rewritten asgl(p)=(p). The study of(p) and its components (p) leads to an intervalp
*pp
2 (p
*0.121±0.008,p
20.161±0.008) where the threshold between ferromagnet and paramagnet forT=0 lies. Analyzing a similar so-called adjoined average lengthl(p) admits further insight. 相似文献