共查询到20条相似文献,搜索用时 492 毫秒
1.
Miroslav Engliš 《Communications in Mathematical Physics》2002,227(2):211-241
Let Ω be a bounded pseudoconvex domain in C
N
, φ, ψ two positive functions on Ω such that − log ψ, − log φ are plurisubharmonic, and z∈Ω a point at which − log φ is smooth and strictly plurisubharmonic. We show that as k→∞, the Bergman kernels with respect to the weights φ
k
ψ have an asymptotic expansion
for x,y near z, where φ(x,y) is an almost-analytic extension of &\phi;(x)=φ(x,x) and similarly for ψ. Further, . If in addition Ω is of finite type, φ,ψ behave reasonably at the boundary, and − log φ, − log ψ are strictly plurisubharmonic
on Ω, we obtain also an analogous asymptotic expansion for the Berezin transform and give applications to the Berezin quantization.
Finally, for Ω smoothly bounded and strictly pseudoconvex and φ a smooth strictly plurisubharmonic defining function for Ω,
we also obtain results on the Berezin–Toeplitz quantization.
Received: 29 December 2000 / Accepted: 14 December 2001 相似文献
2.
S. Kuwata 《International Journal of Theoretical Physics》2009,48(6):1813-1832
We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y) satisfies the homogeneity ∀
λ∈ℝ,φ(λ
x,λ
2
y)=λ
n
φ(x,y), then the parafermionic order p
f
is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x,y) is equivalent to the parasuperconformality of Q and H. The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle. 相似文献
3.
Let a<b,
and H be the (formal) Hamiltonian defined on Ω by
where J:ℤ
d
→ℝ is any summable non-negative symmetric function (J(x)≥0 for all x∈ℤ
d
, ∑
x
J(x)<∞ and J(x)=J(−x)). We prove that there is a unique Gibbs measure on Ω associated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure. 相似文献
(1) |
4.
A. I. Shtern 《Russian Journal of Mathematical Physics》2011,18(2):211-215
Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δ
h
f is defined by the rule Δ
h
f(x) = f(xh) − f(x) (x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H(x + y) = H(x) + H(y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δ
h
f ∈ F for each h ∈ G, there is an additive function H such that f − H ∈ F. Erdős’ conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de
Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional
assumption that the other one-sided difference function ∇
h
f defined by ∇
h
f(x) = f(xh) − f(x) (x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the
family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference
property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δ
h
f for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇
h
f), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie
groups. 相似文献
5.
For aL
∞
(ℝ+)∩L
1
(ℝ+) the truncated Bessel operator B
τ
(a) is the integral operator acting on L
2
[0,τ] with the kernel
where J
ν
stands for the Bessel function with ν>−1. In this paper we determine the asymptotics of the determinant det(I+B
τ
(a)) as τ→∞ for sufficiently smooth functions a for which a(x)≠1 for all x[0,∞). The asymptotic formula is of the form det(I+B
τ
(a))∼G
τ
E with certain constants G and E, and thus similar to the well-known Szeg?-Akhiezer-Kac formula for truncated Wiener-Hopf determinants.
Received: 23 April 2002 / Accepted: 25 September 2002 Published online: 24 January 2003
RID="*"
ID="*" Supported in part by NSF Grant DMS-9970879.
Communicated by J.L. Lebowitz 相似文献
6.
The temperature dependences of the resistivity and of the Seebeck coefficient S is studied in three series of Y1−x
CaxBa2Cu3−x
CoxOy samples (x=0–0.3) differing in oxygen content. It was found that the critical temperature decreases for y≈7.0, and S(T=300 K) increases with doping, whereas oxygen deficiency results in a nonmonotonic variation of these quantities with increasing
x. The band structure parameters have been determined from an analysis of the S(T) relations using a phenomenological theory of electron transport. It was found that an increase in x results in a gradual increase in band asymmetry, which is caused by calcium-induced creation of additional states in the
band responsible for conduction in the normal phase. An analysis has shown that high impurity concentrations in oxygen-deficient
Y1−x
CaxBa2Cu3−x
CoxOy samples bring about an additional ordering of the structure, which may be caused by formation of a cobalt superlattice. It
has also been shown that, in the case of Ca and Co codoping, the dependence of critical temperature on effective conduction-band
width coincides with the universal correlation relation observed in the YBa2Cu3Oy system with single substitutions in various lattice sites.
Fiz. Tverd. Tela (St. Petersburg) 41, 1363–1371 (August 1999) 相似文献
7.
P. Contucci M. Degli Esposti C. Giardinà S. Graffi 《Communications in Mathematical Physics》2003,236(1):55-63
Let {E Σ (N)} ΣΣN be a family of |Σ N |=2 N centered unit Gaussian random variables defined by the covariance matrix C N of elements c N (Σ,τ):=Av(E Σ (N)E τ (N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N 1 +N 2 , and all pairs (Σ,τ)Σ N ×Σ N :
where π k (Σ),k=1,2 are the projections of ΣΣ N into Σ Nk . The condition is explicitly verified for the Sherrington-Kirkpatrick, the even p-spin, the Derrida REM and the Derrida-Gardner GREM models. 相似文献
8.
V. S. Rabinovich 《Russian Journal of Mathematical Physics》2009,16(2):300-308
We consider the class of matrix h-pseudodifferential operators Op h (a) with symbols a = (a ij ) i,j=1 N , where the coefficients a ij ∈ C ∞(? x n × ? ξ n ? C(0, 1] satisfy the estimates |? x β g6 ξ α α ij (x, ξ, h)| ? C αβ 〈ξ〉 m and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a ij (x, ξ) is analytically continued with respect to ξ to a tube domain ? n + i $ \mathcal{B} We consider the class of matrix h-pseudodifferential operators Op
h
(a) with symbols a = (a
ij
)
i,j=1N, where the coefficients a
ij
∈ C
∞(ℝ
x
n
× ℝ
ξ
n
⊗ C(0, 1] satisfy the estimates |ϖ
x
β
g6
ξ
α
α
ij
(x, ξ, h)| ⩽ C
αβ
〈ξ〉
m
and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a
ij
(x, ξ) is analytically continued with respect to ξ to a tube domain ℝ
n
+ i
, where is a bounded domain in ℝ
n
containing the origin. The main results of the paper are the local estimates for solutions of h-pseudodifferential equations.
Let H
h
s
(ℝ
n
, ℂ
N
) be the space of distributions with values in ℂ
N
which is equipped with the norm , let Ω ⊂ ℝ
n
be a bounded open set, let v ∈ C
∞(ℝ
n
), let ▿v(x) ∈ for any x ∈ Ω, and let . Let u
h
(∈ H
h
s
(ℝ
n
,‒
N
)) be a solution of the equation Op
h
(α)u = 0. In this case, for every ϕ ∈ C
0∞ (Ω) such that ϕ(x) = 1 on Supp v and for a sufficiently small h
0 > 0, there exists a constant C > 0 such that the following estimate holds for every h ∈ (0, h
0]:
We apply estimate (1) to local tunnel exponential estimates for the behavior as h → 0 of the eigenfunctions of matrix Schr?dinger, Dirac, and square-root Klein-Gordon operators.
To the memory of Professor V. A. Borovikov 相似文献
((1)) |
9.
Fraydoun Rezakhanlou 《Communications in Mathematical Physics》2000,211(2):413-438
We study the asymptotic behavior of , where u solves the Hamilton–Jacobi equation u
t
+H(x,u
x
) ≡ 0 with H a stationary ergodic process in the x-variable. It was shown in Rezakhanlou–Tarver [RT] that u
ɛ converges to a deterministic function provided H(x,p) is convex in p and the convex conjugate of H in the p-variable satisfies certain growth conditions. In this article we establish a central limit theorem for the convergence by
showing that for a class of examples, u
ɛ(x,t) can be (stochastically) represented as
, where Z(x,t) is a suitable random field. In particular we establish a central limit theorem when the dimension is one and , where ω is a random function that enjoys some mild regularity.
Received: 15 February 1999 / Accepted: 14 December 1999 相似文献
10.
Hyun Seok Yang 《The European Physical Journal C - Particles and Fields》2009,64(3):445-457
We map noncommutative (NC) U(1) gauge theory on ℝ
C
d
×ℝ
NC
2n
to U(N→∞) Yang–Mills theory on ℝ
C
d
, where ℝ
C
d
is a d-dimensional commutative spacetime while ℝ
NC
2n
is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ
C
d
is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ
C
d
. We show that the gauge-Higgs system (A
μ
,Φ
a
) in the U(N→∞) Yang–Mills theory on ℝ
C
d
leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for
d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system
(A
μ
,Φ
a
) in half-BPS configurations describes self-dual Einstein gravity. 相似文献
11.
We apply one of the formalisms of noncommutative geometry to ℝ
N
q
, the quantum space covariant under the quantum group SO
q
(N). Over ℝ
N
q
there are two SO
q
(N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are
metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in
a previous article for the case of ℝ3
q
. As in the case N=3, one has to slightly enlarge the algebra ℝ
N
q
; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ
N
q
. While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance
and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ
N
q
with U
q
so(N) into ℝ
N
q
, an interesting result in itself.
Received: 4 March 2000 / Accepted: 11 October 2000 相似文献
12.
For r(0,1), let Z
r
={xR
2
|dist(x,Z
2)>r/2} and define τ
r
(x,v)=inf{t>0|x+tv∂Z
r
}. Let Φ
r
(t) be the probability that τ
r
(x,v)≥t for x and v uniformly distributed in Z
r
and §1 respectively. We prove in this paper that
as t→+∞. This result improves upon the bounds on Φ
r
in Bourgain-Golse-Wennberg [Commun. Math. Phys. 190, 491–508 (1998)]. We also discuss the applications of this result in the context of kinetic theory.
Received: 2 August 2002 / Accepted: 27 November 2002
Published online: 14 April 2003
Communicated by G. Gallavotti 相似文献
13.
Jonathan Weitsman 《Letters in Mathematical Physics》2011,95(3):275-296
We show that the Yang–Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent,
term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When
a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this
perturbation expansion, the correlation function E(x,y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture
will behave as
E(x,y) ~ |x - y|-2 - 2 dG, E(x,y) \sim |x - y|^{-2 - 2 d_G}, 相似文献
14.
In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t
n
f(t, u(t)), where A is the generator of a C
0-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C
0-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S
p-A defined similarly to the case of S
p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A
u:= A ∩ BUC(ℝ, X) if n = 0 and to t
n
A
u ⊕ w
n
C
0 (ℝ, X) if n ∈ ℕ, where w
n(t) = (1 + |t|)n. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0.
Dedicated to the memory of B. M. Levitan 相似文献
15.
Tetsuya Hattori 《Journal of statistical physics》2007,127(3):609-627
Let W(x,y) = ax
3+ bx
4+ f
5
x
5+ f
6
x
6+ (3 ax
2)2
y+ g
5
x
5
y + h
3
x
3
y
2 + h
4
x
4
y
2 + n
3
x
3
y
3+a
24
x
2
y
4+a
05
y
5+a
15
xy
5+a
06
y
6, and X = , , where the coefficients are non-negative constants, with a > 0, such that X
2(x,x
2)−Y(x,x
2) is a polynomial of x with non-negative coefficients.
Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding
paths on the 3 and 4 dimensional pre-gaskets.
We prove that there exists a unique fixed point (x
f
,y
f
) of Φ in the invariant set .
2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41. 相似文献
16.
Vladimir Rabinovich 《Russian Journal of Mathematical Physics》2012,19(1):107-120
The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e - iw0 t [(x)\dot]0 ( t )d( x - x0 ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x
1, x
2, x
3) ∈ ℝ3 for the space variables, t ∈ ℝ for time, t → x
0(t) ∈ ℝ3 for the vector function defining the motion of the source, ω
0 for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity
ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains
a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]0 ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method
to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application
of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma
and the Cherenkov radiation in dispersive media. 相似文献
17.
J. Bourgain 《Communications in Mathematical Physics》1999,204(1):207-247
In this paper, we consider the following problem. Let iu
t
+Δu+V(x,t)u= 0 be a linear Schr?dinger equation ( periodic boundary conditions) where V is a real, bounded, real analytic potential which is periodic in x and quasi periodic in t with diophantine frequency vector λ. Denote S(t) the corresponding flow map. Thus S(t) preserves the L
2-norm and our aim is to study its behaviour on H
s
(T
D
), s> 0. Our main result is the growth in time is at most logarithmic; thus if φ∈H
s
, then
18.
Topological invariants in terms of the Green’s function in momentum and real space determine properties of smooth textures
within topological media. In space dimension d = 1 the topological invariant N
3 in terms of the Green’s function (ω, k
x
, x) determines the fermion number of the kink, while in space dimension d = 3 the topological invariant N
5 in terms of the Green’s function (ω, k
x
, k
y
, k
z
, z) determines quantization of Hall conductivity in the soliton plane within the topological insulators. 相似文献
19.
F. Schertz D. Kutnyakhov S. Schuppler P. Nagel S. A. Nepijko G. Schönhense 《Applied Physics A: Materials Science & Processing》2011,102(2):253-258
The possibility of measuring the height of an object in emission electron microscopy (EEM) is investigated. If the specimen
is characterized by an equipotential surface with the relief h(x,y), the image is equivalent to a specimen with an ideal flat surface and a corresponding distribution of the electric potential
φ(x,y)=−E
ext
h(x,y). As a consequence of the interaction with the microfields grad φ(x,y), the trajectories of electrons forming the image become deformed, which leads to characteristic image distortion. From EEM,
images obtained at different voltages of the extractor V
ext,φ(x,y) can be derived and thereby h(x,y) is reconstructed. If the surface of the specimen is characterized both by a distribution of the potential and in addition
by a relief h(x,y), then for the reconstruction one needs an additional EEM image taken at a different voltage of the extractor. The maximal
sensitivity to microfields/relief is exploited when using the electron microscope in the mirror operation mode. We illustrate
the performance of the method by means of a test pattern of Au on Si. For quantitative comparison, the same structure was
investigated by atomic force microscope. 相似文献
20.
For operators with a discrete spectrum, {λ
j
2}, the counting function of λ
j
's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑
j
δλ
j
((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ
j
∈ℂ+, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that
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