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1.
We consider a random walk X
n
in ℤ+, starting at X
0=x≥0, with transition probabilities
and X
n+1=1 whenever X
n
=0. We prove
as n
↗∞ when δ∈(1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk. 相似文献
2.
Let A
1,…,A
N
be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle
gives a bound for the quantum generalized covariance in terms of the commutators [A
h
,A
j
]. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case N=2m+1.
Let f be an arbitrary normalized symmetric operator monotone function and let 〈⋅,⋅〉
ρ,f
be the associated quantum Fisher information. Based on previous results of several authors, we propose here as a conjecture
the inequality
whose validity would give a non-trivial bound for any N∈ℕ using the commutators i[ρ,A
h
]. 相似文献
3.
In dimension n > 3 we show the existence of a compactly supported potential in the differentiability class , for which the solutions to the linear Schrödinger equation in,
fail to satisfy an evolution estimate of the form
This contrasts with known results in dimensions n ≤ 3, where a pointwise decay condition on V is generally sufficient to imply dispersive bounds.The obstructions in our example are generated by an expression with scaling law , which becomes dominant in the time interval . 相似文献
4.
Let μ
0 be a probability measure on ℝ3 representing an initial velocity distribution for the spatially homogeneous Boltzmann equation for pseudo Maxwellian molecules.
As long as the initial energy is finite, the solution μ
t
will tend to a Maxwellian limit. We show here that if
, then instead, all of the mass “explodes to infinity” at a rate governed by the tail behavior of μ
0. Specifically, for L0, define
Let B
R
denote the centered ball of radius R. Then for every R,
The explicit rate is estimated in terms of the rate of divergence of η
L
. For example, if η
L
≥Const.L
s
, some s>0,
is bounded by a multiple of e
−[κ3s/(10+9s)]t
, where κ is the absolute value of the spectral gap in the linearized collision operator. Note that in this case, letting B
t
denote the ball of radius e
rt
for any r<κ
s/(10+9s), we still have
.
This result shows in particular that the necessary and sufficient condition for lim
t→∞
μ
t
to exist is that the initial data have finite energy. While the “explosion” of the mass towards infinity in the case of infinite
energy may seem to be intuitively clear, there seems not to have been any proof, even without the rate information that our
proof provides, apart from an analogous result, due to the authors, concerning the Kac equation. A class of infinite energy
eternal solutions of the Boltzmann equation have been studied recently by Bobylev and Cercignani. Our rate information is
shown here to provide a limit on the tails of such eternal solutions.
E. Carlen’s work is partially supported by U.S. National Science Foundation grant DMS 06-00037.
E. Gabetta’s and E. Regazzini’s work is partially supported by Cofin 2004 “Probleme matematici delle teorie cinetiche” (MIUR). 相似文献
5.
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
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6.
Sergio Albeverio Saidakhmat N. Lakaev Tulkin H. Rasulov 《Journal of statistical physics》2007,127(2):191-220
A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number
of particles, is considered. The location of the essential spectrum of H is described. The existence of infinitely many eigenvalues (resp. the finiteness of eigenvalues) below the bottom τess(H) of the essential spectrum of H is proved for the case where the associated Friedrichs model has a threshold energy resonance (resp. a threshold eigenvalue).
For the number N(z) of eigenvalues of H lying below z < τess(H) the following asymptotics is found
Subject Classification: Primary: 81Q10, Secondary: 35P20, 47N50. 相似文献
7.
Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel 总被引：1，自引：1，他引：0
Torsten Ehrhardt 《Communications in Mathematical Physics》2007,272(3):683-698
Let stand for the integral operators with the sine kernels acting on L
2[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of are given by
as α→∞. In this paper we are going to give a proof of these two asymptotic formulas. 相似文献
8.
Qionglei Chen Changxing Miao Zhifei Zhang 《Communications in Mathematical Physics》2007,275(3):861-872
We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition,
we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, namely
where Δ
j
is the frequency localization operator in the Littlewood-Paley decomposition. 相似文献
9.
Henrik Shahgholian 《Communications in Mathematical Physics》2007,271(1):93-101
In this paper we study the behavior of the singular set
for solutions u to the free boundary problem
with , f(x) + g(x) < 0, and . Such problems arise in an eigenvalue optimization for composite membranes. Here we show that if for a singular point , there are r
0 > 0, and c
0 > 0 such that the density assumption
holds, then z is isolated. The density assumption can be motivated by the following example:
Supported in part by the Swedish Research Council. This work is part of the ESF program Global. 相似文献
10.
11.
Alp Arslan Kiraç 《Letters in Mathematical Physics》2008,83(2):149-161
Consider the Mathieu–Hill operator
in , where . We obtain the precise asymptotic formulas for the widths γ
k
of the instability intervals of L. The formula states the isolated terms of arbitrary number in the asymptotics of the sequence γ
k
for large k and verifies the results of Harrell (Am J Math suppl:139–150, 1981) and Avron and Simon (Ann Phys 134:76–84, 1981).
相似文献
12.
In this short note, we study the local times of the fractional Ornstein–Uhlenbeck process X
H
with Hurst index 1/2<H<1 solving the Langevin equation with fractional noise
where ν > 0 and B
H
is a fractional Brownian motion with Hurst index 1/2<H<1. We give Tanaka formula for the process and some properties of local times.
Mathematics Subject Classifications (2000): 60G15, 60J55, 60H05. *The Project-sponsored by SRF for ROCS, SEM. 相似文献
13.
Claudia Valls 《Communications in Mathematical Physics》2006,265(2):305-331
In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems
where α, β, c > 0 are parameters. Those systems model two-dimensional small amplitude long wavelength water waves. For α ≤ 1, this equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every β, c and almost every α ≤ 1, it admits solutions that are quasiperiodic in time. The proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the Boussinesq system to the center manifold, uses arguments of classical perturbation theory by considering the Hamiltonian formulation of the problem and studying the Birkhoff normal form.Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, and through Fundação para a Ciência e a Tecnologia by Programs POCTI/FEDER, POSI, and POCI 2010/Fundo Social Europeu, and the grant SFRH/BPD/14404/2003. 相似文献
14.
Raphaël Côte Carlos E. Kenig Frank Merle 《Communications in Mathematical Physics》2008,284(1):203-225
Given g and f = gg′, we consider solutions to the following non linear wave equation :
Under suitable assumptions on g, this equation admits non-constant stationary solutions : we denote Q one with least energy. We characterize completely the behavior as time goes to ±∞ of solutions (u, u
t
) corresponding to data with energy less than or equal to the energy of Q : either it is (Q, 0) up to scaling, or it scatters in the energy space.
Our results include the cases of the 2 dimensional corotational wave map system, with target , in the critical energy space, as well as the 4 dimensional, radially symmetric Yang-Mills fields on Minkowski space, in
the critical energy space.
Centre National de la Recherche Scientifique.
Institut des Hautes études Scientifiques.
The work of R.C. and F.M. has been supported in part by ANR grant ONDE NONLIN, and the work of C.E.K. has been supported in
part by NSF. 相似文献
15.
We show that all the coefficients of the polynomial
are nonnegative whenever m≤13 is a nonnegative integer and A and B are positive semidefinite matrices of the same size. This has previously been known only for m≤7. The validity of the statement for arbitrary m has recently been shown to be equivalent to the Bessis-Moussa-Villani conjecture from theoretical physics. In our proof,
we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming.
As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric
matrices of the same size, yet not being a sum of hermitian squares and commutators.
Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.
The first author acknowledges the financial support from the state budget by the Slovenian Research Agency (project No. Z1-9570-0101-06).
Supported by the DFG grant “Barrieren”. 相似文献
16.
For an annular cathode in a coaxial diode it has been shown that the averaged electric field strength at the end face of the
cathode, En, depends on the edge thickness h as
. It has been found that the field strength varies with distance from the edge approximately as
. The problem of the electric field strength at the edge of the cathode in a magnetically insulated coaxial diode has been
solved for the case where the cathode emissivity is limited with the use of a model assuming a given internal resistance of
the voltage source.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 71–76, March, 2008. 相似文献
17.
The Radiative Transfer Equation is the nonlinear transport equation
|
相似文献
18.
C. Chris Wu 《Journal of statistical physics》1996,88(5-6):1399-1408
We consider an inhomogeneous contact process on a tree
of degreek, where the infection rate at any site isλ, the death rate at any site in
isδ (with 0 <δ ⩽ 1) and that at any site in
is 1. Denote by
the critical value for thehomogeneous model (i.e.,δ=1) on
and byϑ(δ, λ) the survival probability of the inhomogeneous model on
. We prove that whenk > 4, if
, a subtree embedded in
, with 1 ⩽σ ⩽ √k, then three existsδ
c
σ
strictly between (
) and 1 such that (
) whenδ >δ
c
σ
andϑ(δ, λ
c(
) > 0 whenδ <δ
c
σ
; ifS={o}, the origin of
, then
for anyδ ε (0, 1). 相似文献
19.
The production of charmed mesons
,D
±
, andD
*±
is studied in a sample of 478,000 hadronicZ decays. The production rates are measured to be
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