共查询到20条相似文献,搜索用时 15 毫秒
1.
Serguei I. Iakovlev 《Mathematical Physics, Analysis and Geometry》2006,9(2):109-134
In we consider a family of selfadjoint operators of the Friedrichs model: . Here is the operator of multiplication by the corresponding function of the independent variable , and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel satisfying some smoothness condition. These absolute type operators have one singular point of order . Conditions on the kernel are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity . The sharpness of these conditions is confirmed by counterexamples. 相似文献
2.
Alexis Pokrovski 《Mathematical Physics, Analysis and Geometry》2007,10(3):197-203
Let be the spectrum of in L
2(ℝ), where q is an even almost-periodic complex-valued function with bounded primitive and derivative. It is known that , where is the spectrum of the unperturbed operator. Suppose that the asymptotic approximation to the first asymptotic correction
is given. We prove the formula that recovers the frequencies and the Fourier coefficients of q in terms of Δμ
n
.
相似文献
3.
Asao Arai 《Letters in Mathematical Physics》2007,80(3):211-221
Let H be a self-adjoint operator on a complex Hilbert space . A symmetric operator T on is called a time operator of H if, for all , (D(T) denotes the domain of T) and . In this paper, spectral properties of T are investigated. The following results are obtained: (i) If H is bounded below, then σ(T), the spectrum of T, is either (the set of complex numbers) or . (ii) If H is bounded above, then is either or . (iii) If H is bounded, then . The spectrum of time operators of free Hamiltonians for both nonrelativistic and relativistic particles is exactly identified.
Moreover spectral analysis is made on a generalized time operator.
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from the JSPS. 相似文献
4.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Mathematical Physics, Analysis and Geometry》2009,12(2):109-115
Let σ be a surjective ultraweakly continuous ∗-linear mapping and d be a σ-derivation on a von Neumann algebra . We show that there are a surjective ultraweakly continuous ∗-homomorphism and a Σ-derivation such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous ∗-σ-derivation on , then there is an ultraweakly continuous linear mapping such that d is a ∗-Σ-derivation.
相似文献
5.
Kristian?Bjerkl?v 《Communications in Mathematical Physics》2009,286(1):137-161
We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic (or
logistic) map
for certain choices of and Diophantine ω. 相似文献
6.
Consider in the operator family . P
0 is the quantum harmonic oscillator with diophantine frequency vector ω, F
0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and . Then there exist independent of and an open set such that if and , the quantum normal form near P
0 converges uniformly with respect to . This yields an exact quantization formula for the eigenvalues, and for the classical Cherry theorem on convergence of Birkhoff’s normal form for complex frequencies is recovered.
Partially supported by PAPIIT-UNAM IN106106-2. 相似文献
7.
A Strong Szegő Theorem for Jacobi Matrices 总被引:1,自引:1,他引:0
E. Ryckman 《Communications in Mathematical Physics》2007,271(3):791-820
We use a classical result of Golinskii and Ibragimov to prove an analog of the strong Szegő theorem for Jacobi matrices on
. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary
and sufficient conditions on the spectral measure such that and lie in , the linearly-weighted l
2 space.
An erratum to this article can be found at 相似文献
8.
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr?dinger operator in
with an attractive interaction supported on a closed curve Γ, formally given by −Δ−αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread
Γ in
, homogeneously charged but not conducting, and we ask about the (renormalized) potential-energy minimizer. Both problems
reduce to purely geometric questions about inequalities for mean values of chords of Γ. We prove an isoperimetric theorem
for p-means of chords of curves when p ≤ 2, which implies in particular that the global extrema for the physical problems are always attained when Γ is a circle.
The letter concludes with a discussion of the p-means of chords when p > 2. 相似文献
9.
Jürg Fröhlich B. Lars G. Jonsson Enno Lenzmann 《Communications in Mathematical Physics》2007,274(1):1-30
We study the nonlinear equation
which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters,
m > 0, we prove existence of travelling solitary waves, , for some and with speed |v| < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves
cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type
arguments.
In addition to their existence, we prove orbital stability of travelling solitary waves and pointwise exponential decay of in x. 相似文献
10.
We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on
. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10. 相似文献
11.
The classical linking number lk is defined when link components are zero homologous. In [15] we constructed the affine linking
invariant alk generalizing lk to the case of linked submanifolds with arbitrary homology classes. Here we apply alk to the
study of causality in Lorentzian manifolds.
Let M
m
be a spacelike Cauchy surface in a globally hyperbolic space-time (X
m+1, g). The spherical cotangent bundle ST
*
M is identified with the space of all null geodesics in (X,g). Hence the set of null geodesics passing through a point gives an embedded (m−1)-sphere in called the sky of x. Low observed that if the link is nontrivial, then are causally related. This observation yielded a problem (communicated by R. Penrose) on the V. I. Arnold problem list [3,4]
which is basically to study the relation between causality and linking. Our paper is motivated by this question.
The spheres are isotopic to the fibers of They are nonzero homologous and the classical linking number lk is undefined when M is closed, while alk is well defined. Moreover, alk if M is not an odd-dimensional rational homology sphere. We give a formula for the increment of alk under passages through Arnold
dangerous tangencies. If (X,g) is such that alk takes values in and g is conformal to that has all the timelike sectional curvatures nonnegative, then are causally related if and only if alk . We prove that if alk takes values in and y is in the causal future of x, then alk is the intersection number of any future directed past inextendible timelike curve to y and of the future null cone of x.
We show that x,y in a nonrefocussing (X, g) are causally unrelated if and only if can be deformed to a pair of S
m-1-fibers of by an isotopy through skies. Low showed that if (X, g) is refocussing, then M is compact. We show that the universal cover of M is also compact. 相似文献
12.
We study frame properties of a matrix-valued wave packet system in the matrix-valued function space \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\), where the lower frame condition is controlled by a bounded linear operator \(\mathcal {K}\) on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\) (lower \(\mathcal {K}\)-frame condition, in short). There are many differences between ordinary frames and \(\mathcal {K}\)-frames. The lower \(\mathcal {K}\)-frame condition for matrix-valued wave packet Bessel sequences in \(L^{2}(\mathbb {R}^{d},\mathbb {C}^{s\times r})\) in terms of operators; a trace functional associated with a bounded linear operator on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\); and a series associated with a matrix-valued Bessel sequence is presented. It is shown that matrix-valued wave packet frames are stable under small perturbation with respect to wave packet window functions. 相似文献
13.
Timor Saffary 《Letters in Mathematical Physics》2006,77(3):235-248
The purpose of this paper is to shed more light on the transition from the known massless modular action to the wanted massive one in the case of forward light cones and double cones. The infinitesimal generator δm of the modular automorphism group
is investigated, in particular, some assumptions on its structure are verified explicitly for two concrete examples. 相似文献
14.
We prove that the spectrum of the discrete Schrödinger operator on ?2(?2) is absolutely continuous.
相似文献
$$\begin{array}{@{}rcl@{}} (\psi _{n,m})\mapsto -(\psi _{n + 1,m} +\psi _{n-1,m} + \psi _{n,m + 1} +\psi _{n,m-1})+V_{n}\psi _{n,m} \ , \\ \quad (n, m) \in \mathbb {Z}^{2},\ \left \{ V_{n}\right \}\in \ell ^{\infty }(\mathbb {Z}) \end{array} $$
(1)
15.
Jean-Pierre Magnot 《Letters in Mathematical Physics》2006,75(2):111-127
Using renormalized (or weighted) traces of classical pseudo-differential operators and calculus on formal symbols. We exhibit three cocycles on the Lie algebra of classical pseudo-differential operators $Cl(S^1,\mathbb{C}^n)Using renormalized (or weighted) traces of classical pseudo-differential operators and calculus on formal symbols. We exhibit
three cocycles on the Lie algebra of classical pseudo-differential operators
acting on
. We first show that the Schwinger functional
associated to the Dirac operator is a cocycle on
, and not only on a restricted algebra
Then, we investigate two bilinear functionals
and
, which satisfies
We show that
and
are two cocycles in
, and
and
have the same nonvanishing cohomology class. We finaly calculate
on classical pseudo-differential operators of order 1 and on differential operators of order 1, in terms of partial symbols.
By this last computation, we recover the Virasoro cocyle and the K?hler form of the loop group.
Mathematics Subject Classification (1991). 47G30, 47N50 相似文献
16.
For a given probability distribution λ 1,…,λ m we determine the structure of all such maps defined on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy $$S\Biggl(\sum_{k=1}^m \lambda_k \phi(\rho_k)\Biggr)- \sum_{k=1}^m \lambda_k S\bigl(\phi (\rho_k)\bigr)= S\Biggl(\sum _{k=1}^m \lambda_k \rho_k\Biggr)- \sum_{k=1}^m \lambda_k S(\rho_k) $$ for all possible collections ρ 1,…,ρ m of density operators. 相似文献
17.
We prove bounds on moments of the Smoluchowski coagulation equations with diffusion, in any dimension d ≥ 1. If the collision propensities α(n, m) of mass n and mass m particles grow more slowly than , and the diffusion rate is non-increasing and satisfies for some b
1 and b
2 satisfying 0 ≤ b
2 < b
1 < ∞, then any weak solution satisfies for every and T ∈(0, ∞), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions
are sufficient to ensure uniqueness of a weak solution and its conservation of mass.
This work was performed while A.H. held a postdoctoral fellowship in the Department of Mathematics at U.B.C.
This work is supported in part by NSF grant DMS0307021. 相似文献
18.
We consider unitary analogs of one-dimensional Anderson models on
defined by the product U
ω=D
ω
S where S is a deterministic unitary and D
ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We
prove that the spectrum of U
ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on
together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials
characterized by Verblunsky coefficients of constant modulus and correlated random phases
Mathematics Subject Classification. 82B44, 42C05, 81Q05 相似文献
19.
Laizhen Luo Xiaoyu Li Yuanhong Tao 《International Journal of Theoretical Physics》2016,55(12):5069-5076
We first construct a new maximally entangled basis in bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{kd}\ (k\in Z^{+})\) which is diffrent from the one in Tao et al. (Quantum Inf. Process. 14, 2291 (2015)), then we generalize such maximally entangled basis into arbitrary bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{d^{\prime }}\). We also study the mutual unbiased property of the two types of maximally entangled bases in bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{kd}\). In particular, explicit examples in \(\mathbb {C}^{2} \otimes \mathbb {C}^{4}\), \(\mathbb {C}^{2} \otimes \mathbb {C}^{8}\) and \(\mathbb {C}^{3} \otimes \mathbb {C}^{3}\) are presented. 相似文献
20.
We prove the existence of stationary states for nonlinear Dirac equations of the form: $$i\gamma ^\mu \partial _\mu \psi - m\psi + F(\bar \psi \psi )\psi = 0.$$ We seek solutions which are separable in spherical coordinates and we use a shooting method for solving the associated problem of ordinary differential equations. 相似文献