共查询到20条相似文献,搜索用时 62 毫秒
1.
In this paper, we are interested in the asymptotic properties for the largest eigenvalue of the Hermitian random matrix ensemble,
called the Generalized Cauchy ensemble GCyE, whose eigenvalues PDF is given by
const·?1 £ j < k £ N(xj-xk)2?j=1N(1+ixj)-s-N(1-ixj)-[`(s)]-Ndxj,\textrm{const}\cdot\prod_{1\leq j 2.
If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì Rd, 1 £ d £ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X
c
is the critical state, then it is proved that
ò¥0m(O\Ot0)dt < ¥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and
limt?¥ òO|X(t)-Xc|dx = l < ¥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and Otc{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=Xc(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X
c
(ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), limt ? ¥ òK|X(t)-Xc|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0. 相似文献
3.
Let $\mathcal {A}_{2}(t)$ be the Airy2 process. We show that the random variable $$\sup_{t\leq\alpha} \bigl\{\mathcal {A}_2(t)-t^2 \bigr\}+\min\{0,\alpha \}^2 $$ has the same distribution as the one-point marginal of the Airy2→1 process at time α. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution F GUE(x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution F GOE(41/3 x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every α the distribution has the same right tail decay $e^{-\frac{4}{3} x^{3/2} }$ . 相似文献
4.
We show that the residual entropy, S, for the two-dimensional Blume-Emery-Griffiths model at the antiquadrupolar-ferromagnetic coexistence line satisfies the
following bounds ln(l1,2n,+/l1,2n-1,+) £ S £ (lnl1,k,free)/k\ln(\lambda_{1,2n,+}/\lambda_{1,2n-1,+})\leq S\leq (\ln \lambda_{1,k,\mathit{free}})/k, for all n≥2 and k≥1, where λ
1,n,free
and λ
1,n,+ are the largest eigenvalues of the transfer matrices F
n,free
and F
n,+, respectively. In particular, we have S=0.439396±0.008670. 相似文献
5.
Michel Planat 《International Journal of Theoretical Physics》2010,49(5):1044-1054
In quantum information context, the groups generated by Pauli spin matrices, and Dirac gamma matrices, are known as the single
qubit Pauli group ℘, and two-qubit Pauli group ℘2, respectively. It has been found (Socolovsky, Int. J. Theor. Phys. 43: 1941, 2004) that the CPT group of the Dirac equation is isomorphic to ℘. One introduces a two-qubit entangling orthogonal matrix S basically related to the CPT symmetry. With the aid of the two-qubit swap gate, the S matrix allows the generation of the three-qubit real Clifford group and, with the aid of the Toffoli gate, the Weyl group
W(E
8) is generated (Planat, Preprint , 2009). In this paper, one derives three-qubit entangling groups [(P)\tilde]\tilde{\mathcal{P}} and [(P)\tilde]2\tilde{\mathcal{P}}_{2}, isomorphic to the CPT group ℘ and to the Dirac group ℘2, that are embedded into W(E
8). One discovers a new class of pure three-qubit quantum states with no-vanishing concurrence and three-tangle that we name
CPT states. States of the GHZ and CPT families, and also chain-type states, encode the new representation of the Dirac group and its CPT subgroup. 相似文献
6.
Amy Novick-Cohen 《Journal of statistical physics》2010,141(1):142-157
The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and
low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent
results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, 2009), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility.
For the case of constant mobility, we obtain upper bounds of the form t
1/3 at early times as well as at times t for which
E(t) £ \frac(1-[`(u)]2)4E(t)\le\frac{(1-\overline{u}^{2})}{4}, where E(t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t
1/3 or t
1/4 at early times, depending on the value of E(0), as well as bounds of the form t
1/4 whenever
E(t) £ \frac(1-[`(u)]2)4E(t)\le\frac{(1-\overline{u}^{2})}{4}. 相似文献
7.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
8.
C. Martin Edwards Gottfried T. Rüttimann 《Communications in Mathematical Physics》1999,203(2):269-295
A JBW*-triple B is said to be rectangular if there exists a W*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice P(A)\mathcal{P}(A) of projections in A such that B is isomorphic to the JBW*-triple pAq. Any weak*-closed injective operator space provides an example of a rectangular JBW*-triple. The principal order ideal CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} of the complete *-lattice CP(A)\mathcal{C}\mathcal{P}(A) of centrally equivalent pairs of projections in a W*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete latticeI(B)\mathcal{I}(B) of weak*-closed inner ideals in B and to the complete lattice S(B)\mathcal{S}(B) of structural projections on B. Although not itself, in general, orthomodular, CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e2,f2) and (e2,f2) of elements of CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)}. This is defined and characterized in terms of properties of P(A)\mathcal{P}(A). A W*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on CP(A)(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W*-algebras pAp and qAq of A has a weak*-closed ideal of Type I2, such measures are precisely those that are the restrictions of bounded sesquilinear functionals {m on pAp 2 qAq with the property that the action of the centroid Z(B) of B commutes with the adjoint operation. When B is a complex Hilbert space of dimension greater than two, this result reduces to Gleason's Theorem. 相似文献
9.
Dimitar Grantcharov Ji Hye Jung Seok-Jin Kang Myungho Kim 《Communications in Mathematical Physics》2010,296(3):827-860
In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra
Uq(\mathfrak q(n)){U_q(\mathfrak {q}(n))}. The key ingredients are the triangular decomposition of
Uq(\mathfrak q(n)){U_q(\mathfrak {q}(n))} and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we
prove are the classical limit theorem and the complete reducibility theorem for
Uq(\mathfrak q(n)){U_q(\mathfrak {q}(n))}-modules in the category Oq 3 0{\mathcal {O}_{q}^{\geq 0}}. 相似文献
10.
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense
of Franz (The Theory of Quantum Levy Processes, [math.PR], 2009), Schürmann (White noise on bioalgebras. Volume 1544 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1993) and others, and then formulate and study in details (with a number of interesting examples) a definition of quantum Brownian
motions on those non-commutative manifolds (a la Connes) which are quantum homogeneous spaces of their quantum isometry groups
in the sense of Goswami (Commun Math Phys 285(1):141–160, 2009). We prove that bi-invariant quantum Brownian motion can be ‘deformed’ in a suitable sense. Moreover, we propose a non-commutative
analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics
for a specific example on non-commutative two-torus Aq{\mathcal{A}_\theta} , which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that Aq{\mathcal{A}_\theta} is a non-commutative model of the (locally one-dimensional) ‘leaf-space’ of the Kronecker foliation. 相似文献
11.
Huiying Song Xinyu Zhang Bo-Qiang Ma 《The European Physical Journal C - Particles and Fields》2011,71(2):1542
The light flavor antiquark distributions of the nucleon sea are calculated in the effective chiral quark model and compared
with experimental results. The contributions of the flavor-symmetric sea-quark distributions and the nuclear EMC effect are
taken into account to obtain the ratio of Drell–Yan cross sections σ
pD/2σ
pp, which can match well with the results measured in the FermiLab E866/NuSea experiment. The calculated results also match
the [`(d)](x)-[`(u)](x)\bar{d}(x)-\bar{u}(x) measured in different experiments, but unmatch the behavior of [`(d)](x)/[`(u)](x)\bar{d}(x)/\bar{u}(x) derived indirectly from the measurable quantity σ
pD/2σ
pp by the FermiLab E866/NuSea Collaboration at large x. We suggest to measure again [`(d)](x)/[`(u)](x)\bar{d}(x)/\bar{u}(x) at large x from precision experiments with careful treatment of the experimental data. We also propose an alternative procedure for
experimental data treatment. 相似文献
12.
The complex impedance of the Ag2ZnP2O7 compound has been investigated in the temperature range 419–557 K and in the frequency range 200 Hz–5 MHz. The Z′ and Z′ versus frequency plots are well fitted to an equivalent circuit model. Dielectric data were analyzed using complex electrical
modulus M* for the sample at various temperatures. The modulus plot can be characterized by full width at half-height or in terms of
a non-exponential decay function
f( \textt ) = exp( - \textt/t )b \phi \left( {\text{t}} \right) = \exp {\left( { - {\text{t}}/\tau } \right)^\beta } . The frequency dependence of the conductivity is interpreted in terms of Jonscher’s law:
s( w) = s\textdc + \textAwn \sigma \left( \omega \right) = {\sigma_{\text{dc}}} + {\text{A}}{\omega^n} . The conductivity σ
dc follows the Arrhenius relation. The near value of activation energies obtained from the analysis of M″, conductivity data, and equivalent circuit confirms that the transport is through ion hopping mechanism dominated by the
motion of the Ag+ ions in the structure of the investigated material. 相似文献
13.
Siegfried Bethke 《The European Physical Journal C - Particles and Fields》2009,64(4):689-703
Measurements of α
s, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world
average of as(MZ0)\alpha_{\mathrm{s}}(M_{\mathrm{Z}^{0}}) is derived. Special emphasis is laid on the most recent determinations of α
s. These are obtained from τ-decays, from global fits of electroweak precision data and from measurements of the proton structure function F2, which are based on perturbative QCD calculations up to O(as4)\mathcal{O}(\alpha_{\mathrm{s}}^{4}); from hadronic event shapes and jet production in e+e− annihilation, based on O(as3)\mathcal{O}(\alpha_{\mathrm{s}}^{3}) QCD; from jet production in deep inelastic scattering and from ϒ decays, based on O(as2)\mathcal{O}(\alpha_{\mathrm{s}}^{2}) QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. A pragmatic method is chosen to obtain the world
average and an estimate of its overall uncertainty, resulting in
|