共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
Manuel del Pino Patricio L. Felmer Peter Sternberg 《Communications in Mathematical Physics》2000,210(2):413-446
We examine the asymptotic behavior of the eigenvalue w(h) and corresponding eigenfunction associated with the variational problem m(h) o infy ? H1(W;C ) \fracòW \abs(i?+hA)y2 dx dy òW\absy2 dx dy \mu(h)\equiv\inf_{\psi\in H^{1}(\Omega;{\bf C} )} \frac{\int_{\Omega } \abs{(i\nabla+h{\bf A})\psi}^{2}\,dx\,dy} {\int_{\Omega }\abs{\psi}^{2}\,dx\,dy} in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function w(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section W ì \R2\Omega\subset\R^{2}. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for w while also proving that the first eigenfunction decays to zero somewhere along the sample boundary ?W\partial \Omega when z is not a disc. For interior decay, we demonstrate that the rate is exponential. 相似文献
3.
In this paper we obtain violations of general bipartite Bell inequalities of order \({\frac{\sqrt{n}}{\log n}}\) with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor. 相似文献
4.
We consider a fixed quantum measurement performed over n identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon’s 12th theorem, we show that in the case of a single qubit, the number of distinguishable states is
, where (α1,α2) is the angle interval from which the states are chosen. In the general case of an N-dimensional Hilbert space and an area Ω of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is
. The optimal distribution is uniform over the domain in Cartesian coordinates. 相似文献
5.
S. K. Chandra 《Czechoslovak Journal of Physics》1973,23(6):589-593
The perturbation method of Lindstedt is applied to study the non linear effect of a nonlinear equation $$\nabla ^2 {\rm E} - \frac{1}{{c^2 }}\frac{{\partial ^2 {\rm E}}}{{\partial t^2 }} - \frac{{\omega _0^2 }}{{c^2 }}{\rm E} + \frac{{2v}}{{c^2 }}\frac{{\partial {\rm E}}}{{\partial t}} + E^2 \left[ {\frac{{\partial {\rm E}}}{{\partial t}} \times A} \right] = 0,$$ where (A. E)=0 andA,c, ω 0 andν are constants in space and time. Amplitude dependent frequency shifts and the solution up to third order are derived. 相似文献
6.
H. W. Grießhammer M. R. Schindler R. P. Springer 《The European Physical Journal A - Hadrons and Nuclei》2012,48(1):7
We calculate the (parity-violating) spin-rotation angle of a polarized neutron beam through hydrogen and deuterium targets,
using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading
independent low-energy parameters that characterize hadronic parity violation from few-body observables in one systematic
and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Our result for
np spin rotation is $\frac{1}
{\rho }\frac{{d\varphi _{PV}^{np} }}
{{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1}
{2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1}
{2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1}
{\rho }\frac{{d\varphi _{PV}^{np} }}
{{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1}
{2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1}
{2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), while for nd spin rotation we obtain $\frac{1}
{\rho }\frac{{d\varphi _{PV}^{nd} }}
{{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1}
{2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1}
{2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1}
{2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1}
{\rho }\frac{{d\varphi _{PV}^{nd} }}
{{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1}
{2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1}
{2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1}
{2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), where the g
(X-Y), in units of $MeV^{ - \frac{3}
{2}}$MeV^{ - \frac{3}
{2}}, are the presently unknown parameters in the leading-order parity-violating Lagrangian. Using naıve dimensional analysis
to estimate the typical size of the couplings, we expect the signal for standard target densities to be $\left| {\frac{{d\varphi _{PV} }}
{{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}}
{m}$\left| {\frac{{d\varphi _{PV} }}
{{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}}
{m} for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations
indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system. 相似文献
7.
Oscar M. Perdomo 《Mathematical Physics, Analysis and Geometry》2012,15(1):17-37
In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean
spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures,
in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every
h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of
S1n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S1n+1\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and
5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that
can be extended to closed hypersurfaces. 相似文献
8.
Munaim A. Mashkour 《International Journal of Theoretical Physics》1976,15(10):717-721
We give here a new exact solution to the exterior Einstein field equations for a rotating infinite cylinder. The solution is characterized by an everywhere singular metric. In the Papapetrou canonical coordinates, the 3-force acting on a radially moving test particle is $f^\alpha = \left( {G\frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{\lambda }{\rho },{\text{ 0,}} - \frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{{C\upsilon }}{\rho }{\text{ }}} \right)$ where λ>0.f 1 andf 3 are, respectively, the gravitational and Coriolis forces. The gravitational force is, therefore, repulsive. 相似文献
9.
Li-Yun Hu Shi-You Liu Kai-Min Zheng Fang Jia Hong-Yi Fan 《International Journal of Theoretical Physics》2014,53(2):380-389
We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively. 相似文献
10.
LetS ?=??Δ+V, withV smooth. If 0<E 2V(x), the spectrum ofS ? nearE 2 consists (for ? small) of finitely-many eigenvalues,λ j (?). We study the asymptotic distribution of these eigenvalues aboutE 2 as ?→0; we obtain semi-classical asymptotics for $$\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)} $$ with \(\hat f \in C_0^\infty \) , in terms of the periodic classical trajectories on the energy surface \(B_E = \left\{ {\left| \xi \right|^2 + V(x) = E^2 } \right\}\) . This in turn gives Weyl-type estimates for the counting function \(\# \left\{ {j;\left| {\sqrt {\lambda _j (\hbar )} - E} \right| \leqq c\hbar } \right\}\) . We make a detailed analysis of the case when the flow onB E is periodic. 相似文献
11.
Feng Chen Bao-long Fang Rui He Hong-yi Fan 《International Journal of Theoretical Physics》2014,53(8):2846-2854
We explore the time-evolution law of the optical field of degenerate parametric amplifier (DPA) in dissipative channel. It turns out that its density operator at initial time ρ 0 = A exp(E ? a ?2) exp(a ? alnλ) exp(E a 2) evolves into \(\rho (t)= \frac {A}{\lambda ^{\prime }}\) \(\exp \left (\frac {E^{\ast }e^{-2\kappa t}a^{\dag 2}}{ \lambda ^{\prime 2}}\right )\exp \left \{a^{\dag }a\ln \frac {[\lambda -(\lambda ^{2}-4|E|^{2})T]e^{-2\kappa t}}{\lambda ^{\prime 2}}\right \} \exp \left (\frac { Ee^{-2\kappa t}a^{2}}{\lambda ^{\prime 2}}\right ),\) where κ is the damping constant of the channel, T = 1 ? e ?2κt , and \(\lambda ^{\prime }\equiv \sqrt {(1-\lambda T)^{2}-4|E|^{2}T^{2}}.\) We employ the method of integration (or summation) within an ordered (normally ordered or antinormally ordered) of operators to overcome the obstacles in the process of calculation. 相似文献
12.
H. Mohammadi S. J. Akhtarshenas F. Kheirandish 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,62(3):439-447
We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in
the presence of intrinsic decoherence. The usefulness of such a system for performance of
the quantum teleportation protocol T0\mathcal{T}_0
and entanglement teleportation protocol T1\mathcal{T}_1
is also investigated. The results depend on the initial conditions and the parameters of
the system. The roles of system parameters such as the inhomogeneity of the magnetic field
b and the spin-orbit interaction parameter D, in
entanglement dynamics and fidelity of teleportation, are studied for both product and
maximally entangled initial states of the resource. We show that for the product and
maximally entangled initial states, increasing D amplifies the effects of
dephasing and hence decreases the asymptotic entanglement and fidelity of the
teleportation. For a product initial state and specific interval of the magnetic field
B, the asymptotic entanglement and hence the fidelity of teleportation
can be improved by increasing B. The XY and XYZ Heisenberg systems
provide a minimal resource entanglement, required for realizing efficient teleportation.
Also, in the absence of the magnetic field, the degree of entanglement is preserved for
the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1}
{{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1}
{{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The
same is true for the maximally entangled initial states
$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1}
{{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1}
{{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the
absence of spin-orbit interaction D and the inhomogeneity parameter
b. Therefore, it is possible to perform quantum teleportation protocol
T0\mathcal{T}_0
and entanglement teleportation T1\mathcal{T}_1,
with perfect quality, by choosing a proper set of parameters and employing one of these
maximally entangled robust states as the initial state of the resource. 相似文献
13.
The production of charmed mesons
,D
±
, andD
*±
is studied in a sample of 478,000 hadronicZ decays. The production rates are measured to be
相似文献
14.
In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the following steady problem: $$v \cdot \nabla _{x}F =\frac{1}{{\rm K}_{\rm n}}Q(F,F),\qquad (x,v)\in \Omega \times \mathbf{R}^{3}, \quad \quad (0.1) $$ v · ? x F = 1 K n Q ( F , F ) , ( x , v ) ∈ Ω × R 3 , ( 0.1 ) $$F(x,v)|_{n(x)\cdot v<0} = \mu _{\theta}\int_{n(x) \cdot v^{\prime}>0}F(x,v^{\prime})(n(x)\cdot v^{\prime})dv^{\prime},\quad x \in\partial \Omega,\quad \quad (0.2) $$ F ( x , v ) | n ( x ) · v < 0 = μ θ ∫ n ( x ) · v ′ > 0 F ( x , v ′ ) ( n ( x ) · v ′ ) d v ′ , x ∈ ? Ω , ( 0.2 ) where Ω is a bounded domain in ${\mathbf{R}^{d}, 1 \leq d \leq 3}$ R d , 1 ≤ d ≤ 3 , Kn is the Knudsen number and ${\mu _{\theta}=\frac{1}{2\pi \theta ^{2}(x)} {\rm exp} [-\frac{|v|^{2}}{2\theta (x)}]}$ μ θ = 1 2 π θ 2 ( x ) exp [ - | v | 2 2 θ ( x ) ] is a Maxwellian with non-constant(non-isothermal) wall temperature θ(x). Based on new constructive coercivity estimates for both steady and dynamic cases, for ${|\theta -\theta_{0}|\leq \delta \ll 1}$ | θ - θ 0 | ≤ δ ? 1 and any fixed value of Kn, we construct a unique non-negative solution F s to (0.1) and (0.2), continuous away from the grazing set and exponentially asymptotically stable. This solution is a genuine non-equilibrium stationary solution differing from a local equilibrium Maxwellian. As an application of our results we establish the expansion ${F_s=\mu_{\theta_0}+\delta F_{1}+O(\delta ^{2})}$ F s = μ θ 0 + δ F 1 + O ( δ 2 ) and we prove that, if the Fourier law holds, the temperature contribution associated to F 1 must be linear, in the slab geometry. 相似文献
15.
We prove the existence of bubbling solutions for the following Chern-Simons-Higgs equation:
|