共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary
conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is
on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε
−2|log ε|−1 where Ω is the rotational velocity and the coupling parameter is written as ε
−2 with ε≪1. Three critical speeds can be identified. At
\varOmega = \varOmegac1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for
|loge| << \varOmega < \varOmegac2 ~ e-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For
\varOmega 3 \varOmega c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε
−2|log ε|−1 vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at
\varOmega = \varOmegac3 ~ e-2|loge|-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated
by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break
rotational symmetry in the whole parameter range, including the giant vortex phase. 相似文献
2.
Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L
kk
= k
2, and the matrix B is off-diagonal, with nonzero entries B
k,k+1 = B
k+1,k
= k
α
, 0 ≤ α < 2. The spectrum of L + zB is discrete. For small |z| the nth eigenvalue E
n
(z), E
n
(0) = n
2, is a well-defined analytic function. Let R
n
be the convergence radius of its Taylor’s series about z = 0. It is proved that
Rn £ C(a) n2-a \textif\enspace 0 £ a < 11 /6R_n \leq C(\alpha) n^{2-\alpha}\quad \text{if}\enspace 0 \leq \alpha <11 /6 相似文献
3.
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
4.
Dian-Yong Chen Xiang Liu Xue-Qian Li 《The European Physical Journal C - Particles and Fields》2011,71(11):1808
To solve the discrepancy between the experimental data on the partial widths and lineshapes of the dipion emission of ϒ(4S) and the theoretical predictions, we suggest that there is an additional contribution, which had not been taken into account
in previous calculations. Noticing that the mass of ϒ(4S) is above the production threshold of B[`(B)]B\bar{B}, the contribution of the sequential process
\varUpsilon(4S)? B[`(B)]? \varUpsilon(nS)+S?\varUpsilon(nS)+p+p-\varUpsilon(4S)\to B\bar{B}\to \varUpsilon(nS)+S\to\varUpsilon(nS)+\pi^{+}\pi^{-} (n=1,2) may be sizable, and its interference with that from the direct production would be important. The goal of this work
is to investigate if a sum of the two contributions with a relative phase indeed reproduces the data. Our numerical results
on the partial widths and the lineshapes
d\varGamma(\varUpsilon(4S)?\varUpsilon(2S,1S)p+p-)/d(mp+p-)d\varGamma(\varUpsilon(4S)\to\varUpsilon(2S,1S)\pi^{+}\pi^{-})/d(m_{\pi ^{+}\pi^{-}}) are satisfactorily consistent with the measurements; thus the role of this mechanism is confirmed. Moreover, with the parameters
obtained by fitting the data of the Belle and BaBar collaborations, we predict the distributions dΓ(ϒ(4S)→ϒ(2S,1S)π
+
π
−)/dcosθ, which have not been measured yet. 相似文献
5.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
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