共查询到20条相似文献,搜索用时 31 毫秒
1.
Tadahiro Oh 《Communications in Mathematical Physics》2009,292(1):217-236
We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space [^(b)]sp,¥{\widehat{b}^s_{p,\infty}} , sp < −1, contains the support of the white noise. Then, we prove local well-posedness in [^(b)]sp, ¥{\widehat{b}^s_{p, \infty}} for p = 2 + ,
s = -\frac12+{s = -\frac{1}{2}+} such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical
proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21]. 相似文献
2.
Natarajan Subramanian Louise H. Kellogg Donald L. Turcotte 《Journal of statistical physics》2009,136(5):926-944
We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We
extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421–432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional
incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE).
We use the cellular flow model developed in Solomon and Mezic (Nature 425:376–380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density
function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient
of variation of the Gaussian distribution does not decrease with time as
t-\frac12t^{-\frac{1}{2}}
. However, it is observed that stretching becomes exponential log S∼t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour
of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for
strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as
t-\frac12t^{-\frac{1}{2}}
. This behavior is consistent with a random multiplicative stretching process. 相似文献
3.
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
4.
E. V. Gryzlova A. N. Grum-Grzhimailo A. I. Magunov S. I. Strakhova 《Optics and Spectroscopy》2010,109(1):59-65
Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically.
The optical activity arises in the vicinity of the autoionizing state 5p
5(2
P
1/2)8s′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
as a result of its coupling via the laser field with the discrete state 5p
5(2
P
3/2)7p
$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
. Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the
possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with
the broad autoionizing state 5p
5(2
P
1/2)6d′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
induced by the overlap of the Rydberg autoionizing series in xenon are studied. 相似文献
5.
F. Rahaman Peter K. F. Kuhfittig K. Chakraborty M. Kalam D. Hossain 《International Journal of Theoretical Physics》2011,50(9):2655-2665
This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal
matter and a quintessence dark energy field having a characteristic parameter ω
q
such that
-1 < wq < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω
q
is extremely close to
-\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable
for modeling dark matter. 相似文献
6.
Anil Kumar Yadav 《International Journal of Theoretical Physics》2011,50(5):1664-1670
The present study deals with dissipative future universe without big rip in context of Eckart formalism. The generalised Chaplygin
gas, characterised by equation of state
p=-\fracAr\frac1ap=-\frac{A}{\rho^{\frac{1}{\alpha}}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late time. It is demonstrated that,
if the cosmic dark energy behaves like a fluid with equation of state p=ωρ; ω<−1 as well as Chaplygin gas simultaneously then the big rip problem does not arise and the scale factor is found to be regular
for all time. 相似文献
7.
José Ignacio Rosado 《Foundations of Physics》2011,41(7):1200-1213
The quantum state of a d-dimensional system can be represented by a probability distribution over the d
2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution
can be represented by a vector of
\mathbb Rd2-1\mathbb {R}^{d^{2}-1} in a (d
2−1)-dimensional simplex, we will call this set of vectors Q\mathcal{Q}. Other way of represent a d-dimensional system is by the corresponding Bloch vector also in
\mathbb Rd2-1\mathbb {R}^{d^{2}-1}, we will call this set of vectors B\mathcal{B}. In this paper it is proved that with the adequate scaling B=Q\mathcal{B}=\mathcal{Q}. Also we indicate some features of the shape of Q\mathcal{Q}. 相似文献
8.
Yu. S. Surovtsev T. Branz T. Gutsche V. E. Lyubovitskij 《Physics of Particles and Nuclei》2010,41(6):990-993
In a model-independent approach the data on ππ → ππ, K
$
\bar K
$
\bar K
, ηη, ηη′ in the I
G
J
PC
= 0+0++ channel and on the Kπ scattering in the $
I\left( {J^P } \right) = \frac{1}
{2}\left( {0^ + } \right)
$
I\left( {J^P } \right) = \frac{1}
{2}\left( {0^ + } \right)
channel are analyzed jointly for studying the status and QCD nature of the f
0- and the K*0-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q
$
\bar q
$
\bar q
). In the Kπ-scattering data analysis, the proof for the K*0(900) is given. 相似文献
9.
TheD-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a (D + 1)-dimensional quantized space-time. ForD=3, it includes Snyder algebra as a special case. The deformed Poincaré transformations leaving the algebra invariant are identified. Uncertainty relations are studied. In the case ofD=1 and one nonvanishing parameter, the bound-state energy spectrum and wavefunctions of the Dirac oscillator are exactly obtained. 相似文献
10.
We consider Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime (β < 1) has order n log n, whereas the mixing-time in the case β > 1 is exponential in n. Recently, Levin, Luczak and Peres proved that for any fixed β < 1 there is cutoff at time with a window of order n, whereas the mixing-time at the critical temperature β = 1 is Θ(n
3/2). It is natural to ask how the mixing-time transitions from Θ(n log n) to Θ(n
3/2) and finally to exp (Θ(n)). That is, how does the mixing-time behave when β = β(n) is allowed to tend to 1 as n → ∞. In this work, we obtain a complete characterization of the mixing-time of the dynamics as a function of the temperature,
as it approaches its critical point β
c
= 1. In particular, we find a scaling window of order around the critical temperature. In the high temperature regime, β = 1 − δ for some 0 < δ < 1 so that δ
2
n → ∞ with n, the mixing-time has order (n/δ) log(δ
2
n), and exhibits cutoff with constant and window size n/δ. In the critical window, β = 1± δ, where δ
2
n is O(1), there is no cutoff, and the mixing-time has order n
3/2. At low temperature, β = 1 + δ for δ > 0 with δ
2
n → ∞ and δ = o(1), there is no cutoff, and the mixing time has order .
Research of J. Ding and Y. Peres was supported in part by NSF grant DMS-0605166. 相似文献
11.
We consider the KP-I and gKP-I equations in \mathbbR × (\mathbbR/2p\mathbbZ){{\mathbb{R}}\,\times\,({\mathbb{R}}/2\pi{\mathbb{Z}})}. We prove that the KdV soliton with subcritical speed 0 < c < c* is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig (Ann Math Stud 163:181–211, 2007). For supercritical speeds c > c*, in the spirit of the work by Duyckaerts and Merle (GAFA 18:1787–1840, 2009), we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation. 相似文献
12.
In an addendum to the recent systematic Hermitization of certain N by N matrix Hamiltonians H
(N)(λ) (Znojil in J. Math. Phys. 50:122105, 2009) we propose an amendment H
(N)(λ,λ) of the model. The gain is threefold. Firstly, the updated model acquires a natural mathematical meaning of Runge-Kutta approximant
to a differential PT\mathcal{PT}-symmetric square well in which P\mathcal{P} is parity. Secondly, the appeal of the model in physics is enhanced since the related operator C\mathcal{C} of the so called “charge” (the requirement of observability of which defines the most popular Bender’s metric Q = PC\Theta=\mathcal{PC}) becomes also obtainable (and is constructed here) in an elementary antidiagonal matrix form at all N. Last but not least, the original phenomenological energy spectrum is not changed so that the domain of its reality (i.e.,
the interval of admissible couplings λ∈(−1,1)) remains the same. 相似文献
13.
We construct a family of self-adjoint operators D N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D
N
,
N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space
\mathbb CPlq{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0+-dimensional equivariant even spectral triples. If ℓ is odd and
N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8. 相似文献
14.
Wan-Fang Liu Li-Hua Zhang Chun-Jie Li 《International Journal of Theoretical Physics》2010,49(10):2463-2475
In terms of quantum Fisher information (QFI), a quantity χ
2 was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ
2<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality
χ
2<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ
2 is equal to the second kind of spin squeezing parameter x22\xi _{2}^{2}. For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition,
we extend the concept of the QFI and χ
2, and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ
2 in symmetric pure states to arbitrary pure states. 相似文献
15.
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
16.
S. G. Karshenboim 《Physics of Particles and Nuclei Letters》2009,6(6):450-454
Oscillations of neutral meson (K
0-$
\overline {K^0 }
$
\overline {K^0 }
, D
0-$
\overline {D^0 }
$
\overline {D^0 }
, and B
0-$
\overline {B^0 }
$
\overline {B^0 }
are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc
2—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct
for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field
of the galaxy center, we obtain the estimate from experimental data on K
0-$
\overline {K^0 }
$
\overline {K^0 }
oscillations:
$
\left| {\left( {\frac{{m_g }}
{{m_i }}} \right)_{K^0 } - \left( {\frac{{m_g }}
{{m_i }}} \right)_{\overline {K^0 } } } \right| \leqslant 8 \times 10^{ - 13} , at C.L. = 90\%
$
\left| {\left( {\frac{{m_g }}
{{m_i }}} \right)_{K^0 } - \left( {\frac{{m_g }}
{{m_i }}} \right)_{\overline {K^0 } } } \right| \leqslant 8 \times 10^{ - 13} , at C.L. = 90\%
相似文献
17.
Recent observations on Type-Ia supernovae and low density (Ω
m
=0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity
type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω
x
=0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the
dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to
reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis
remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also
explained why for dark energy the parameter
w=-\frac23w=-\frac{2}{3}
. Noting that w=1 for stiff matter and
w=\frac13w=\frac{1}{3}
for radiation;
w=-\frac23w=-\frac{2}{3}
is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately
released as ‘radiation’ contributing “
+\frac13+\frac{1}{3}
”, making
w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3}
. When dark energy is released free at Z=80,
w=-\frac23w=-\frac{2}{3}
. But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the
w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1
. This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several
estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many
candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a
possible candidate for dark energy. 相似文献
18.
Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant
candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric
A{\mathcal{A}} -D{\mathcal{D}} -E{\mathcal{E}} models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl
Phys B 491:659–688, 1997). 相似文献
19.
H. Amirhashchi H. Zainuddin Anirudh Pradhan 《International Journal of Theoretical Physics》2011,50(8):2531-2545
Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using
the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations
the expansion θ in the model is considered as proportional to the eigen value s2 2\sigma^{2}_{~2} of the shear tensor sj i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density
of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well
as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings
and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from
recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed. 相似文献
20.
H.?W.?Grie?hammer M.?R.?Schindler 《The European Physical Journal A - Hadrons and Nuclei》2010,46(1):73-83
We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” Effective Field Theory
(EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we
conclude that no such interactions are needed at leading order, O(eQ-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix
2S\frac12\ensuremath ^2S_{\frac{1}{2}} and
2P\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta
I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ0)\ensuremath {O}(\epsilon Q^0) . This observation is based on the approximate realisation of Wigner’s combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating
three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory
to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon
interactions from three-nucleon experiments. 相似文献
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