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1.
On Noncommutative Multi-Solitons 总被引:2,自引:0,他引:2
Rajesh Gopakumar Matthew Headrick Marcus Spradlin 《Communications in Mathematical Physics》2003,233(2):355-381
We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The
existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic
energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ2)
k
/S
k
. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ2/ℤ
k
, cylinder, and T
2
. However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli
space provides an explicit K?hler resolution of (ℝ4)
k
/S
k
. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ
d
, which for d>2 (and k>3) is not smooth and can have multiple branches.
Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002
Communicated by R.H. Dijkgraaf 相似文献
2.
基于带输运模型理论建立了 LiNbO3 晶体屏蔽光伏孤子的时空演化动力学方程, 用有限差分方法求解发现, LiNbO3 晶体中明、暗屏蔽光伏孤子存在大的自偏转, 并且光孤子形状变得具有不对称性, 偏转方向的曲线斜率绝对值变大, 偏转反方向的曲线斜率绝对值变小. 分析研究表明影响其自偏转度和形变的因素包括受主浓度 NA, 暗辐射强度 Id 和外加电场 E0 . 其他条件不变的情况下NA 越大, 明孤子的自偏转度与形变越小, 暗孤子的自偏转度与形变反而越大; 对于 Id , 它对明暗孤子的影响是相同的, Id 越小, 晶体里诱导出的空间电荷场越容易达到饱和, 当信号光中心光强与暗辐射强度之比为 10-1时无饱和现象产生; 随着 E0 数值的增大, 明孤子的自偏转度和形变减小, 而暗孤子的自偏转度和形变反而增大. 相似文献
3.
D. Mihalache D. Mazilu F. Lederer H. Leblond B. A. Malomed 《The European physical journal. Special topics》2009,173(1):245-254
We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning)
three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are
observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the
formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large
values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments. 相似文献
4.
We consider the quasi-geostrophic equation with the dissipation term, κ (-Δ)α θ, In the case , Constantin-Cordoba-Wu [6] proved the global existence of strong solution in H
1
and H
2
under the assumption of small L
∞
-norm of initial data. In this paper, we prove the global existence in the scale invariant Besov space, B
2−2α
2,1
, for initial data small in the B
2−2α
2,1
norm. We also prove a global stability result in B
1
2,1
.
Received: 24 April 2002 / Accepted: 29 July 2002 Published online: 10 December 2002
Communicated by P. Constantin 相似文献
5.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
6.
The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric
turbulence is derived. It is shown that the angular spread θ
sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition
of the intensity. However, the θ
sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition
of the cross-spectral density function. For the superposition of the cross-spectral density function, θ
sp of GSM array beams with smaller coherence length σ
0, smaller waist width w
0, smaller beam number N, and larger separation distance x
d
are less affected by turbulence than of those with larger σ
0,w
0,N, and smaller x
d
; while, for the superposition of the intensity, the effect of turbulence on θ
sp is independent of N and x
d
. In addition, the angular spread is nearly the same for the two types of superposition when σ
0 or w
0 is small enough, or x
d
is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition
which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence. 相似文献
7.
V. N. Likhachev T. Yu. Astakhova G. A. Vinogradov 《Russian Journal of Physical Chemistry B, Focus on Physics》2011,5(6):1023-1037
In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity
process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce
the time of computation of heat conductivity at ΔT → 0. The threshold temperature T
thr is found to behave as T
thr ∼ N
−3, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T
thr, phonon heat conductivity is dominant; at T > T
thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat
conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium
process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de
Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires
further study. 相似文献
8.
We study a soliton solution of a path-averaged (in the spectral domain) propagation equation governing the transmission of
a chirped breather pulse in the fiber lines with dispersion compensation. We demonstrate that the averaged Hamiltonian model
correctly describes features of the chirped soliton observed in numerical simulations and experiments. We show that the Hamiltonian
is bounded from below if the average dispersion is anomalous 〈 d〉>0); that, together with the condition H
sol<0, indicates stability of dispersion-managed solitons in this region.
Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 791–795 (10 December 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
9.
S.?Liu H.?Kn?ckel E.?Tiemann 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,60(2):269-277
We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting
from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate
the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component
case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong
nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when
the strength of the NOL (γ
1) is less than that of the LOL (V
0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true
for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive
IAI makes the component solitons wider. For γ
1 > V
0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ
1 < V
0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii
equations numerically. 相似文献
10.
Xuguang Lu 《Journal of statistical physics》2006,124(2-4):517-547
The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L
1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ
*|γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫0
π
b(cos θ)sin 3θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L
∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy. 相似文献
11.
Jean-Paul Boucher 《Hyperfine Interactions》1989,49(1-4):423-438
Topological excitations play a crucial role in antiferromagnetic chains. In the present review, we focus on the dynamical
fluctuations induced by these quasi-particles, trying to show how they can be observed experimentally. In particular the pulsed
nuclear magnetic resonance (NMR) technique can probe these fluctuations at very low frequency. In the same context, neutron
spin echo (NSE) measurements are briefly mentioned. A discussion of soliton magnetic resonance (SMR) measurements in also
presented: they reveal the existence of internal precessions in the solitons (Dyons) and they show that the uniform (q=0) soliton modes can be detected directly. The experimental data to be discussed were obtained on three compounds: TMMC which
provides good examples for “broad” solitons and CsCoCl3 for “narrow” solitons. A discussion of NMR data obtained with NENP is given in the context of the Haldane's conjecture.
Member of Equipe de Recherche CNRS no. 216. 相似文献
12.
This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m
t
+ m
x
u + 3mu
x
= 0, m = u − u
xx
. Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim|x|→ ∞
u =A ≠0, or possesses the regular peakon solutions ce
− |x − ct| ∈ H
1 (c is the wave speed) only when lim|x|→ ∞
u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth
solitons and cusp solitons of the DP equation.
相似文献
13.
用数值方法证实了亮、暗屏蔽光伏孤子在有外加电场的LiNbO3晶体中都可以发生大自偏转,并验证了这种自偏转现象不但与晶体中受主浓度NA有关而且还与外加电场E0有关. 在E0相同的条件下,NA越小这种自偏转现象越明显,在NA相同的条件下,E0越大自偏转现象越明显. 还发现亮、暗屏蔽光伏孤子的自偏转现象不同:亮屏蔽光伏孤子整体都发生明显偏转,暗屏蔽光伏孤子的偏转只是发生在一侧,其极值位置和另一侧几乎不发生偏转.
关键词:
自偏转
空间孤子
光折变效应 相似文献
14.
Roberto Longo 《Communications in Mathematical Physics》2003,237(1-2):7-30
Given an irreducible local conformal net 𝒜 of von Neumann algebras on S
1
and a finite-index conformal subnet ℬ⊂𝒜, we show that 𝒜 is completely rational iff ℬ is completely rational. In particular
this extends a result of F. Xu for the orbifold construction. By applying previous results of Xu, many coset models turn out
to be completely rational and the structure results in [27] hold. Our proofs are based on an analysis of the net inclusion
ℬ⊂𝒜; among other things we show that, for a fixed interval I, every von Neumann algebra intermediate between ℬ(I) and 𝒜(I) comes from an intermediate conformal net ℒ between ℬ and 𝒜 with ℒ(I)=. We make use of a theorem of Watatani (type II case) and Teruya and Watatani (type III case) on the finiteness of the
set ℑ(𝒩,ℳ) of intermediate subfactors in an irreducible inclusion of factors 𝒩⊂ℳ with finite Jones index [ℳ:𝒩]. We provide
a unified proof of this result that gives in particular an explicit bound for the cardinality of ℑ(𝒩,ℳ) which depends only
on [ℳ:𝒩].
Received: 21 December 2001 / Accepted: 28 February 2002
Published online: 14 March 2003
RID="⋆"
ID="⋆" Supported in part by MIUR and INDAM-GNAMPA.
Communicated by K. Fredenhagen 相似文献
15.
F. Schümann S. Zavatarelli L. Gialanella U. Greife M. Junker D. Rogalla C. Rolfs F. Strieder H.P. Trautvetter 《The European Physical Journal A - Hadrons and Nuclei》1998,2(4):337-342
Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θlab=165° and E
lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given
by the Rutherford scattering law, σR(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σR(E,θ)=(1+Ue/E)−1, where U
e is an atomic screening potential energy. The deduced average value, U
e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies.
Received: 25 May 1998 相似文献
16.
There are various situations in which it is natural to ask whether a given collection of k functions, ρ
j
(r
1,…,r
j
), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ
j
’s for this to be true. Our primary examples are X=ℝ
d
, X=ℤ
d
, and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently
small densities ρ
1(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when
X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example
in which a uniform density ρ and translation invariant ρ
2 are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established. 相似文献
17.
Pan Wang Bo Tian Wen-Jun Liu Qi-Xing Qu Min Li Kun Sun 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,61(3):701-708
Under investigation in this paper are two extended Korteweg-de Vries
(eKdV) equations in fluids with the second-order nonlinear and
dispersive terms. Based on the Ablowitz-Kaup-Newell-Segur system,
the Lax pair and infinitely many conservation laws are derived. By
virtue of the Hirota method and symbolic computation, the bilinear
forms and N-soliton solutions for the two eKdV equations are
obtained, respectively. Relevant propagation properties and
interaction behaviors of the solitons are illustrated graphically.
The collisions for the η profile are proved to be elastic
through the asymptotic analysis. Types of collisions (head-on or
overtaking collisions) can be controlled when we adjust the sign of
the velocity v. Velocities of solitons are related to c
4 and
α during the collisions. Moreover, there is not a direct
proportion relationship between the velocity v and amplitude a
during the collisions. On the one hand, the soliton with the larger
amplitude travels faster and catches up with the smaller one. On the
other hand, the soliton with the smaller amplitude travels faster
and catches up with the larger one. 相似文献
18.
We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple
geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a non-trivial magnetic
flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any
reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau
level for unit magnetic charge appear at the crossing of the two non-contractible circles α−, β− with holonomies h
α-(A)=h
β-(A)=−1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly.
Received: 6 April 1999 / Accepted: 21 October 2000 相似文献
19.
E. A. Kuznetsov 《Journal of Experimental and Theoretical Physics》1999,89(1):163-172
The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element
of the four-wave interaction has an additional smallness, is studied. It is that shown for optical solitons striction can
weaken the Kerr nonlinearity. It is shown that solitons with a finite amplitude discontinuity at the critical soliton velocity,
equal to the minimum phase velocity of linear waves, are unstable while solitons with a soft transition remain stable with
respect to one-dimensional perurbations. Two-and three-dimensional solitons near threshold are unstable with respect to modulation
perturbations.
Zh. éksp. Teor. Fiz. 116, 299–317 (July 1999) 相似文献
20.
C?t?lin I. Carstea 《Communications in Mathematical Physics》2010,300(2):487-528
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from
\mathbbR2+1 ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d
ρ
2 + g(ρ)2
dθ2, g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u
tt
+ u
rr
+ r
−1
u
r
= r
−2
g(u)g′(u), λ(t) = t
−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0. 相似文献