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94.
We consider a non-local regularization of nonlinear hyperbolic conservation laws in several space variables. The regularization is motivated by the theory of phase dynamics and is based on a convolution operator. We formulate the initial value problem and begin by deriving a priori estimates which are independent of the regularization parameter. Following Hwang and Tzavaras we establish a kinetic decomposition associated with the problem under consideration, and we conclude that the sequence of solutions generated by the non-local model converges to a weak solution of the corresponding hyperbolic problem. Depending on the scaling introduced in the non-local dispersive term, this weak limit is either a classical Kruzkov solution satisfying all entropy inequalities or, more interestingly, a nonclassical entropy solution in the sense defined by LeFloch, that is, a weak solution satisfying a single entropy inequality and containing undercompressive shock waves possibly selected by a kinetic relation. Finally, we illustrate our analytical conclusions with numerical experiments in one spatial variable. 相似文献
96.
Daniel J. Arrigo David A. Ekrut Jackson R. Fliss Long Le 《Journal of Mathematical Analysis and Applications》2010,371(2):813-820
The nonclassical symmetries of a class of Burgers' systems are considered. This study was initialized by Cherniha and Serov with a restriction on the form of the nonclassical symmetry operator. In this paper we remove this restriction and solve the determining equations to show that (1) a new form of a Burgers' system exists that admits a nonclassical symmetry and (2) a Burgers' system exists that is linearizable. 相似文献
97.
We introduce a new formulation of nonclassicality in weak measurements based on probabilistic behavior of “quasi-moments” of a weakly measured observable. New definition determines existence of classical probabilistic interpretation and can be applied equally to quantum systems without classical counterpart in the usual sense. We show that the only consistent approach to define classicality in weak measurements should be based on the proper behavior of “quasi-moments” according to Bochner's theorem. 相似文献
98.
We consider the interaction between an f-deformed Bose–Einstein condensate and a single-mode quantized light field. By using the Gardiner’s phonon operators, we find that there exists a natural deformation in the model which modifies the Bogoliubov approximation under the condition of large but finite number of particles in condensate. This approach introduces an intrinsically deformed Bose–Einstein condensate, where the deformation parameter, well-defined by the particle number N in condensate, controls the strength of the associated nonlinearity. By introducing the deformed Gardiner’s phonon operators we modify the very dilute-gas approximation through including atomic collisions in condensate. The rate of atomic collisions κ, as a new deformation parameter in the deformed Bose–Einstein condensate, controls the nonlinearity related to the atomic collisions. We show that by controlling the nonlinearities in the f-deformed atomic condensate through the two atomic parameters N and κ, it is possible to generate and manipulate the nonclassical quantum statistical properties of radiation field, such as, the sub-Poissonian photon statistics and quadrature squeezing. Also, it is possible to control the collapses and revivals phenomena in the average number of photons by atomic parameters N and κ. 相似文献
99.
H. Prakash P. Kumar 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,46(2):359-363
We study amplitude-squared squeezing of the Hermitian operator Zθ=Z1
cosθ+Z2 sin θ, in the most general superposition state
, of two coherent states
and
. Here operators Z1,2 are defined by
, a is annihilation operator, θ is angle, and
complex numbers C1,2 , α, β are arbitrary and only
restriction on these is the normalization condition of the state
. We define the condition for a state
to be amplitude-squared squeezed for the operator Zθ
if squeezing parameter
, where N=a+a and
. We find
maximum amplitude-squared squeezing of Zθ in the superposed
coherent state
with minimum value 0.3268 of the
parameter S for an infinite combinations with α- β= 2.16
exp [±i(π/4) + iθ/2],
and with
arbitrary values of (α+β) and θ. For this minimum
value of squeezing parameter S, the expectation value of photon number can
vary from the minimum value 1.0481 to infinity. Variations of the parameter
S with different variables at maximum amplitude-squared squeezing are also
discussed. 相似文献
100.
光子消灭算符高次幂本征态的振幅N次方压缩 总被引:4,自引:0,他引:4
本文研究了光子消灭算符高次幂ak(k≥3)的k个正交归一本征态的振幅N次方压缩特性,结果表明,当k为偶数时,这些本征态均可存在振幅N次方(N=(m+1/2)k,m=0,1,2,…)压缩。 相似文献