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1.
Nazakat Ullah 《Pramana》1985,24(1-2):27-29
The linearization technique of random phase approximation is applied to the anharmonic oscillator to find a modified perturbation
series. It is shown that for the anharmonic termλx
4, the ground state energyE
0 upto the second order of perturbation is given byE
0=(35/48) (3/4)1/3
λ
1/3 asλ→∞. 相似文献
2.
The exponent λ of the structure function F2 ∼x
−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ
2 and as a function ofQ
2 at fixedx and compared with the most recent data from H1 相似文献
3.
The quantum version of a nonlinear oscillator, previously analyzed at the classical level, is studied first in one dimension
and then in two dimensions. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx
2)−1 and with a λ-dependent nonpolynomial rational potential. The quantization procedure analyzes the existence of Killing vectors
and makes use of an invariant measure. It is proved that this system can be considered as a model of the quantum harmonic
oscillator on two-dimensional spaces of constant curvature.
The text was submitted by the authors in English. 相似文献
4.
S. Brajamani P. S. Mazumdar S. K. Chowdhury Sukanya Sur 《International Journal of Theoretical Physics》1991,30(4):487-493
The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d
2/dx
2+x
2+x
2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels. 相似文献
5.
B. Montegu A. Laugier J. Chevallier J. C. Guillaume 《Applied Physics A: Materials Science & Processing》1980,22(4):403-408
The wavelength (λ) and composition (x) modulations are used simultaneously in order to obtain the second derivative ∂2
R/∂λ∂x of the reflectivity. A great sensitivity to a small composition difference is obtained. This method is applied to the determination
of the compositional profile for a ternary alloy Mg
x
Zn1−x
Te withx<0.01. A good agreement is observed with the theoretical profile calculated on the basis of a regular associated solution
model. 相似文献
6.
Shi-Min Xu Xing-Lei Xu Hong-Qi Li 《International Journal of Theoretical Physics》2008,47(6):1654-1662
The intermediate representation (namely intermediate coordinate-momentum representation) |x〉
λ,ν
are introduced and employed to research the expression of the operator
in intermediate representation |x〉
λ,ν
. The systematic Hamilton operator
of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ,ν,τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate
representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained
in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon
transformation of Wigner operator is just the projectional operator |x〉
λ,ν
λ,ν
〈x|, and the Radon transformation of Wigner function is just a margin distribution. 相似文献
7.
We study the characteristic features of certain statistical quantities near critical bifurcations such as onset of chaos,
sudden widening and band-merging of chaotic attractor and intermittency in a periodically driven Duffing-van der Pol oscillator.
At the onset of chaos the variance of local expansion rate is found to exhibit a self-similar pattern. For all chaotic attractors
the variance Σn(q) of fluctuations of coarse-grained local expansion rates of nearby orbits has a single peak. However, multiple peaks are
found just before and just after the critical bifurcations. On the other hand, Σn (q) associated with the coarse-grained state variable is zero far from the bifurcations. The height of the peak of Σn(q) is found to increase as the control parameter approached the bifurcation point. It is maximum at the bifurcation point.
Power-law variation of maximal Lyapunov exponent and the mean value of the state variablex is observed near sudden widening and intermittency bifurcations while linear variation is seen near band-merging bifurcation.
The standard deviation of local Lyapunov exponent λ(X,L) and the local mean valuex(L) of the coordinatex calculated after everyL time steps are found to approach zero in the limitL → ∞ asL
-Β. Β is sensitive to the values of control parameters. Further weak and strong chaos are characterized using the probability
distribution of ak-step difference quantity δxk = xi+k
x
i. 相似文献
8.
S. K. Bose 《Letters in Mathematical Physics》1979,3(4):259-264
We obtain here a perturbative solution of the generalx
2q+2
anharmonic damped oscillator in the coherent state representation. The solution does not contain any secular term and shows, explicitly, the damping and the anharmonic effects. 相似文献
9.
We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal
equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the
reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three
asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes
continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ2τ → 0 and the critical case λ2τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a
non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative
regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction
Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model
whose asymptotic effective evolution is generated by this Lindblad operator. 相似文献
10.
We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)λ/2, around the steady state f(x) = x ?(3+λ)/2 with ${\lambda \in (1, 2)}We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel
K(x, y) = (xy)λ/2, around the steady state f(x) = x
−(3+λ)/2 with l ? (1, 2){\lambda \in (1, 2)} . Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles
distributions described by such models. 相似文献
11.
B. I. Ermolaev S. I. Manayenkov M. G. Ryskin 《Zeitschrift fur Physik C Particles and Fields》1995,69(1):259-267
The smallx behaviour of the non-singlet structure function is studied within the double logarithmic approximation (DLA) of perturbative
QCD. Since there is neitherk
T norθ ordering in the ladder Feynman graphs, the predicted non-singlet quark densities for the HERA kinematical range (x∼10−3) exceed the values calculated from the small-x approximation of the conventional Altarelli-Parisi evolution by a factor up to ten.
Supported in part by the grant R26000 from the International Science Foundation and in part by Volkswagen Stiftung 相似文献
12.
In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE
n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω
2
x
2+λx
2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed
in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge
this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially
obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given. 相似文献
13.
J. F. Cariñena 《The European physical journal. Special topics》2008,160(1):51-60
Milne–Pinney equation
[(x)\ddot]=-w2(t)x+ k/x3\ddot x=-\omega^2(t)x+ k/{x^3}
is usually studied together with the time-dependent harmonic oscillator
[(y)\ddot]+w2(t) y=0\ddot y+\omega^2(t) y=0
and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first
equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization
of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used
to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger
and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint. 相似文献
14.
Hiroshi Isozaki 《Communications in Mathematical Physics》2001,222(2):371-413
We construct a generalized Fourier transformation ℱ(λ) associated with the 3-body Schr?dinger operator H=−Δ+Σ
a
V
a
(x
a
) and characterize all solutions of (H−λ)u= 0 in the Agmon–H?rmander space ℬ* as the image of ℱ(λ)*. These stationary solutions admit asymptotic expansions in ℬ* in terms of spherical waves associated with scattering channels.
Received: 20 September 2000 / Accepted: 20 May 2001 相似文献
15.
S. Kuwata 《International Journal of Theoretical Physics》2009,48(6):1813-1832
We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y) satisfies the homogeneity ∀
λ∈ℝ,φ(λ
x,λ
2
y)=λ
n
φ(x,y), then the parafermionic order p
f
is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x,y) is equivalent to the parasuperconformality of Q and H. The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle. 相似文献
16.
Energy eigenvalues and 〈x
2〉
n
for the oscillators having potential energyV(x)=(ω
2
x
2/2)+λ<x
2r
>x
2s
have been determined for various values ofλ, r, s andn using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers.
Variation of the evaluated quantities and of the renormalization parameter withλ, r, s andn has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative
formalism of perturbation theory developed by Kim and Sukhatme (J. Phys.
A25 647 (1992)). 相似文献
17.
The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like
an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V
HC
(x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with
〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q
o| = π/d) and experience a mutual repulsive force (zero point repulsion) f
o
=h
2/2md
3 which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual
collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining
a correct microscopic understanding of widely different many-body systems. 相似文献
18.
The energy levels of a two-dimensional system are calculated for the rational potential,V(x, y; λ, g)=x
2+y
2+λ[x
2/(1+gx
2)+y
2/(1+gy
2)+a
xxx4+a
xyx2
y
2+a
yyy4] using the inner product technique over a wide range of values of the perturbation parameters (g, λ) and for various eigenstates. 相似文献
19.
The finite-element approach to lattice field theory is both highly accurate (relative errors 1/N
2, whereN is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this Letter, we construct matrix elements for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian isH=p
2/2+q
2k
/2k. Construction of such matrix elements does not require solving the implicit equations of motion. Low-order approximations turn out to be quite accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator groundstate gives a result for thek=2 anharmonic oscillator groundstate energy accurate to better than 1% while a two-state approximation reduces the error to less than 0.1%. Accurate wavefunctions are also extracted. Analogous results may be obtained in the continuum, but there the computation is more difficult, and not generalizable to field theories in more dimensions. 相似文献
20.
In this paper we show that for a.e. x∈[ 0,2 π) the operators defined on as
and with Dirichlet condition ψ− 1= 0, have pure point spectrum in with exponentially decaying eigenfunctions where δ > 0 and are small. As it is a simple consequence of known techniques that for small λ one has [− 2 +δ, 2−δ]⊂ spectrum (H(x)) for a.e.x∈[ 0, 2 π), we thus established Anderson localization on the spectrum up to the edges and the center. More general potentials
than cosine can be treated, but only those energies with nonzero spectral density are allowed. Finally, we prove the same
result for operators on the whole line ℤ with potential , where A:?2→?2 is a hyperbolic toral automorphism, F∈C
1(?2), ∫F= 0, and λ small. The basis for our analysis is an asymptotic formula for the Lyapunov exponent for λ→ 0 by Figotin–Pastur,
and generalized by Chulaevski–Spencer. We combine this asymptotic expansion with certain martingale large deviation estimates
in order to apply the methods developed by Bourgain and Goldstein in the quasi-periodic case.
Received: 28 January 2000 / Accepted: 14 June 2000 相似文献