共查询到20条相似文献,搜索用时 31 毫秒
1.
An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle
pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given
by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied
with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for
expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions.
Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly
demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion
of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process,
however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical
state. 相似文献
2.
S. V. Prants 《Journal of Experimental and Theoretical Physics》2009,109(5):751-761
A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed. 相似文献
3.
We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion. 相似文献
4.
采用二维谐振子相干态为初始态,在形变原子核系统分别为规则和混沌两种情况下,对其在相空间中的时间行为进行了傅里叶分析,特别比较了混沌系统中波包宽度在整个时间段与达到饱和后两个阶段的傅里叶分析结果.指出系统的混沌运动是由于大量能级免交叉的出现在波包运动的初始阶段就破坏了波包内部的规则结构,波包各成分间的协同性被破坏,波包的运动成为混沌.此后,波包内各成分对波包运动的贡献开始相同,能级之间的免交叉对波包运动的影响也不再明显. 相似文献
5.
We analyze the semiclassical evolution of Gaussian wave packets in chaotic systems. We show that after some short time a Gaussian wave packet becomes a primitive WKB state. From then on, the state can be propagated using the standard time-dependent WKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold. 相似文献
6.
7.
Sergio De Nicola Renato Fedele Duan Jovanovi Margarita A. Manko Vladimir I. Manko 《Entropy (Basel, Switzerland)》2021,23(5)
The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton’s law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space. 相似文献
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10.
This paper studies the quantum dynamics of electrons in a surface
quantum well in the time domain with autocorrelation of wave packet.
The evolution of the wave packet for different manifold eigenstates with
finite and infinite lifetimes is investigated analytically. It is
found that the quantum coherence and evolution of the surface electronic
wave packet can be controlled by the laser central energy and
electric field. The results show that the finite lifetime of excited
states expedites the dephasing of the coherent electronic wave
packet significantly. The correspondence between classical and
quantum mechanics is shown explicitly in the system. 相似文献
11.
Fabio Benatti Thomas Hudetz Andreas Knauf 《Communications in Mathematical Physics》1998,198(3):607-688
We review the notion of dynamical entropy by Connes, Narnhofer and Thirring and relate it to Quantum Chaos. A particle in
a periodic potential is used as an example. This is worked out in the classical and the quantum mechanical framework, for
the single particle as well as for the corresponding gas.
The comparison does not only support the general assertion that quantum mechanics is qualitatively less chaotic than classical
mechanics. More specifically, the same dynamical mechanism by which a periodic potential leads to a positive dynamical entropy
of the classical particle may reduce the dynamical entropy of the quantum gas in comparison to free motion.
Received: 26 June 1997 / Accepted: 13 April 1998 相似文献
12.
Chaotic Motion of a Nucleon in Mean Field Potential With Octupole Deformation (I) The Formalism of the Propagation of Coherent States in Potential 下载免费PDF全文
The temporal variation characteristics of nonstationary wave functions are investigated, which enables us to carry out the study of quantum chaotic dynamics with the same starting point as in corresponding classical case, especially to realize the sensitivity of the quantum state with respect to the initial condition. Here the coherent states under the dynamical symmetry of asymmetrical two dimensional harmonic oscillator, in which the minimum uncertainty Principle is satisfied, are usedas an initial state. The formalism of the temporal variation of the expectation values and the uncertainty measurements of canonical variables of the quantum state under the broken symmetry by the additional octupole deformed potential is fulfilled. 相似文献
13.
A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation
of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic
if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This
definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in
terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the
dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically,
proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under
chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism
towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’ 相似文献
14.
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of Ks to combine with Lewis–Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in detail. 相似文献
15.
利用含时波包法研究了强飞秒泵浦-探测激光场中激光脉宽对非绝热耦合NaI分子波包运动的影响.发现波包的振荡周期随脉宽增长而增大,而振荡幅度随脉宽增长而减小.非绝热效应引起的波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.研究表明调节激光场脉宽可实现对波包运动的控制从而控制态布居的选择性分布.研究结果可以为实验上实现分子的光控制以及量子调控过程提供一定的参考. 相似文献
16.
The possibility to formulate classical statistical mechanics in terms of the complex wave function and density matrix obeying
the evolution equation is discussed. It is shown that the modulus squared of the introduced wave function of the classical
particle has the same physical meaning as the modulus squared of the wave function of the quantum particle. The tomographic
probabilities are studied for both classical and quantum states. Integrals of motion and their relation to the propagators
are discussed. 相似文献
17.
The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spin correlations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the other hand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity. 相似文献
18.
量子参数激励单摆的局域效应研究 总被引:1,自引:1,他引:0
分析了二能级原子在振幅调制主波场中动量扩散模型。这是一个量子参数激励单摆系统。这个量子系统在经典极限下表现混沌行为。在相同参数条件下,这个系统具有动力学特征。 相似文献
19.
Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave
LI Hui HAI Wen-Hua XU Jun 《理论物理通讯》2008,49(1):143-152
We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions. 相似文献
20.
LIN Qiong-Gui 《理论物理通讯》2006,45(5):919-922
In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet.
In classical physics there is no precise counterpart to the
center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for
the electromagnetic wave. We propose a center-of-energy velocity to
describe the entire motion of general wave packets in classical
physical systems. It is a measurable quantity, and is well defined
for both continuous and discrete systems. For electromagnetic wave
packets it is a generalization of the velocity of energy transport.
General wave packets in several classical systems are studied and the
center-of-energy velocity is calculated and expressed in terms of the
dispersion relation and the Fourier coefficients. These systems
include string subject to an external force, monatomic chain and
diatomic chain in one dimension, and classical Heisenberg model in
one dimension. In most cases the center-of-energy velocity reduces to
the group velocity for quasi-monochromatic wave packets. Thus it also
appears to be the generalization of the group velocity. Wave packets
of the relativistic Dirac equation are discussed briefly. 相似文献