一维受迫谐振子量子运动的经典特性

对经典一维受迫谐振子量子化,求解量子化后体系的时间演化算符.应用相空间准概率分布函数,研究了体系的量子特性.研究结果表明,初始为真空态,经过时间演化,系统波函数是一个二维高斯波包;波包中心的振幅和相位受到作用力的调制,成为调幅、调相波,波包中心的运动与经典受迫谐振子的运动形式相同.     

Quantum Dynamical Behavior of the Morse Oscillator: the Wigner Function Approach

We explore the quantum dynamical behavior of the Morse oscillator in the phase space using the Wigner function. For an initial wave packet excited with Gaussian probability distribution, we calculate the associated Wigner function and compute its time evolution. By calculating the marginal probabilities, we study the formation of quantum carpets both in the position space and in the momentum space. In addition, in view of these probabilities, we present the time evolution of the position and momentum expectation values. The structure of quantum carpets and the time-evolved expectation values mimic the emergence of quantum revivals and fractional revivals.     

非对易相空间中的狄拉克振子的能级和Wigner函数

非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并利用非对易相空间量子力学的代数关系,讨论了非对易相空间中狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.     

Semiclassical propagation of Gaussian wave packets

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.     

Quantum interference effect of a mesoscopic ring interrupted by a tunnelbarrier

We show that a scattering matrix can be used to calculate the transmission probability for a pure mesoscopic ring that has a circumference short compared with the phase coherence length that is interrupted by a clean tunnel barrier. The oscillation exhibits a period of 2π or π, depending on the thickness of the barrier, as a function of the electrostatic phase shift that arises from the etectrostatic potential applied to one branch of the ring. These results are independent of the parity of k_FL (k_F is the Fermi wave number, L is half of the path length of the ring.).     

Dynamic quantum revivals in phase space

We explain quantum revivals and fractional revivals in phase space of the Fermi?CUlam accelerator. We derive analytic expressions of the Wigner distribution function for the driven system describing quantum interferences in position and momentum space. We assume that the fractional revival times are nonrecurrent under certain conditions and display randomness in the occurrence of the phenomenon at these times.     

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on ΔkF and 2ΔkF, respectively. Here ΔkF=π(n_↑−n_↓) denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces k=ΔkF, which has recently been observed in numerous numerical studies.     

Wigner trajectories of a Gaussian wave packet perturbed by a weak potential

Trajectories along which phase-space points of the Wigner distribution function move are computed for a Gaussian wave packet moving under the influence of a weak perturbative potential. The potentials considered are a potential step, a potential barrier, and a periodic potential. Trajectories computed exhibit the complex, nonlocal nature of quantum dynamics. It is seen that quantum interference, which takes place in the time development of the wave packet, is taken care of in a simple way by the Wigner trajectory method presented here.     

Study on wave packet dynamics of E~1Σ_g~+ state of Li_2 with femtosecond-resolved photoelectron spectra

Wave packet dynamics of the Li₂ molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li₂ molecule are calculated. The time-resolved wave packet theory is used to reasonably interpret the phenomena of the photoelectron spectra for different parameters. Our calculation shows that the loss of the wave packets in the shelf state area of E{ }^1\Sigma_g^ + plays a prominent role in the process of photoionization with the increase of the delay time. Moreover, the oscillation of the wave packet on the E{ }^1\Sigma_g^ + curve symbolizes a decreasing process of energy.     

Photoemission of a single-electron wave packet in a strong laser field

The radiation emitted by a single-electron wave packet in an intense laser field is considered. A relation between the exact quantum formulation and its classical counterpart is established via the electron's Wigner function. In particular, we show that the wave packet, even when it spreads to the scale of the wavelength of the driving laser field, cannot be treated as an extended classical charge distribution, but rather behaves as a pointlike emitter carrying information on its initial quantum state. We outline an experimental setup dedicated to put this conclusion to the test.     

Decay of the Loschmidt echo for quantum states with sub-planck-scale structures

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than variant Planck's over 2pi [W. H. Zurek, Nature (London) 412, 712 (2001)]]. We investigate the influence of those sub-Planck-scale structures on the sensitivity to an external perturbation of the state's time evolution. While we do find an accelerated decay of the Loschmidt Echo for an extended state in comparison to a localized wave packet, the acceleration is described entirely by the classical Lyapunov exponent and hence cannot originate from quantum interference.     

Quantum distribution functions in the phase space of cylindrical coordinates

Cohen's quantum distribution function (QDF) is treated in cylindrical coordinates, and both the Wigner and Terletskii-Blokhintsev QDFs are obtained as special cases. It is shown that the Terletskii -Blokhintsev representation provides the simplest expression in the phase space of the dynamic variables      

Discrete and generalized phase space techniques in critical quantum spin chains

We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\frac{1}{2}$ systems. We develop a general formula relating the phase space techniques and the thermodynamical quantities of spin models, which we apply to single, bipartite and multi-partite systems governed by the XY and the XXZ models. Our approach allows us to introduce a novel way to represent, detect, and distinguish first-, second- and infinite-order quantum phase transitions. Furthermore, we show that the factorization phenomenon of the XY model is only directly detectable by quantities based on the square root of the bipartite reduced density matrix. We establish that phase space techniques provide a simple, experimentally promising tool in the study of many-body systems and we discuss their relation with measures of quantum correlations and quantum coherence.