单粒子共振态的实稳定方法研究

基于实稳定方法的基本思想，在坐标空间求解了一维势阱和三维球对称势阱中的单粒子共振态，得到的共振能量、宽度和波函数等与散射相移法以及耦合常数的解析延拓方法的结果一致. 关键词： 共振态 实稳定方法 相移 共振宽度     

Renormalization method for the quantum system of interacting resonances

The procedure of constructing quasi-energy functions and a quasi-energy spectrum on the basis of renormalization of the hamiltonian is considered for a nonlinear quantum system in an external periodic field.     

Application of the stabilization method to interacting resonances

The stabilization method is applied to the case of interacting resonances in the photo-dissociation of van der Waals clusters composed by a rare gas atom bound to a dihalogen molecule. The study of an illustrative two-dimensional model consisting in a T-shaped NeI₂ molecule shows the adequacy of the method whenever the projection of the stabilization wave functions on the assumed prepared initial state is accounted for. The agreement of the fragmentation cross-sections with some previous results using the effective resolvent method and accurate close-coupling calculations is excellent. The method reveals its utility as a complementary tool since allows, through the analysis of the stabilization wave function in terms of zero-order levels, a precise characterization of the resonant states involved. Received 5 April 2002 / Received in final form 24 May 2002 Published online 19 July 2002     

On the description of low energy nuclear resonances with the help of quantum green's functions

It is shown how the appearance of low energy nuclear resonances in the elastic channel can be described with the help of quantumGreen's functions. After the development of the general theory a model is sketched which can be used to perform explicit calculations.     

Arnold resonances and quantum states

The dynamics of one electron interacting with a linear chain of heavy atoms bears a strong similarity with the propagation of a classical wave in a periodic non linear medium. Arnold resonances of the dynamical system play a central role. Some of the quantum states associated with these resonances are delocalized and contribute to phenomena such as Peierls dimerization while other ones are localized and are similar to the gap solitons of the classical wave theory, we call them Braggons. Complex Braggons containing several electrons inside the same localized profile are also described.     

The distant source method for computing lattice green functions

A method is proposed by which a good approximation to a Green function on a large lattice may be obtained by performing a few successive Green function computations on smaller sublattices. This alleviates the constraints imposed by limited computer memory, because less data are needed per computation, and speed, because numerical algorithms converge faster for smaller systems.     

1/N series for quantum anharmonic oscillator eigenvalues and green functions

The large orders of the 1/N series for the O(N)-symmetric anharmonic oscillator are computed here in the functional approach. We explicitly give the Kth order of the 1/N series up to O(K^?1) for all energy eigenvalues and for the two-point Green function. Our results are derived considering solutions in a finite (but large) time interval (euclidean time).     

Generalization of uncertainty relation for quantum and stochastic systems

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross–Pitaevskii equation and the Navier–Stokes–Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

Dark resonances for ground-state transfer of molecular quantum gases

One possible way to produce ultra-cold, high-phase-space-density quantum gases of molecules in the rovibronic ground state is given by molecule association from quantum-degenerate atomic gases on a Feshbach resonance and subsequent coherent optical multi-photon transfer into the rovibronic ground state. In ultra-cold samples of Cs₂ molecules, we observe two-photon dark resonances that connect the intermediate rovibrational level |v=73,J=2〉 with the rovibrational ground state |v=0,J=0〉 of the singlet X ¹ Σ _g ⁺ ground-state potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level |v=73,J=2〉 by two-photon transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the two-photon resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state |v=0,J=0〉.     

SS-HORSE method for studying resonances

A new method for analyzing resonance states based on the Harmonic-Oscillator Representation of Scattering Equations (HORSE) formalism and analytic properties of partial-wave scattering amplitudes is proposed. The method is tested by applying it to the model problem of neutral-particle scattering and can be used to study resonance states on the basis of microscopic calculations performed within various versions of the shell model.     

Classical scaling theory of quantum resonances

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.     

Imaging transport resonances in the quantum Hall effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a dc bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than 4 orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.     

Particle-hole optical model and strength functions for high-energy giant resonances

A formulation of the particle-hole optical model is proposed for describing the contribution of the fragmentation effect to the formation of strength functions for high-energy giant resonances. The model is based on the Bethe-Goldstone equation for the energy-averaged particle-hole Green’s function. In this equation, the particle-hole interaction that is induced by a virtual excitation of multiquasiparticle configurations and in which, upon averaging over energy, an imaginary part is contained is taken into account. An analogy with the single-quasiparticle optical model is discussed.     

Observation of high-order quantum resonances in the kicked rotor

Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.     

On the method of double-time green functions in the theory of spin systems

The thermodynamics of the Ising model in a transverse field is considered within RPA. Contrary to the conventional approach, the order parameter is determined by the free energy while the sum rules are used to check the accuracy for the computed correlation functions.     

Generalization of the transfer-integral method for two- and three-dimensional crystals

The ground-state expectation value can be evaluated for arbitrary interactions (including those with a hard core) if all occurring many-body wavefunctions are assumed to be products of single-particle functions and nearest-neighbor correlation functions.