非线性三能级体系的绝热朗道-齐纳隧穿

研究了绝热条件下非线性三能级体系的朗道-齐纳隧穿.通过研究体系的本征值和本征态，发现当非线性不是很强时，三个能级的结构与线性情况相似，但中间能级所对应本征态的性质分段，这种分段导致绝热定理被破坏，引起所谓的绝热隧穿现象.由于本征态的不稳定性，造成隧穿率的混乱.当非线性较强时，能级结构发生非常复杂的扭曲，使绝热定理被更加严重地破坏.还讨论了这个模型在三势阱波色-爱因斯坦凝聚体系中的可能应用. 关键词： 三能级 朗道-齐纳隧穿 隧穿率     

Adiabatic pumping in interacting systems

A dc current can be pumped through an interacting system by periodically varying two independent parameters such as the magnetic field and a gate potential. We present a general expression for the adiabatic pumping current in interacting systems, written in terms of instantaneous properties of the system at equilibrium, and find the limits of its applicability. This expression generalizes the scattering approach for noninteracting particles. We apply our formula for a quantum critical system that exhibits the two-channel Kondo effect, where single particle excitations are not well defined. We find that if the quantum critical point is contained in the pumping trajectory, the pumped spin between the channels approaches h, and if it is not contained in the trajectory, the spin approaches zero when the temperature T --> 0. We discuss the non-Fermi liquid features of this system at finite T.     

Adiabatic theorem for finite dimensional quantum mechanical systems

A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. An explicitly integrable two-level system is considered as an example. It is demonstrated that the error estimate given by the adiabatic theorem cannot be improved.     

Adiabatic time-dependent Hartree-Fock theory with the consistency condition

Adiabatic time-dependent Hartree-Fock (atdhf) theory, including the authors’ work in this field, has been summarised. In response to the criticism of Yamamuraet al the role of curvature in preventing the choice ofpure rpa mode as the solution near the static Hartree-Fock minimum has been discussed.     

Adiabatic geometric phase in the nonlinear coherent coupler

We introduce the concept of geometric phase to the nonlinear coherent coupler. With considering the adiabatic change of the distance-dependent phase mismatch, we calculate the adiabatic geometric phase related to the supermode of the coupler analytically. We find that the phase depends on the input light intensity explicitly. In particular, in the low and high intensity limits, the phase equals half of the area on the Poincare sphere enclosed by the evolution loop of the system. At the critical intensity where different supermodes merge, the phase diverges, which can be considered as the signal of a continuous phase transition.     

Adiabatic quantum computation in open systems

We analyze the performance of adiabatic quantum computation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.     

Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems

Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.     

Adiabatic elimination for systems of Brownian particles with nonconstant damping coefficients

We discuss the problem of eliminating the momentum variable in the phase space Langevin equations for a system of Brownian particles in two related situations: (i) position-dependent damping and (ii) existence of hydrodynamic interactions. We discuss the problems associated with the conventional elimination and we develop an alternative elimination procedure, in the Lagevin framework, which leads to the correct Smoluchowski equation. We give a heuristic argument on the basis of stochastic differential equations for the Smoluchowski limit and establish rigorously the limit for the general case of position-dependent friction and diffusion coefficents.     

Adiabatic invariants theory of near-integrable systems with damping

Adiabatic invariants expressed in terms of spectral data are used to integrate the non-linear Schrödinger, sine-Gordon, and 3-wave interaction equations in the presence of damping. One result, for the 3-wave interaction, is that the intensities of the three wave packets behave as though they damp separately each with its own damping constant.     

Adiabatic dynamics in open quantum critical many-body systems

The purpose of this work is to understand the effect of an external environment on the adiabatic dynamics of a quantum critical system. By means of scaling arguments we derive a general expression for the density of excitations produced in the quench as a function of its velocity and of the temperature of the bath. We corroborate the scaling analysis by explicitly solving the case of a one-dimensional quantum Ising model coupled to an Ohmic bath.     

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.     

Faddeev-Born-Oppenheimer equations for molecular three-body systems: Adiabatic calculation of 9Be

The low-lying states of ⁹Be are calculated in the α-particle cluster model. The calculation is performed using a rotationally invariant molecular formulation of the three-body problem based on the Faddeev equations, which are solved for the α + n + α system in the adiabatic limit with the α-α interaction turned off. The resulting two-centre wave function is used to formulate an ansatz for the solution of the full hamiltonian of the system where all three particles interact. Unlike the traditional molecular approach, the ansatz we propose allows for the coupling between the movement of the light particle and the rotational motion of the heavy particles. This leads to a set of coupled ordinary differential equations for the three-body wave function that has good total angular momentum and parity. Although only one Born-Oppenheimer molecular energy curve is considered, all adiabatic corrections due to Coriolis coupling effects, mass polarization and derivatives of the two-centre wave function with respect to the separation distance between the α-particles are taken into account. Comparison with exact Faddeev results is presented for the ground-state energies of ⁹Be in a model problem where the α-α interaction is turned off. The validity of the molecular approach for small mass ratios between the heavy particle and the light particle is studied in a very general framework.     

Dyson-Wick expansions for nonlinear bose systems

We give the general relation between different values of the equal-time contractions in the Dyson-Wick expansion of the S-matrix and different factor orderings of the noncommuting operators in the interaction hamiltonian. Different orderings lead to different expansions with different Feynman rules.     

Adiabatic state conversion and pulse transmission in optomechanical systems

Optomechanical systems with strong coupling can be a powerful medium for quantum state engineering of the cavity modes. Here, we show that quantum state conversion between cavity modes of distinctively different wavelengths can be realized with high fidelity by adiabatically varying the effective optomechanical couplings. The conversion fidelity for gaussian states is derived by solving the Langevin equation in the adiabatic limit. Meanwhile, we also show that traveling photon pulses can be transmitted between different input and output channels with high fidelity and the output pulse can be engineered via the optomechanical couplings.     

Chaotification for a class of nonlinear systems

More and more attention has been focused on effectively generating chaos via simple physical devices. The problem of creating chaotic attractors is considered for a class of nonlinear systems with backlash function in this paper. By utilizing the Silnikov heteroclinic and homoclinic theorems, some sufficient conditions are established to guarantee that the nonlinear system has horseshoe-type chaos. Examples and simulations are given to verify the effectiveness of the theoretical results.     

Adiabatic elimination based on functional differentiation in the nonlinear and spatially distributed cases

A method of adiabatic elimination is proposed based on the use of the Furutsu-Novikov formula. A case of two nonlinear Langevin equations and a spatially distributed problem typical for the nonlinear wave propagation in random media have been considered. The method not only permits adiabatic elimination of the fast-decaying variable from the equation for the slow-decaying one but also allows for the return effect of the slow-decaying subsystem on the fast-decaying one.