General approach to quantum-classical hybrid systems and geometric forces

We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.     

Nonexponential dynamics and competition between quasi-trapped states in an N-atomic micromaser

Transient processes are examined for the reduced density matrix (RDM) of the quantum mode of a micromaser pumped by clusters of N two-level atoms. The RDM dynamics consists of the fast and slow stages. The hierarchy of time scales is explained by the fact that the spectrum of the operator of RDM evolution contains groups of eigenvalues concentrated near zero and unity. A convenient basis for describing the fast stage is provided by a set of eigenvectors and adjoint vectors of Jordan cells related to the degenerate zero eigenvalue. The dynamics of the adjoint vector as a function of the number of passed clusters is nonexponential. One adjoint vector transforms jumpwise into the neighboring vector upon the passage of the next cluster. The slow stage of dynamics is controlled by the quasi-trapped states (QTSs) of the field. These states are the generalization of the trapped states of the ideal one-atom model and can be represented as linear combinations of the long-lived eigenvectors of the evolution operator with eigenvalues close to unity. An important feature of the QTSs is their stability to fluctuations of the number of atoms in clusters and to the field relaxation rate.     

具有多分界面的非线性电路中的非光滑分岔

本文分析了具有多分界面的非线性电路在不同时间尺度下的快慢动力学行为. 在一定的参数条件下,系统的周期解为簇发解,表现出明显的快慢效应. 根据状态变量变化的快慢,把全系统划分为快子系统和慢子系统两组. 根据快慢分析法将慢变量看作快子系统的控制参数,分析了快子系统的平衡点在向量场不同区域内的稳定性. 非光滑系统的分岔与向量场的分界面密切相关,对于具有快慢效应的两时间尺度非光滑系统,快子系统的分岔则取决于分界面两侧平衡点的性质. 通过在临界面引入广义Jacobi矩阵,讨论了快子系统非光滑分岔的类型,即多次穿越分 关键词： 非线性电路 多分界面 非光滑分岔 快慢效应     

Topological Properties of the Born–Oppenheimer Approximation and Implications for the Exact Spectrum

The Born–Oppenheimer approximation can generally be applied when a quantum system is coupled with another comparatively slower system which is treated classically: for a fixed classical state, one considers a stationary quantum vector of the quantum system. Geometrically, this gives a vector bundle over the classical phase space of the slow motion. The topology of this bundle is characterized by integral Chern classes. In the case where the whole system is isolated with a discrete energy spectrum, we show that these integers have a direct manifestation in the qualitative structure of this spectrum: the spectrum is formed by groups of levels and these integers determine the precise number of levels in each group.     

Quantum theory on protein folding

The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is shown that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation-transition Hamiltonian the nonradiative matrix element was calculated and a general formulas for protein folding rate was deduced. The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted. By using temperature dependence data the multi-torsion correlation was studied. The decoherence time of quantum torsion state is estimated. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.     

Extra revivals in cooperative atomic inversion in a cavity

We investigate collective and quantum properties of the atomic inversion of A two-level atoms interacting with a strong quantum field of a single-mode loss-free cavity. The dynamics consists of A fast scales of Rabi oscillations, each featuring collapses and revivals. The first revival of the second quasiharmonic scale can be observed with large cooperativity, demonstrating altogether the existence of the extra sidebands of the resonance fluorescence spectrum. There are also A slow cooperative scales which form the slow envelope of the inversion, which for large cooperativity can split the revivals. For the case of half excited initial atomic state the energy exchange between the field and atomic system is strongly suppressed, and there is an average energy loss by the atoms.     

Fluctuations in a fluid under a stationary heat flux. I. General theory

We present the basic formulas for a unified treatment of the correlation functions of the hydrodynamic variables in a fluid between two horizontal plates which is exposed to a stationary heat flux in the presence of a gravity field (Rayleigh-Bénard system). Our analysis is based on fluctuating hydrodynamics. In this paper (I) we show that in the nonequilibrium stationary state the hydrodynamic fluctuations evolve on slow and fast time scales that are widely separated. A time scale perturbation theory is used to diagonalize the hydrodynamic operator partially. This enables us to derive the eigenvalue equations for the nonequilibrium hydrodynamic modes. Therein we take into account the variation of the macroscopic quantities with position. The correlation functions are formally expressed in terms of the nonequilibrium modes. In paper II the slow hydrodynamic modes (viscous and viscoheat modes) will be determined explicitly for ideal heat-conducting plates with stick boundary conditions and used to compute the slow part of the correlation functions; in paper III the fast hydrodynamic modes (sound modes) will be explicitly determined for stick boundary conditions and used to compute the fast part of the correlation functions. In these papers we will also compute the shape and intensity of the lines measured in light scattering experiments.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Evidence of quantum interference in transport properties of a triple quantum dot T-shape system

We consider the transport and the noise characteristic in the case of a triple quantum dots T-shape system where two of the dots form a two-level system and the other works in a detector-like setup. Our theoretical results are obtained using the equation of motion method for the case of zero and finite on-site Coulomb interaction in the detector dot. We present analytic results for the electronic Green’s functions in the system’s component quantum dots, and we used numerical calculations to evaluate the system’s transport properties. The transport trough the T-shaped system can be controlled by varying the coupling between the two-level system dots or the coupling between the detector dot and the exterior electrodes. The system’s conductance presents Fano dips for both strong (fast detector) and weak coupling (slow detector) between the detector dot and the external electrodes. Due to stronger electronic correlations the noise characteristics in the case of a slow detector are much higher. This setup may be of interest for the practical realization of qubit states in quantum dots systems.     

Measurement of energy eigenstates by a slow detector

We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.     

Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.     

回音壁微腔光力系统的相干控制与完全相干透射

本文研究了两侧同时输入的回音壁模谐振双微腔光力系统中电磁诱导透明的相干调控.通过改变双微腔两侧探测场的强度比值及相位差,可以有效控制电磁诱导透明窗口的宽度和深度,对探测场的吸收和色散等性质实施显著的影响,并且能够在特殊频率处产生关于探测场的完全相干透射现象.     

Coherent atom interactions mediated by dark-state polaritons

We suggest a technique to induce effective, controllable interactions between atoms that is based on Raman scattering into an optical mode propagating with a slow group velocity. The resulting excitation corresponds to the creation of spin-flipped atomic pairs in a way that is analogous to correlated photon emission in optical parametric amplification. The technique can be used for fast generation of entangled atomic ensembles, spin squeezing, and applications in quantum information processing.     

Effective fault-tolerant quantum computation with slow measurements

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.     

Conservation Laws and optimal system of extended quantum Zakharov-Kuznetsov equation

In this paper, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is further explored. The equation is shown to be self-adjoint and conserved vector is constructed according to the related theorem. Then the corresponding optimal system of one-dimensional subgroups is determined. Similarity reductions of the equation under optimal system of subgroups are performed. As a result, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is reduced into a linear PDE with two independent variables.     

原子辅助光力系统中快慢光的量子调控

随着纳米科技以及半导体技术的迅猛发展,光力诱导透明、快慢光和光存储以及其他在光力系统中发现的量子光学和非线性光学效应成为人们目前研究的热点.本文将薄膜腔光力系统同被束缚在腔中的二能级冷原子系综相耦合,通过直接在薄膜振子上引入弱辅助驱动场来研究该原子辅助光力系统中原子和相位对量子相干性质及其快慢光的调控.经过分析发现,通过改变辅助驱动场的强度可直接实现对光力诱导透明窗口深度的调控,通过改变辅助场与探测场之间的相位差,可实现输出的探测场在"吸收"、"透明"和"增益"之间相互转换,进而对弱探测场进行动态调控实现光开关.与此同时,还发现系统的群延迟时间随相位差的改变呈周期性变化.通过调节相位差及原子数,不但可以改变群延迟时间,还可实现快慢光之间的相互转换.     

An elementary model of torus canards

We study the recently observed phenomena of torus canards. These are a higher-dimensional generalization of the classical canard orbits familiar from planar systems and arise in fast-slow systems of ordinary differential equations in which the fast subsystem contains a saddle-node bifurcation of limit cycles. Torus canards are trajectories that pass near the saddle-node and subsequently spend long times near a repelling branch of slowly varying limit cycles. In this article, we carry out a study of torus canards in an elementary third-order system that consists of a rotated planar system of van der Pol type in which the rotational symmetry is broken by including a phase-dependent term in the slow component of the vector field. In the regime of fast rotation, the torus canards behave much like their planar counterparts. In the regime of slow rotation, the phase dependence creates rich torus canard dynamics and dynamics of mixed mode type. The results of this elementary model provide insight into the torus canards observed in a higher-dimensional neuroscience model.     

Optomechanically induced amplification and perfect transparency in double-cavity optomechanics

We study optomechanically induced amplification and perfect transparency in a double-cavity optomechanical system. We find that if two control lasers with appropriate amplitudes and detunings are applied to drive the system, optomechanically induced amplification of a probe laser can occur. In addition, perfect optomechanically induced transparency, which is robust to mechanical dissipation, can be realized by the same type of driving. These results indicate important progress toward signal amplification, light storage, fast light, and slow light in quantum information processes.     

介电极化新概念--边界屏蔽理论

熟知的介电极化只是一种快效应,还有一种慢效应。慢极化效应使电介质的极化偏离了麦克斯韦方程组描述的规律,引入边界屏蔽电荷的概述２来描述介质的极化过程,可以固避电介质内部复杂的电位移运动,从而能用屏蔽电荷激发的量子统计理论来说明驻极体和铁电体的许多性质。