Localized solution of a simple nonlinear quantum Langevin equation

A simple nonlinear quantum Langevin equation is introduced as phenomenological equation for quantum brownian motion. Easy calculations yield a unique localized wave function in the stationary regime. The given example may encourage more general use of nonlinear quantum Langevin equations for damped quantum systems, e.g. in measurement theory, in heavy ion physics, etc.     

Nonlinear quantum dynamical semigroups for many-body open systems

The notion of a nonlinear quantum dynamical semigroup is introduced, and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework. The construction of nonlinear quantum dynamical semigroups is carried out for two different mean-field models. First a mean-field coupling between a system of noninteracting subsystems and the bath is investigated. As examples, a nonlinear frictional Schrödinger equation and a model for a quantum Boltzmann equation are discussed. Second, a many-body system with mean-field interaction coupled to a bath is considered. Here, again, the form of the generator is derived; however, it cannot be obtained rigorously, except for some particular examples. Finally, the quantum Ising-Weiss model is briefly studied.     

Nonlinear Theory of Quantum Brownian Motion

A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from the quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the classical Einstein diffusion constant.     

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schr?dinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.     

Thermo-Quantum Diffusion

A new approach to the thermo-quantum diffusion is proposed and a nonlinear quantum Smoluchowski equation is derived, which describes classical diffusion in the field of the Bohm quantum potential. A nonlinear thermo-quantum expression for the diffusion front is obtained, being a quantum generalization of the classical Einstein law. The quantum diffusion at zero temperature is also described and a new dependence of the position dispersion on time is derived. A stochastic Bohm-Langevin equation is also proposed.     

Localized plasmons in quantum plasmas

We consider the nonlinear interactions between finite amplitude electron and ion plasma oscillations in a fermionic quantum plasma. Accounting for the quantum statistical electron pressure and the quantum Bohm potential, we derive a set of coupled nonlinear equations that govern the dynamics of modulated electron plasma oscillations (EPOs) in the presence of the nonlinear ion oscillations (NLIOs). We numerically study stationary solutions of our coupled nonlinear equations. We find that the quantum parameter H (equal to the ratio between the plasmonic and electron Fermi energy densities) introduces new features to the electron density and electric potential humps of localized NLIOs in the absence of EPOs. Furthermore, the nonlinear coupling between the EPOs and NLIOs gives rise to a new class of envelope solitons composed of bell shaped electric field envelope of the EPOs, which are trapped in the electron density hole (and an associated negative oscillatory electric potential) that is produced by the ponderomotive force of the EPOs. The knowledge of the localized plasmonic structures is of immense value for interpreting experimental observations in dense quantum plasmas.     

光学简并三波混频中的量子非破坏测量

运用半经典量子理论方法建立了光学简并三波混频在两输入场均不为零的情况下的理论模型 ,讨论了在两输入场均不为零时系统的动力学行为以及相应的量子非破坏测量 (QND)特性。研究结果表明 ,该系统的最佳量子非破坏测量工作点与以往的情况不同 ,不是出现在非线性共振点处而是在双稳转变点     

加偏置电场的双曲线量子阱中线性与三阶非线性光学吸收系数的计算

利用紧致密度矩阵近似方法,研究了加偏置电场双曲线量子阱中的线性与三阶非线性光学吸收系数. 得到了该系统中的线性与三阶非线性光学吸收系数的解析表达式.分析了势阱的形状、外加电场的大小以及入射光场的强度对吸收系数的影响规律. 文章以典型的AlxGa1－xAs/ GaAs双曲线量子阱为例作了数值计算.结果表明：随着势阱宽度的增加,系统的吸收系数将减小;随着外加电场的增加,系统的非对称性增加,系统的吸收系数将增加;随着外加光场强度的增加,系统的吸收系数将减小,并且当光强增加到一定值时会出现明显的饱和吸收现象,这一结论为进一步的实验研究提供了相应的理论依据.     

Nonlinear quantum mechanics: Results and open questions

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.     

On the Feynman proof of the exact relation between a class of path sums and the general nonlinear Fokker-Planck equation

A simple sum over paths will be considered for the general nonlinear diffusion process described by complex coordinates. In order to derive the corresponding stochastic differential equation the Feynman method used in quantum mechanics will be generalised for the present case of a coordinate dependent variance or diffusion function by means of a nonlinear coordinate transformation. The resulting equation will be seen to be the general nonlinear Fokker-Planck equation. The relevance of the present formulation for nonequilibrium phenomena, such as for example those occuring in nonlinear quantum optics, will be discussed.     

Vanishing and emerging of absorption quantum beats from electron spin coherence in GaAs quantum wells

We report experimental studies of absorption quantum beats induced by electron spin coherence in GaAs quantum wells. Absorption quantum beats occur for strongly localized excitons, but nearly vanish for mobile excitons in the third order nonlinear optical response. Pronounced quantum beats for mobile excitons emerge in an unusual fifth order process. These results, along with a qualitative analysis based on the use of N-exciton eigenstates, elucidate how the manifestation of electron spin coherence in the excitonic nonlinear optical response can differ fundamentally from that in an atomic system.     

磁场中耦合量子线的三阶非线性光学吸收率

本文研究了磁场中耦合量子线的三阶非线性光学吸收率,并且利用密度矩阵算符理论导出了三阶非线性光学吸收率的解析表达式.最后,以GaAs/Al_xGa_1-xAs耦合量子线为例作了数值计算,并绘出了三阶非线性光学吸收率与磁场B,光子能量h-ω以及间隔D之间的依赖关系.     

Exploring Tripartite Quantum Correlations: Entanglement Witness and Quantum Discord

In this study, we explore the tripartite quantum correlations by employing the quantum relative entropy as a distance measure. First, we evaluate the explicit expression for nonlinear entanglement witness (EW) of tripartite systems in the four dimensional space that lends itself to a straightforward algorithm for finding closest separable state (CSS) to the generic state. Then using nonlinear EW with specific feasible regions (FRs), quantum discord is derived analytically for the three-qubit and tripartite systems in the four dimensional space. Furthermore, we explicitly figure out the additivity relation of quantum correlations in tripartite systems.     

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j=j₀.     

Quantum ion acoustic solitary waves in electron-ion plasmas: A Sagdeev potential approach

Linear and nonlinear ion acoustic waves are studied in unmagnetized electron-ion quantum plasmas. Sagdeev potential approach is employed to describe the nonlinear quantum ion acoustic waves. It is found that density dips structures are formed in the subsonic region in a electron-ion quantum plasma case. The amplitude of the nonlinear structures remains constant and the width is broadened with the increase in the quantization of the system. However, the nonlinear wave amplitude is reduced with the increase in the wave Mach number. The numerical results are also presented.     

Quantum theory of light and noise polarization in nonlinear optics

We present a consistent quantum theory of the electromagnetic field in nonlinearly responding causal media, with special emphasis on Chi(2) media. Starting from QED in linearly responding causal media, we develop a method to construct the cubic Hamiltonian expressed in terms of the complex nonlinear susceptibility in a quantum mechanically consistent way. In particular, we show that the method yields the nonlinear noise polarization, which together with the linear one is responsible for intrinsic quantum decoherence.     

Quantum Decoherence of Charge Qubit Coupled to Nonlinear Nanomechanical Resonator

When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.     

Nonlinear thermoelectric response due to energy-dependent transport properties of a quantum dot

Quantum dots are useful model systems for studying quantum thermoelectric behavior because of their highly energy-dependent electron transport properties, which are tunable by electrostatic gating. As a result of this strong energy dependence, the thermoelectric response of quantum dots is expected to be nonlinear with respect to an applied thermal bias. However, until now this effect has been challenging to observe because, first, it is experimentally difficult to apply a sufficiently large thermal bias at the nanoscale and, second, it is difficult to distinguish thermal bias effects from purely temperature-dependent effects due to overall heating of a device. Here we take advantage of a novel thermal biasing technique and demonstrate a nonlinear thermoelectric response in a quantum dot which is defined in a heterostructured semiconductor nanowire. We also show that a theoretical model based on the Master equations fully explains the observed nonlinear thermoelectric response given the energy-dependent transport properties of the quantum dot.