Hierarchical description for a non-Markoff relaxation process

A phenomenal model is proposed in this paper to describe a non-Markoff relaxation process. The main feature of the model is the fractal time concept introduced to take account of the coupling of a relaxation mode with a heat bath. The theoretical investigation indicates that a weakly non-Markoff relaxation process can be related to a set of hierarchically distributed Markoff relaxation processes and the fractal exponential law exp [?(t/τ)^1?σ] is the character of a non-Markoff relaxation process. Calculations about the temperature and time scale dependence of the exponent σ have been made, and comparison with recent experiments is also given.     

Dressed mode description of optical bistability

We generalize and simplify the definition of mode variables given in Haken's theory of phase transitions in systems far from thermal equilibrium. The Maxwell-Bloch equations for absorptive optical bistability in a ring cavity are rephrased in such a way that the boundary conditions for the field become a simple periodicity condition in space without retardation in time. From this formulation of the Maxwell-Bloch equations we derive the time evolution equations for the mode variables, which describe the dressed mode dynamics. The coefficients of these equations are analytically evaluated in the limit of small transmittivity of the mirrors. Some applications are indicated.     

Dressed mode description of optical bistability

We start from the dressed mode formulation of optical bistability, given in a previous paper. By performing anexact adiabatic elimination of the atomic modes, we derive a closed system of time evolution equations for the field modes, that play the role of order parameters. In particular in the simplest setting of two unstable modes the problem is reduced to a set of only two differential equations in time, that fully include both nonlinearity and propagation. Thus we can describe self-pulsing in terms of a simple two-dimensional phase space, which allows for treating cw and pulsing states on the same footing. We determine thefull domain of existence of the self-pulsing state and describe how this state varies with the control parameters. In particular we find hysteresis cyclesof novel type, that involve both cw and pulsing states, thereby enriching the phenomenology of Optical Bistability. A part of the boundary of the domain of existence of the self-pulsing state is found to be a line of Hopf bifurcations, which points out the existence of ahigher order bifurcation in our system. In conclusion, our procedure exploits and develops in the best way Haken's theory of generalized Ginzburg-Landau equations for phase-transition-like phenomena in systems far from thermal equilibrium.     

Entanglement and the process of measuring the position of a quantum particle

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computed on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process.     

水溶性TGA-CdTe量子点的超快弛豫动力学过程探究

本文以三个不同粒径(1^#:2.3 nm, 2^#:2.8 nm和3^#:3.5 nm)的巯基乙酸包覆的CdTe量子点(thioglycolic acid capped CdTe quantum dots, TGA-CdTe QDs)样品为研究对象, 其时间相关单光子计数(time-correlated single photon counting, TCSPC)实验得到的时间分辨光谱显示, 三个量子点的荧光平均寿命依次是～6 ns, ～10 ns和～12 ns, 其动力学过程包括慢过程和快过程两部分. 随其粒径尺寸的增加, 其慢过程延长, 快过程在变短. 然后, 通过瞬态吸收和荧光上转换两种基于飞秒的时间分辨光谱技术, 对TGA-CdTe量子点的带间弛豫过程做了探究. 实验结果显示, 三个TGA-CdTe量子点样品, 随其粒径增大, 最高激发态和最低激发态填充速率减慢, 其中, 最高激发态从0.33 ps增加至0.79 ps; 最低激发态从0.53 ps增至～1 ps. 另外, 由瞬态吸收和荧光上转换两种时间分辨手段相结合, 可得到CdTe量子点带间弛豫的完整图像, 结果显示了TGA-CdTe 量子点的一个本征特征:即在基态漂白恢复过程中的初始上升阶段, 荧光上转换信号要慢于瞬态吸收信号. 这可以为量子点在光电转换应用上提供帮助.     

Alternating-current relaxation of a rotating metallic particle

Based on a first-principles approach,we establish an alternating-current(AC) relaxation theory for a rotating metallic particle with complex dielectric constant ε_α=ε_α-iσ_α/ω_0.Here εα is the real part,σ_α the conductivity,ω_0 the angular frequency of an AC electric field,and i=-1~(1/2).Our theory yields an accurate interparticle force,which is in good agreement with the existing experiment.The agreement helps to show that the relaxations of two kinds of charges,namely,surface polarized charges(described by ε_α) and free charges(corresponding to σ_α),contribute to the unusually large reduction in the attracting interparticle force.This theory can be adopted to determine the relaxation time of dynamic particles in various fields.     

Finite-dimensional quantum mechanics of a particle

This paper analyzes the possible implications of interpreting the finitedimensional representations of canonically conjugate quantum mechanical position, and momentum operators of a particle consistent with Weyl's form of Heisenberg's commutation relation as the actual position, and momentum operators of the particle when it is confined to move within a finite spatial domain, and regarding the application of current quantum mechanical formalism based on Heisenberg's relation to such a situation as an asymptotic approximation. In the resulting quantum mechanical formalism the discrete and finite position and momentum spectra of a particle depend on its rest mass and the spatial domain of confinement. Such a finite-dimensional quantum mechanics may be very suitable for describing the physics of particles confined to move within very small regions of space.     

Cole-Davidson dielectric relaxation as a self-similar relaxation process

An effort has been undertaken to understand the nature of one type of non-exponential relaxation, namely Cole-Davidson relaxation. Toward this end, a model of relaxation as a self-similar process is proposed. An equation containing operators of fractional integration and differentiation is obtained and solved, which the relaxation function obeys in this case. Fiz. Tverd. Tela (St. Petersburg) 39, 101–105 (January 1997)     

Spin-wave relaxation in a quantum hall ferromagnet

We study spin wave relaxation in quantum Hall ferromagnet regimes. Spin-orbit coupling is considered as a factor determining spin nonconservation, and external random potential as a cause of energy dissipation making spin-flip processes irreversible. We compare this relaxation mechanism with other relaxation channels existing in a quantum Hall ferromagnet. The article is published in the original.     

Free fall of a spin-zero quantum particle

The acceleration operators are derived for a spin-zero quantum particle near an observation point which is at rest in a static, spherically symmetric gravitational field. The expectation value of the acceleration of the center of gravity of an arbitrary wave packet is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 36–41, June, 1976.     

A quantum formulation of the relaxation process and transport coefficients of magnetized plasma

From a quantum collective approach, the momentum relaxation time, through both electron-electron and electron-ion interactions, is obtained based on electron wave functions interacting with the continuum oscillations (plasma waves). The theoretical model presented gives a consistent and complete set of transport coefficients for a dense magnetized plasma. This unified scheme of long- and short-range interactions gives conductivity formulas which are free from the usual Debye length, which loses its physical meaning as an upper impact parameter for relatively high-density, coupled plasma.     

New approach to a description of relativistic particle collisions

Relativistic particle collisions are described by the 2-form of a cross product of particle momentum 1-forms. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 42–45, December, 2008.     

二维量子点中极化子的自旋弛豫

在考虑Rashba自旋-轨道耦合的条件下, 采用二次幺正变换和变分方法研究了二维抛物量子点中由于电子与体纵光学声子的耦合作用形成的极化子在基态Zeeman分裂能级上的自旋弛豫过程.这一过程主要是通过吸收或发射一个形变势或压电声学声子完成.具体分析了强、弱耦合两种极限下极化子自旋弛豫率与外磁场、量子点半径、Landau因子参数、Rashba自旋轨道耦合参数的变化关系. 关键词： 自旋弛豫 极化子 Rashba自旋轨道耦合 量子点     

Nuclear-spin-lattice relaxation in a bilayer quantum Hall system

We examined the electron spin degree of freedom around the total Landau-level filling factor ν=1 in a bilayer system via nuclear spins. In a balanced bilayer system, nuclear-spin-lattice relaxation rate 1/T₁, which probes low-energy electron spin fluctuations, increases gradually as the system is driven from the quantum Hall (QH) state through a phase transition to the compressible state. This result demonstrates that the electron spin degree of freedom is not frozen either in the QH or compressible states. Furthermore, as the density difference between the two layers is increased from balanced bilayer to monolayer configurations, 1/T₁ around ν=1 shows a rapid yet smooth increase. This suggests that pseudospin textures around the bilayer ν=1 system evolves continuously into the spin texture for the monolayer system.