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quantum diffusion in bilateral doped chains

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Chinese Physics B 2011年第7期20卷 345-350页

作者：金福报张凯旺钟建新 Department of Physics Xiangtan University

In this paper, we quantitatively study the quantum diffusion in a bilateral doped chain, which is randomly doped on both sides. A tight binding approximation and quantum dynamics are used to calculate the three electronic characteristics： autocorrelation function C（t）, the mean square displacement d（t） and the participation number P（E） in different doping situations. The results show that the quantum diffusion is more sensitive to the small ratio of doping than to the big one, there exists a critical doping ratio qo, and C（t）, d（t） and P（E） have different variation trends on different sides of qo. For the self-doped chain, the doped atoms have tremendous influence on the central states of P（E）, which causes the electronic states distributed in other energy bands to aggregate to the central band （E = 0） and form quasi-mobility edges there. All of the doped systems experience an incomplete transition of metal-semiconductor-metal.

关键词： quantum diffusion doped chain metal semiconductor transition

Periodic oscillation of quantum diffusion in coupled one-dimensional systems

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Science China(Physics,Mechanics & Astronomy) 2022年第4期65卷 95-103页

作者： JinYi Jiang YanYan Lu Chao Wang Rémy Mosseri JianXin Zhong Hunan Key Laboratory of Micro-Nano Energy Materials and Devices School of Physics and OptoelectronicsXiangtan UniversityXiangtan 411105China Laboratoire de Physique Théorique de la Matière Condensée Sorbonne UniversitéCentre National de la Recherche ScientifiqueParis F-75005France

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping *** of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.

关键词： quantum diffusion periodic oscillation localization coupled systems

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Periodic electron oscillation in coupled two-dimensional lattices

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Chinese Physics B 2023年第7期32卷 142-149页

作者：陆艳艳王超将金益刘洁钟建新 Hunan Key Laboratory of Micro-Nano Energy Materials and Devices School of Physics and OptoelectronicsXiangtan UniversityHunan 411105China

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian *** show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal *** frequency of this oscillation is determined by the strength of the interlayer ***,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered *** numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene *** the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer *** findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.

关键词： quantum diffusion periodic oscillation coupled systems disorder Anderson localization

Entropy and Irreversibility in Classical and quantum Mechanics

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Journal of Modern Physics 2011年第6期2卷 519-532页

作者： V.A.Antonov Boris P.Kondratyev Main(Pulkovo)Astronomical Observatory Saint PetersburgRussia Udmurt State University IzhevskRussia

Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.

关键词： Markov Chains Irreversibility in Classical and quantum Mechanics Lindblad Equation Caldeira-Leggett Equation quantum diffusion Schrodinger’s Cat Paradox Heisenberg’s Uncertainty Relation Collapse of Wave Function Effect of Sokolov