Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

Quantum diffusion in bilateral doped chains

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.

Periodic oscillation of quantum diffusion in coupled one-dimensional systems

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 strength.Existence 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.

Entropy and Irreversibility in Classical and Quantum Mechanics

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.

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We 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 directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,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 lattices.Our 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 systems.Unlike 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 coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.

Non-Markovian entanglement transfer to distant atoms in a coupled superconducting resonator

We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits,which are embedded in a coupled superconducting resonator.The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion(NMQSD)method.Based on the solution,we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time.That is to say,the non-Markovian environment can enhance the entanglement transfer.It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated intercavity coupling.Moreover,with the initial anti-correlated state,the entanglement between the cavity fields can be almost completely transferred to the separated atoms.Lastly,we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.