Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Quantum dynamics of charge transfer on the one-dimensional lattice: Wave packet spreading and recurrence

Vladimir Nikolaevich Likhachev, O. I. Shevaleevskiǐ, George A Vinogradov

Published Jan 1, 2016• 10 citations
Publisher

Abstract

The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation.The lattice consists of N equal sites and one impurity site (donor).The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor.The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2.The wave packet width grows with time ∼ t 1/3 and its amplitude decreases ∼ t -1/3 .The wave packet reflects multiply from the lattice ends.Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

DOI
10.1088/1674-1056/25/1/018708

Related papers

Quantum dynamics of charge transfer on the one-dimensional lattice： Wave packet spreading and recurrence

Лихачев, Shevaleevskii

The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

中国物理B：英文版•Jan 1, 2016•0 citations

Integral Characteristics of Wave Packets in the Problem of the Evolution of A Wave Function on A One-Dimensional Lattice

V. N. Likhachov, George A Vinogradov

We consider the quantum dynamics of charge transfer on a lattice in the tight-binding approximation and analytically calculate the integral characteristics of the wave packet propagating along the lattice. We focus on calculating the mean and root-mean-square displacements. We also obtain expressions for higher-order moments as series for squares of Bessel functions, which might be independently interesting.

Theoretical and Mathematical Physics•Nov 1, 2018•0 citations

The Green’s Function in the Problem of Charge Dynamics on A One-Dimensional Lattice with An Impurity Center

Vladimir Nikolaevich Likhachev, George A Vinogradov

In the “tight-binding” approximation (the Hückel model), we consider the evolution of the charge wave function on a semi-infinite one-dimensional lattice with an additional energy U at a single impurity site. In the case of the continuous spectrum (for |U| < 1) where there is no localized state, we construct the Green’s function using the expansion in terms of eigenfunctions of the continuous spectrum and obtain an expression for the time Green’s function in the form of a power series in U. It unexpectedly turns out that this series converges absolutely even in the case where the localized state is added to the continuous spectrum. We can therefore say that the Green’s function constructed using the states of the continuous spectrum also contains an implicit contribution from the localized state.

Theoretical and Mathematical Physics•Jul 1, 2018•1 citation

Propagation of !D Electron wave equations in lattice system

Fahrudin Nugroho

The propagation of one dimensional electron wave function in periodic potential have been simulated. Gaussian wave function was chose to simulate the wave packet for the electron. The simulation or periodic potential shows that it follows Bloch theorem. Many problems related with the shape of potential are simulated also. Initial energy chose as tested parameter, which correspond to the speed of wave packet and related with the energy of the electron, and its show that for greater energy the spreading of wave packet become slower. The dynamical parameter makes possibilities to evaluate the propagation every time we need.

•May 16, 2009•0 citations

Coherent Spatial Control of Wave Packet Dynamics on Quantum Lattices

Ilia Tutunnikov, Chern Chuang, Jianshu Cao

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.

arXiv:2311.07254•The Journal of Physical Chemistry Letters•Dec 15, 2023•6 citations

Wave-packet dynamics in the one-dimensional extended Hubbard model

K. A. Al-Hassanieh, Julián Rincón, Elbio R. Dagotto +1 more

Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, $U$ and $V$, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on $V$. For small and intermediate values of $V$, both velocities increase with $V$. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by $V$. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.

arXiv:1309.5119•Physical Review B•Jul 3, 2013•14 citations
The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation.The lattice consists of N equal sites and one impurity site (donor).The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor.The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2.The wave packet width grows with time ∼ t 1/3 and its amplitude decreases ∼ t -1/3 .The wave packet reflects multiply from the lattice ends.Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.
The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.
In the “tight-binding” approximation (the Hückel model), we consider the evolution of the charge wave function on a semi-infinite one-dimensional lattice with an additional energy U at a single impurity site. In the case of the continuous spectrum (for |U| < 1) where there is no localized state, we construct the Green’s function using the expansion in terms of eigenfunctions of the continuous spectrum and obtain an expression for the time Green’s function in the form of a power series in U. It unexpectedly turns out that this series converges absolutely even in the case where the localized state is added to the continuous spectrum. We can therefore say that the Green’s function constructed using the states of the continuous spectrum also contains an implicit contribution from the localized state.
The propagation of one dimensional electron wave function in periodic potential have been simulated. Gaussian wave function was chose to simulate the wave packet for the electron. The simulation or periodic potential shows that it follows Bloch theorem. Many problems related with the shape of potential are simulated also. Initial energy chose as tested parameter, which correspond to the speed of wave packet and related with the energy of the electron, and its show that for greater energy the spreading of wave packet become slower. The dynamical parameter makes possibilities to evaluate the propagation every time we need.
Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, UUU and VVV, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on VVV. For small and intermediate values of VVV, both velocities increase with VVV. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by VVV. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.