Statistical properties related to angle variables in Hamiltonian map approach for one-dimensional tight-binding models with localization

Yanxu Chen and Longyan Gong ()
Additional contact information
Yanxu Chen: Nanjing University of Posts and Telecommunications
Longyan Gong: Nanjing University of Posts and Telecommunications

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 1, 1-10

Abstract: Abstract The Hamiltonian map approach transforms a one-dimensional (1D) discrete Schrödinger equation to a classical two-dimensional (2D) iterative equation with action-angle variables $$(r_n,\theta _n)$$ ( r n , θ n ) at the nth iterative step. The corresponding Hamiltonian describes a linear parametric oscillator with time-dependent linear periodic delta kicks. We use a $$\theta $$ θ -related order parameter R to measure the degree of instability of trajectory $$\{(r_n,\theta _n)\}$$ { ( r n , θ n ) } . Two prototypical models, i.e., the 1D Anderson model and the 1D slowly varying incommensurate potential model, are as examples. All states are localized in the former model, and states may be extended, localized and critical in the latter model. In the two models, we find R increases with the Lyapunov exponent and the inverse localization tensor (they are inversely proportional to localization length), so the instability of trajectory relates to Anderson localization. Graphic abstract

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-022-00477-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-022-00477-9

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-022-00477-9

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().