scholarly journals Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII

2013 ◽  
Vol 88 (13) ◽  
Author(s):  
Jan Carl Budich ◽  
Eddy Ardonne
Keyword(s):  
Time Reversal ◽  
Topological Invariant ◽  
One Dimensional

scholarly journals Topological entropy and partially hyperbolic diffeomorphisms

2008 ◽  
Vol 28 (3) ◽  
pp. 843-862 ◽  
Author(s):  
YONGXIA HUA ◽  
RADU SAGHIN ◽  
ZHIHONG XIA
Keyword(s):  
Topological Entropy ◽  
Topological Invariant ◽  
Compact Manifolds ◽  
Two Dimensional ◽  
One Dimensional ◽  
Hyperbolic Diffeomorphisms ◽  
Lower Semi ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms

AbstractWe consider partially hyperbolic diffeomorphisms on compact manifolds. We define the notion of the unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, we prove the following two results: if the center foliation is one-dimensional, then the topological entropy is locally a constant; and if the center foliation is two-dimensional, then the topological entropy is continuous on the set of all $C^{\infty }$ diffeomorphisms. The proof uses a topological invariant we introduced, Yomdin’s theorem on upper semi-continuity, Katok’s theorem on lower semi-continuity for two-dimensional systems, and a refined Pesin–Ruelle inequality we proved for partially hyperbolic diffeomorphisms.

scholarly journals A note on one-dimensional chaotic maps under time reversal

1992 ◽  
Vol 24 (1) ◽  
pp. 219-220 ◽  
Author(s):  
H. Tong ◽  
B. Cheng
Keyword(s):  
Time Series ◽  
Time Reversal ◽  
Chaotic Maps ◽  
Time Series Models ◽  
Deterministic Models ◽  
One Dimensional ◽  
Stochastic Time Series ◽  
Stochastic Time

We have furnished further examples on the connection between some standard one-dimensional chaotic deterministic models and stochastic time series models via time reversal.

scholarly journals Anisotropic Heisenberg form of RKKY interaction in the one-dimensional spin-polarized electron gas

2016 ◽  
Vol 30 (32) ◽  
pp. 1650234 ◽  
Author(s):  
M. M. Valizadeh
Keyword(s):  
Time Reversal ◽  
Magnetic Moments ◽  
Electron Gas ◽  
Time Reversal Symmetry ◽  
Interaction Study ◽  
Rkky Interaction ◽  
One Dimensional ◽  
Indirect Exchange ◽  
Spin Polarized ◽  
The One

We study the indirect exchange interaction between two localized magnetic moments, known as Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, in a one-dimensional (1D) spin-polarized electron gas. We find explicit expressions for each term of this interaction, study their oscillatory behaviors as a function of the distance between two magnetic moments, [Formula: see text], and compare them with the known results for RKKY interaction in the case of 1D standard electron gas. We show this interaction can be written in an anisotropic Heisenberg form, [Formula: see text], coming from broken time-reversal symmetry of the host material.

scholarly journals The bifurcation set as a topological invariant for one-dimensional dynamics

Nonlinearity ◽  
2021 ◽  
Vol 34 (3) ◽  
pp. 1366-1388
Author(s):  
Gabriel Fuhrmann ◽  
Maik Gröger ◽  
Alejandro Passeggi
Keyword(s):  
Topological Invariant ◽  
One Dimensional ◽  
Bifurcation Set
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