topological invariants
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2022 ◽  
Vol 1048 ◽  
pp. 221-226
Author(s):  
K. Pattabiraman ◽  
M. Kameswari ◽  
M. Seenivasan

Degree related topological invariants are the bygone and most victorioustype of graph invariants so far. In this article, we are interested in finding the generalized inverse indeg invariant of the nanostar dendrimers D[r],fullerene dendrimerNS4[r], and polymer dendrimerNS5[r]. Keywords: nanotubes; inverse indeg invariant; nanostar dendrimers; fullerene dendrimer; polymer dendrimer


2021 ◽  
Vol 127 (27) ◽  
Author(s):  
Kunkun Wang ◽  
Tianyu Li ◽  
Lei Xiao ◽  
Yiwen Han ◽  
Wei Yi ◽  
...  

2021 ◽  
pp. 110-117
Author(s):  
A. Tsudik ◽  
A. Glushkov ◽  
V. Ternovsky ◽  
P. Zaichko

The advanced results of computing the dynamical and topological invariants (correlation dimensions values, embedding, Kaplan-York dimensions, Lyapunov’s exponents, Kolmogorov entropy etc) of the dynamics time series of the  relativistic backward-wave tube with accounting for  dissipation and space charge field and other effects are presented for chaotic and hyperchaotic regimes. It is solved a system of equations for unidimensional relativistic electron phase and field unidimensional complex amplitude.  The data obtained make more exact earlier presented preliminary data for  dynamical and topological invariants of the relativistic backward-wave tube dynamics in  chaotic regimes and allow to describe a scenario of transition to chaos in temporal dynamics.   


2021 ◽  
pp. 140-155
Author(s):  
S.V. Kirianov ◽  
A. Mashkantsev ◽  
I. Bilan ◽  
A. Ignatenko

Nonlinear chaotic dynamics of the of the chaotic laser diodes with an additional optical injection  is computed within rate equations model, based on the a set of rate equations for the slave laser electric complex amplitude and carrier density. To calculate the system dynamics in a chaotic regime the known chaos theory and non-linear analysis methods such as a correlation integral algorithm, the Lyapunov’s exponents and  Kolmogorov entropy analysis are used. There are listed the data of computing dynamical and topological invariants such as the correlation, embedding and Kaplan-Yorke dimensions, Lyapunov’s exponents, Kolmogorov entropy etc. New data on topological and dynamical invariants are computed and firstly presented.


Author(s):  
Pasquale Marra ◽  
Angela Nigro

Abstract Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: Indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1666
Author(s):  
Anastasia V. Frolkova

The study of topological invariants of phase diagrams allows for the development of a qualitative theory of the processes being researched. Studies of the properties of objects in the same equivalence class may be carried out with the aim of predicting the properties of unexplored objects from this class, or predicting the behavior of a whole system. This paper describes a number of topological invariants in vapor–liquid, vapor–liquid–liquid and liquid–liquid equilibrium diagrams. The properties of some invariants are studied and illustrated. It is shown that the invariant of a diagram with a miscibility gap can be used to distinguish equivalence classes of phase diagrams, and that the balance equation of the singular-point indices, based on the Euler characteristic, may be used to analyze the binodal-surface structure of a quaternary system.


2021 ◽  
Vol 38 (12) ◽  
pp. 127101
Author(s):  
Yunqing Ouyang ◽  
Qing-Rui Wang ◽  
Zheng-Cheng Gu ◽  
Yang Qi

In recent years, great success has been achieved on the classification of symmetry-protected topological (SPT) phases for interacting fermion systems by using generalized cohomology theory. However, the explicit calculation of generalized cohomology theory is extremely hard due to the difficulty of computing obstruction functions. Based on the physical picture of topological invariants and mathematical techniques in homotopy algebra, we develop an algorithm to resolve this hard problem. It is well known that cochains in the cohomology of the symmetry group, which are used to enumerate the SPT phases, can be expressed equivalently in different linear bases, known as the resolutions. By expressing the cochains in a reduced resolution containing much fewer basis than the choice commonly used in previous studies, the computational cost is drastically reduced. In particular, it reduces the computational cost for infinite discrete symmetry groups, like the wallpaper groups and space groups, from infinity to finity. As examples, we compute the classification of two-dimensional interacting fermionic SPT phases, for all 17 wallpaper symmetry groups.


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