scholarly journals Post-quench evolution of complexity and entanglement in a topological system

2020 ◽  
Vol 811 ◽  
pp. 135919
Author(s):  
Tibra Ali ◽  
Arpan Bhattacharyya ◽  
S. Shajidul Haque ◽  
Eugene H. Kim ◽  
Nathan Moynihan
Keyword(s):  
Evolution Of Complexity ◽  
Topological System

scholarly journals Particle-antiparticle duality and fractionalization of topological chiral solitons

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chang-geun Oh ◽  
Sang-Hoon Han ◽  
Seung-Gyo Jeong ◽  
Tae-Hwan Kim ◽  
Sangmo Cheon
Keyword(s):  
Chiral Symmetry ◽  
Time Reversal ◽  
Chiral Symmetry Breaking ◽  
Chain Model ◽  
Fractional Charge ◽  
Topological Solitons ◽  
Practical Applications ◽  
Topological System ◽  
Ssh Model ◽  
Chiral Solitons

AbstractAlthough a prototypical Su–Schrieffer–Heeger (SSH) soliton exhibits various important topological concepts including particle-antiparticle (PA) symmetry and fractional fermion charges, there have been only few advances in exploring such properties of topological solitons beyond the SSH model. Here, by considering a chirally extended double-Peierls-chain model, we demonstrate novel PA duality and fractional charge e/2 of topological chiral solitons even under the chiral symmetry breaking. This provides a counterexample to the belief that chiral symmetry is necessary for such PA relation and fractionalization of topological solitons in a time-reversal invariant topological system. Furthermore, we discover that topological chiral solitons are re-fractionalized into two subsolitons which also satisfy the PA duality. As a result, such dualities and fractionalizations support the topological $$\mathbb {Z}_4$$ Z 4 algebraic structures. Our findings will inspire researches seeking feasible and promising topological systems, which may lead to new practical applications such as solitronics.

scholarly journals A concept for fault diagnosis combining Case-Based Reasoning with topological system models

2020 ◽  
Vol 53 (2) ◽  
pp. 8217-8224
Author(s):  
Jonas Zinn ◽  
Birgit Vogel-Heuser ◽  
Felix Ocker
Keyword(s):  
Fault Diagnosis ◽  
Case Based Reasoning ◽  
System Models ◽  
Topological System ◽  
Case Based

scholarly journals A topological lens for a measure-preserving system

2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
Positive Entropy ◽  
Topological Properties ◽  
Topologically Transitive ◽  
Topological System ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Dynamical Properties

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).

scholarly journals Simulating Floquet topological phases in static systems

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Selma Franca ◽  
Fabian Hassler ◽  
Ion Cosma Fulga
Keyword(s):  
Topological Insulators ◽  
Topological Phases ◽  
Topological System ◽  
Reflection Matrix ◽  
Back Scattering ◽  
Scattering Matrices ◽  
Floquet Operator ◽  
Static Systems ◽  
Time Periodic ◽  
External Driving

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.

LONG TERM TRENDS AND THE EVOLUTION OF COMPLEXITY

1977 ◽  
pp. 1-4 ◽  
Author(s):  
Ilya Prigogine ◽  
Peter M. Allen ◽  
Robert Herman
Keyword(s):  
Evolution Of Complexity ◽  
Long Term Trends

Evolution of Complexity

Evolution ◽  
2020 ◽  
Author(s):  
Robin Dunbar
Keyword(s):  
Evolution Of Complexity

Why do some species eat others? Life began as microscopic single-celled organisms making their own energy from sunlight and other chemical resources. At some point, some of these creatures found it less effort just to eat their neighbors and acquire the energy they had gone...

Sign in / Sign up

Export Citation Format

Share Document