scholarly journals Equivalent topological invariants for one-dimensional Majorana wires in symmetry classD

2013 ◽  
Vol 88 (7) ◽  
Author(s):  
Jan Carl Budich ◽  
Eddy Ardonne
Keyword(s):  
Topological Invariants ◽  
One Dimensional

scholarly journals Topological invariants and interacting one-dimensional fermionic systems

2012 ◽  
Vol 86 (20) ◽  
Author(s):  
Salvatore R. Manmana ◽  
Andrew M. Essin ◽  
Reinhard M. Noack ◽  
Victor Gurarie
Keyword(s):  
Topological Invariants ◽  
One Dimensional ◽  
Fermionic Systems

The application of numerical topological invariants in simulations of knotted rings: A comprehensive Monte Carlo approach

2020 ◽  
pp. 2150005
Author(s):  
Franco Ferrari ◽  
Yani Zhao
Keyword(s):  
Monte Carlo ◽  
Discrete Version ◽  
Topological Invariants ◽  
One Dimensional ◽  
Knot Invariants ◽  
Knot Invariant ◽  
Sampling Process ◽  
Energy Domain ◽  
Sharp Corners ◽  
Monte Carlo Framework

In this work, a general Monte Carlo framework is proposed for applying numerical knot invariants in simulations of systems containing knotted one-dimensional ring-shaped objects like polymers and vortex lines in fluids, superfluids or other quantum liquids. A general prescription for smoothing the sharp corners appearing in discrete knots consisting of segments joined together is provided. Smoothing is very important for the correct evaluation of numerical knot invariants. A discrete version of framing is adopted in order to eliminate singularities that are possibly arising when computing the invariants. The presented algorithms for smoothing, eliminating potentially dangerous singularities and speeding up the calculations are quite general and can be applied to any discrete knot defined off- or on-lattice. This is one of the first attempts to use numerical knot invariants in order to avoid potential topology breakings during the sampling process taking place in computer simulations, in which millions of knot conformations are randomly generated. As an application, the energy domain of knotted polymer rings subjected to short-range interactions is studied using the so-called Vassiliev knot invariant of degree 2.

scholarly journals Entanglement topological invariants for one-dimensional topological superconductors

2020 ◽  
Vol 101 (8) ◽  
Author(s):  
P. Fromholz ◽  
G. Magnifico ◽  
V. Vitale ◽  
T. Mendes-Santos ◽  
M. Dalmonte
Keyword(s):  
Topological Invariants ◽  
One Dimensional ◽  
Topological Superconductors

scholarly journals Topological invariants to characterize universality of boundary charge in one-dimensional insulators beyond symmetry constraints

2020 ◽  
Vol 101 (16) ◽  
Author(s):  
Mikhail Pletyukhov ◽  
Dante M. Kennes ◽  
Jelena Klinovaja ◽  
Daniel Loss ◽  
Herbert Schoeller
Keyword(s):  
Topological Invariants ◽  
One Dimensional ◽  
Symmetry Constraints

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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