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

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

Symmetry constraints, molecular recognition and crystal engineering. Comparative structural studies of urea–butanedioic and urea–E-butanedioic acid (2:1) cocrystals

1996 ◽  
Vol 52 (6) ◽  
pp. 1048-1056 ◽  
Author(s):  
V. Videnova-Adrabińska
Keyword(s):  
Hydrogen Bond ◽  
Crystal Engineering ◽  
Three Dimensional ◽  
Structural Studies ◽  
Hydrogen Bond Interaction ◽  
Space Group ◽  
One Dimensional ◽  
Hydrogen Bond Interactions ◽  
Symmetry Constraints ◽  
Butanedioic Acid

The crystal structures of two urea–dicarboxylic acid (2:1) cocrystals have been determined. Urea–butanedioic acid forms monoclinic crystals, space group P21/c (No. 14), with a = 5.637 (4), b = 8.243 (3), c = 12.258 (3) Å, β = 96.80 (5)°, V = 565.6 (8) Å3, Z = 2. Urea–E-butenedioic acid also forms monoclinic crystals, space group P21/c (No. 14), with a = 5.540 (1), b = 8.227 (1), c = 12.426 (3) Å, β = 97.22 (3)°, V = 561.9 (2) Å3, Z = 2. The geometry and the conformation of both molecular aggregates and the three-dimensional networks formed are very similar. The two strongest hydrogen-bond interactions are constrained in the formation of the heteroaggregates, the third hydrogen-bond interaction is used to self-associate the heteroaggregates in one-dimensional chains, whereas the next three weaker hydrogen bonds interconnect the chains into well organized three-dimensional networks.

scholarly journals Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Barun Halder ◽  
Suranjana Ghosh ◽  
Pradosh Basu ◽  
Jayanta Bera ◽  
Boris Malomed ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Optical Lattice ◽  
Einstein Condensate ◽  
Experimental Realization ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Symmetry Properties ◽  
Symmetry Constraints ◽  
Localized Patterns ◽  
Bose Einstein

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.

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