Exceptional nexus with a hybrid topological invariant

Science ◽  
2020 ◽  
Vol 370 (6520) ◽  
pp. 1077-1080 ◽  
Author(s):  
Weiyuan Tang ◽  
Xue Jiang ◽  
Kun Ding ◽  
Yi-Xin Xiao ◽  
Zhao-Qing Zhang ◽  
...  
Keyword(s):  
Parameter Space ◽  
Branch Point ◽  
Topological Charge ◽  
Higher Order ◽  
Topological Invariant ◽  
Wave Functions ◽  
Major Advance ◽  
Fundamental Understanding ◽  
Berry Phases ◽  
Complex Planes

Branch-point singularities known as exceptional points (EPs), which carry a nonzero topological charge, can emerge in non-Hermitian systems. We demonstrate with both theory and acoustic experiments an “exceptional nexus” (EX), which is not only a higher-order EP but also the cusp singularity of multiple exceptional arcs (EAs). Because the parameter space is segmented by the EAs, the EX possesses a hybrid topological invariant (HTI), which consists of distinct winding numbers associated with Berry phases accumulated by cyclic paths on different complex planes. The HTI is experimentally characterized by measuring the critical behaviors of the wave functions. Our findings constitute a major advance in the fundamental understanding of non-Hermitian systems and their topology, possibly opening new avenues for applications.

scholarly journals Electroweak axion string and superconductivity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Yoshihiko Abe ◽  
Yu Hamada ◽  
Koichi Yoshioka
Keyword(s):  
Electric Current ◽  
Early Universe ◽  
Parameter Space ◽  
Cosmic String ◽  
Topological Charge ◽  
Attractive Force ◽  
Electroweak Scale ◽  
Large Current

Abstract We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zeromodes. We construct three types of electroweak axion string solutions. Among them, the string with W-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.

scholarly journals NUMERICAL STUDY OF CHARGE AND STATISTICS OF LAUGHLIN QUASIPARTICLES

1999 ◽  
Vol 14 (04) ◽  
pp. 537-557 ◽  
Author(s):  
HEIDI KJØNSBERG ◽  
JAN MYRHEIM
Keyword(s):  
Numerical Study ◽  
Finite Size ◽  
Expected Value ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Filling Fraction ◽  
Slow Convergence ◽  
Berry Phases ◽  
Size Correction ◽  
Finite Size Correction

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasiparticles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasiholes our results confirm that the charge and statistics parameter are e/3 and 1/3, respectively. For the quasielectron charge we find a slow convergence towards the expected value of -e/3, with a finite size correction for N electrons of approximately -0.13e/N. The statistics parameter for the quasielectrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. The anyon model works well for the quasiholes, but requires singular two-anyon wave functions for modelling two Laughlin quasielectrons.

General coalescence conditions for the exact wave functions. II. Higher-order relations for many-particle systems

2014 ◽  
Vol 140 (21) ◽  
pp. 214103 ◽  
Author(s):  
Yusaku I. Kurokawa ◽  
Hiroyuki Nakashima ◽  
Hiroshi Nakatsuji
Keyword(s):  
Higher Order ◽  
Particle Systems ◽  
Wave Functions ◽  
Order Relations

Exact wave functions and nonadiabatic Berry phases of a time-dependent harmonic oscillator

1995 ◽  
Vol 52 (4) ◽  
pp. 3352-3355 ◽  
Author(s):  
Jeong-Young Ji ◽  
Jae Kwan Kim ◽  
Sang Pyo Kim ◽  
Kwang-Sup Soh
Keyword(s):  
Harmonic Oscillator ◽  
Wave Functions ◽  
Time Dependent ◽  
Berry Phases

scholarly journals Constraining protoplanetary discs with exoplanetary dynamics: Kepler-419 as an example

2020 ◽  
Vol 499 (1) ◽  
pp. 106-115
Author(s):  
Mohamad Ali-Dib ◽  
Cristobal Petrovich
Keyword(s):  
Parameter Space ◽  
Time Scale ◽  
Space Exploration ◽  
Semimajor Axis ◽  
Higher Order ◽  
Mean Motion Resonances ◽  
Close Encounters ◽  
Natural Result ◽  
Core Accretion ◽  
Orbital Migration

ABSTRACT We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations liberating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disc. We follow the proposal by Petrovich, Wu, & Ali-Dib that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disc and extend it by using direct N-body simulations and models for the evolution of the gas discs, including photoevaporation. Based on a parameter space exploration, we find that in order to reproduce the system the initial disc mass had to be at least 95 MJup and dissipate on a time-scale of at least 104 yr. This mass is consistent with the upper end of the observed disc masses distribution, and the dissipation time-scale is consistent with photoevaporation models. We study the properties of such discs using simplified 1D thin-disc models and show that they are gravitationally stable, indicating that the two planets must have formed via core accretion and thus prone to disc migration. We hence finally investigate the sensitivity of this mechanism to the outer planet’s semimajor axis, and find that the nearby 7:1, 8:1, and 9:1 mean-motion resonances can completely quench this mechanism, while even higher order resonances can also significantly affect the system. Assuming the two planets avoid these high-order resonances and close encounters, the dynamics seems to be rather insensitive to planet c semimajor axis, and thus orbital migration driven by the disc.

A general toolbox for the calculation of higher-order molecular properties using SCF wave functions at the one-, two- and four-component levels of theory

2012 ◽  
Author(s):  
Kenneth Ruud ◽  
Radovan Bast ◽  
Bin Gao ◽  
Andreas J. Thorvaldsen ◽  
Ulf Ekström ◽  
...  
Keyword(s):  
Higher Order ◽  
Wave Functions ◽  
Molecular Properties ◽  
The One

scholarly journals SCHRÖDINGER EQUATION FOR HEAVY MESONS EXPANDED IN 1/mQ

1996 ◽  
Vol 11 (03) ◽  
pp. 257-266 ◽  
Author(s):  
TAKAYUKI MATSUKI
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Higher Order ◽  
Wave Functions ◽  
Heavy Mesons ◽  
Higher Order Corrections

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schrödinger equation for [Formula: see text] bound states described by a Hamiltonian, we systematically develop a perturbation theory in 1/mQ which enables one to solve the Schrödinger equation to obtain masses and wave functions of the bound states in any order of 1/mQ. There also appear negative components of the wave function in our formulation which contribute also to higher order corrections to masses.

Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space

2007 ◽  
Vol 46 (6) ◽  
pp. 1666-1701 ◽  
Author(s):  
E. Hernández ◽  
A. Jáuregui ◽  
A Mondragón ◽  
L. Nellen
Keyword(s):  
Parameter Space ◽  
Branch Point ◽  
Branch Cuts
Sign in / Sign up

Export Citation Format

Share Document