eigenvalue spectrum
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2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Jianwen Zhou ◽  
Zijian Jiang ◽  
Tianqi Hou ◽  
Ziming Chen ◽  
K. Y. Michael Wong ◽  
...  

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Simon Ekhammar ◽  
Bengt E. W. Nilsson

Abstract We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS4 and are important for the corresponding $$ \mathcal{N} $$ N = 1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS4 was derived for this compactification. Some comments are also made concerning the G2 holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.


Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2721
Author(s):  
Jian Zhu ◽  
Da Huang ◽  
Haijun Jiang ◽  
Jicheng Bian ◽  
Zhiyong Yu

The system model on synchronizability problem of complex networks with multi-layer structure is closer to the real network than the usual single-layer case. Based on the master stability equation (MSF), this paper studies the eigenvalue spectrum of two k-layer variable coupling windmill-type networks. In the case of bounded and unbounded synchronization domain, the relationships between the synchronizability of the layered windmill-type networks and network parameters, such as the numbers of nodes and layers, inter-layers coupling strength, are studied. The simulation of the synchronizability of the layered windmill-type networks are given, and they verify the theoretical results well. Finally, the optimization schemes of the synchronizability are given from the perspective of single-layer and multi-layer networks, and it was found that the synchronizability of the layered windmill-type networks can be improved by changing the parameters appropriately.


2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Zhichan Hu ◽  
Domenico Bongiovanni ◽  
Dario Jukić ◽  
Ema Jajtić ◽  
Shiqi Xia ◽  
...  

AbstractHigher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.


2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Hwancheol Jeong ◽  
Chulwoo Jung ◽  
Seungyeob Jwa ◽  
Jangho Kim ◽  
Jeehun Kim ◽  
...  

2021 ◽  
Author(s):  
Wang Yutian ◽  
Songnian Fu ◽  
jian kong ◽  
Andrey Komarov ◽  
Mariusz Klimczak ◽  
...  

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Feimei Yang ◽  
Zhen Jia ◽  
Yang Deng

In this study, we studied the eigenvalue spectrum and synchronizability of two types of double-layer hybrid directionally coupled star-ring networks, namely, the double-layer star-ring networks with the leaf node pointing to the hub node (Network I) and the double-layer star-ring networks with the hub node pointing to the leaf node (Network II). We strictly derived the eigenvalue spectrum of the supra-Laplacian matrix of these two types of networks and analyzed the relationship between the synchronizability and the structural parameters of networks based on the master stability function theory. Furthermore, the correctness of the theoretical results was verified through numerical simulations, and the optimum structural parameters were obtained to achieve the optimal synchronizability.


Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 462
Author(s):  
Dan Allan ◽  
Niklas Hörnedal ◽  
Ole Andersson

In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.


2021 ◽  
Author(s):  
Ilya Mullyadzhanov ◽  
Rustam Mullyadzhanov ◽  
Andrey Gelash

<p>The one-dimensional nonlinear Schrodinger equation (NLSE) serves as a universal model of nonlinear wave propagation appearing in different areas of physics. In particular it describes weakly nonlinear wave trains on the surface of deep water and captures up to certain extent the phenomenon of rogue waves formation. The NLSE can be completely integrated using the inverse scattering transform method that allows transformation of the wave field to the so-called scattering data representing a nonlinear analogue of conventional Fourier harmonics. The scattering data for the NLSE can be calculated by solving an auxiliary linear system with the wave field playing the role of potential – the so-called Zakharov-Shabat problem. Here we present a novel efficient approach for numerical computation of scattering data for spatially periodic nonlinear wave fields governed by focusing version of the NLSE. The developed algorithm is based on Fourier-collocation method and provides one an access to full scattering data, that is main eigenvalue spectrum (eigenvalue bands and gaps) and auxiliary spectrum (specific phase parameters of the nonlinear harmonics) of Zakharov-Shabat problem. We verify the developed algorithm using a simple analytic plane wave solution and then demonstrate its efficiency with various examples of large complex nonlinear wave fields exhibiting intricate structure of bands and gaps. Special attention is paid to the case when the wave field is strongly nonlinear and contains solitons which correspond to narrow gaps in the eigenvalue spectrum, see e.g. [1], when numerical computations may become unstable [2]. Finally we discuss applications of the developed approach for analysis of numerical and experimental nonlinear wave fields data.</p><p>The work was supported by Russian Science Foundation grant No. 20-71-00022.</p><p>[1] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210 (2018).</p><p>[2] A. Gelash and R. Mullyadzhanov, Physical Review E 101, 052206 (2020).</p>


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