Fourth order exceptional points with spinning resonators

2022 ◽  
Author(s):  
Haoye Qin ◽  
Yiheng Yin ◽  
Ming Ding
Keyword(s):  
Fourth Order ◽  
Light Propagation ◽  
High Efficiency ◽  
Optical Resonators ◽  
Second Order ◽  
Exceptional Points ◽  
Enhanced Sensitivity ◽  
Order Case ◽  
Symmetric Systems

Abstract Investigation of exceptional points mostly focuses on the second order case and employs the gain-involved parity-time (PT) symmetric systems. Here, we propose an approach to implementing fourth order exceptional points (FOEPs) using directly coupled optical resonators with rotation. On resonance, the system manifests FOEP through tuning the spinning velocity to targeted values. Eigenfrequency bifurcation and enhanced sensitivity for nanoparticle have been presented. Also, near FOEP, nonreciprocal light propagation exhibits great boost and dramatic change, which may be applied to high-efficiency isolators and circulators.

scholarly journals Integrity basis for a second-order and a fourth-order tensor

1982 ◽  
Vol 5 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Josef Betten
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Tensor Function ◽  
Order Tensor ◽  
Isotropic Tensor ◽  
Anisotropic Properties ◽  
Isotropic Tensor Function ◽  
Fourth Order Tensor

In this paper a scalar-valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth-order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second-order and a fourth-order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

A perturbation method and the limit-point case of even order symmetric differential expressions

1983 ◽  
Vol 94 (1-2) ◽  
pp. 121-135 ◽  
Author(s):  
Bernhard Mergler ◽  
Bernd Schultze
Keyword(s):  
Perturbation Method ◽  
Fourth Order ◽  
Limit Point ◽  
Perturbation Theorem ◽  
Order Case ◽  
Even Order ◽  
Limit Point Case ◽  
New Perturbation ◽  
Bounded Perturbations

SynopsisWe give a new perturbation theorem for symmetric differential expressions (relatively bounded perturbations, with relative bound 1) and prove with this theorem a new limit-point criterion generalizing earlier results of Schultze. We also obtain some new results in the fourth-order case.

scholarly journals Second order splitting of a class of fourth order PDEs with point constraints

2020 ◽  
Vol 89 (326) ◽  
pp. 2613-2648
Author(s):  
Charles M. Elliott ◽  
Philip J. Herbert
Keyword(s):  
Fourth Order ◽  
Second Order
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