Algebraic approach and Berry phase of a Hamiltonian with a general SU(1, 1) symmetry

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

Nature Communications ◽

10.1038/s41467-020-20349-z ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 1

Author(s):

Fei Wang ◽

Xuepeng Wang ◽

Yi-Fan Zhao ◽

Di Xiao ◽

Ling-Jie Zhou ◽

...

Keyword(s):

Hall Effect ◽

Electric Fields ◽

First Principles ◽

Berry Phase ◽

Condensed Matter ◽

Anomalous Hall Effect ◽

First Principles Calculations ◽

Sign Reversal ◽

Berry Curvature ◽

Topological Materials

AbstractThe Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

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A hybrid broadband metalens operating at ultraviolet frequencies

Scientific Reports ◽

10.1038/s41598-021-81956-4 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Farhan Ali ◽

Serap Aksu

Keyword(s):

Dielectric Material ◽

Berry Phase ◽

Uv Light ◽

Fdtd Method ◽

Numerical Aperture ◽

Limited Range ◽

Unit Cell ◽

Dielectric Constants ◽

Phase Method ◽

Frequency Range

AbstractThe investigation on metalenses have been rapidly developing, aiming to bring compact optical devices with superior properties to the market. Realizing miniature optics at the UV frequency range in particular has been challenging as the available transparent materials have limited range of dielectric constants. In this work we introduce a low absorption loss and low refractive index dielectric material magnesium oxide, MgO, as an ideal candidate for metalenses operating at UV frequencies. We theoretically investigate metalens designs capable of efficient focusing over a broad UV frequency range (200–400 nm). The presented metalenses are composed of sub-wavelength MgO nanoblocks, and characterized according to the geometric Pancharatnam–Berry phase method using FDTD method. The presented broadband metalenses can focus the incident UV light on tight focal spots (182 nm) with high numerical aperture ($$\hbox {NA}\approx 0.8$$ NA ≈ 0.8 ). The polarization conversion efficiency of the metalens unit cell and focusing efficiency of the total metalens are calculated to be as high as 94%, the best value reported in UV range so far. In addition, the metalens unit cell can be hybridized to enable lensing at multiple polarization states. The presented highly efficient MgO metalenses can play a vital role in the development of UV nanophotonic systems and could pave the way towards the world of miniaturization.

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Enhancing the Optical Efficiency of Near-Eye Displays with Liquid Crystal Optics

Crystals ◽

10.3390/cryst11020107 ◽

2021 ◽

Vol 11 (2) ◽

pp. 107

Author(s):

Tao Zhan ◽

En-Lin Hsiang ◽

Kun Li ◽

Shin-Tson Wu

Keyword(s):

Virtual Reality ◽

Liquid Crystal ◽

High Efficiency ◽

Berry Phase ◽

Optical Element ◽

Liquid Crystal Polymer ◽

Proof Of Concept ◽

Optical Efficiency ◽

Crystal Polymer ◽

Light Efficiency

We demonstrate a light efficient virtual reality (VR) near-eye display (NED) design based on a directional display panel and a diffractive deflection film (DDF). The DDF was essentially a high-efficiency Pancharatnam-Berry phase optical element made of liquid crystal polymer. The essence of this design is directing most of the display light into the eyebox. The proposed method is applicable for both catadioptric and dioptric VR lenses. A proof-of-concept experiment was conducted with off-the-shelf optical parts, where the light efficiency was enhanced by more than 2 times.

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Target space entanglement in quantum mechanics of fermions and matrices

Journal of High Energy Physics ◽

10.1007/jhep08(2021)046 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Sotaro Sugishita

Keyword(s):

Mutual Information ◽

Ground State ◽

Entanglement Entropy ◽

Algebraic Approach ◽

Upper Bounds ◽

Wave Functions ◽

Target Space ◽

Single Interval ◽

Area Law ◽

Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

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