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Yan Peng - One of the best experts on this subject based on the ideXlab platform.
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no hair theorem for bound state massless static Scalar fields outside horizonless neumann compact stars
Physics Letters B, 2019Co-Authors: Yan PengAbstract:Abstract We study no-hair theorem for horizonless objects, being subject to Neumann boundary conditions. For massive Scalar fields, a no hair theorem for Neumann compact stars was proved by us in a previous paper, where the Nonzero Scalar field mass condition is essential in the proof. In the present work, for massless Scalar fields, we prove a no hair theorem, which claims that bound-state massless static Scalar fields cannot exist outside asymptotically flat horizonless neutral Neumann compact stars.
Huang Hau-wen - One of the best experts on this subject based on the ideXlab platform.
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Finite-dimensional irreducible modules of the universal DAHA of type $(C_1^\vee,C_1)$
2020Co-Authors: Huang Hau-wenAbstract:Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a Nonzero Scalar in $\mathbb F$ that is not a root of unity. The universal DAHA (double affine Hecke algebra) $\mathfrak H_q$ of type $(C_1^\vee,C_1)$ is a unital associative $\mathbb F$-algebra defined by generators and relations. The generators are $\{t_i^{\pm 1}\}_{i=0}^3$ and the relations assert that \begin{gather*} t_it_i^{-1}=t_i^{-1} t_i=1 \quad \hbox{for all $i=0,1,2,3$}; \\ \hbox{$t_i+t_i^{-1}$ is central} \quad \hbox{for all $i=0,1,2,3$}; \\ t_0t_1t_2t_3=q^{-1}. \end{gather*} In this paper we describe the finite-dimensional irreducible $\mathfrak H_q$-modules from many viewpoints and classify the finite-dimensional irreducible $\mathfrak H_q$-modules up to isomorphism. The proofs are carried out in the language of linear algebra
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The universal DAHA of type $(C_1^\vee,C_1)$ and Leonard triples
2020Co-Authors: Huang Hau-wenAbstract:Assume that $\mathbb F$ is an algebraically closed field and $q$ is a Nonzero Scalar in $\mathbb F$ that is not a root of unity. The universal Askey--Wilson algebra $\triangle_q$ is a unital associative $\mathbb F$-algebra generated by $A,B, C$ and the relations state that each of $$ A+\frac{q BC-q^{-1} CB}{q^2-q^{-2}}, \qquad B+\frac{q CA-q^{-1} AC}{q^2-q^{-2}}, \qquad C+\frac{q AB-q^{-1} BA}{q^2-q^{-2}} $$ is central in $\triangle_q$. The universal DAHA $\mathfrak H_q$ of type $(C_1^\vee,C_1)$ is a unital associative $\mathbb F$-algebra generated by $\{t_i^{\pm 1}\}_{i=0}^3$ and the relations state that \begin{gather*} t_it_i^{-1}=t_i^{-1} t_i=1 \quad \hbox{for all $i=0,1,2,3$}; \\ \hbox{$t_i+t_i^{-1}$ is central} \quad \hbox{for all $i=0,1,2,3$}; \\ t_0t_1t_2t_3=q^{-1}. \end{gather*} It was given an $\mathbb F$-algebra homomorphism $\triangle_q\to \mathfrak H_q$ that sends \begin{eqnarray*} A &\mapsto & t_1 t_0+(t_1 t_0)^{-1}, \\ B &\mapsto & t_3 t_0+(t_3 t_0)^{-1}, \\ C &\mapsto & t_2 t_0+(t_2 t_0)^{-1}. \end{eqnarray*} Therefore any $\mathfrak H_q$-module can be considered as a $\triangle_q$-module. Let $V$ denote a finite-dimensional irreducible $\mathfrak H_q$-module. In this paper we show that $A,B,C$ are diagonalizable on $V$ if and only if $A,B,C$ act as Leonard triples on all composition factors of the $\triangle_q$-module $V$.Comment: arXiv admin note: text overlap with arXiv:2003.0625
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Finite-dimensional modules of the universal Askey--Wilson algebra and DAHA of type $(C_1^\vee,C_1)$
'Springer Science and Business Media LLC', 2020Co-Authors: Huang Hau-wenAbstract:Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a Nonzero Scalar in $\mathbb F$ that is not a root of unity. The universal Askey--Wilson algebra $\triangle_q$ is a unital associative $\mathbb F$-algebra defined by generators and relations. The generators are $A,B, C$ and the relations state that each of $$ A+\frac{q BC-q^{-1} CB}{q^2-q^{-2}}, \qquad B+\frac{q CA-q^{-1} AC}{q^2-q^{-2}}, \qquad C+\frac{q AB-q^{-1} BA}{q^2-q^{-2}} $$ is central in $\triangle_q$. The universal DAHA (double affine Hecke algebra) $\mathfrak H_q$ of type $(C_1^\vee,C_1)$ is a unital associative $\mathbb F$-algebra generated by $\{t_i^{\pm 1}\}_{i=0}^3$ and the relations state that \begin{gather*} t_it_i^{-1}=t_i^{-1} t_i=1 \quad \hbox{for all $i=0,1,2,3$}; \\ \hbox{$t_i+t_i^{-1}$ is central} \quad \hbox{for all $i=0,1,2,3$}; \\ t_0t_1t_2t_3=q^{-1}. \end{gather*} Each $\mathfrak H_q$-module is a $\triangle_q$-module by pulling back via the injection $\triangle_q\to \mathfrak H_q$ given by \begin{eqnarray*} A &\mapsto & t_1 t_0+(t_1 t_0)^{-1}, \\ B &\mapsto & t_3 t_0+(t_3 t_0)^{-1}, \\ C &\mapsto & t_2 t_0+(t_2 t_0)^{-1}. \end{eqnarray*} We classify the lattices of $\triangle_q$-submodules of finite-dimensional irreducible $\mathfrak H_q$-modules. As a consequence, for any finite-dimensional irreducible $\mathfrak H_q$-module $V$, the $\triangle_q$-module $V$ is completely reducible if and only if $t_0$ is diagonalizable on $V$.Comment: arXiv admin note: text overlap with arXiv:1906.0916
Jinming Dong - One of the best experts on this subject based on the ideXlab platform.
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predicted quantum topological hall effect and noncoplanar antiferromagnetism in k_ 0 5 rho_ 2
Physical Review Letters, 2016Co-Authors: Jian Zhou, Qifeng Liang, Hongming Weng, Y B Chen, Yanfeng Chen, Jinming DongAbstract:: The quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic insulator with a Nonzero Chern number in the presence of spin-orbit coupling (SOC) but in the absence of applied magnetic fields. Associated metallic chiral edge states host dissipationless current transport in electronic devices. This intriguing QAH phase has recently been observed in magnetic impurity-doped topological insulators, albeit, at extremely low temperatures. Based on first-principles density functional calculations, here we predict that layered rhodium oxide K_{0.5}RhO_{2} in the noncoplanar chiral antiferromagnetic state is an unconventional three-dimensional QAH insulator with a large band gap and a Neel temperature of a few tens of Kelvins. Furthermore, this unconventional QAH phase is revealed to be the exotic quantum topological Hall effect caused by Nonzero Scalar spin chirality due to the topological spin structure in the system and without the need of net magnetization and SOC.
Peng Yan - One of the best experts on this subject based on the ideXlab platform.
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Spontaneous Scalarization of Gauss-Bonnet black holes surrounded by massive Scalar fields
'Elsevier BV', 2020Co-Authors: Peng YanAbstract:For massless Scalar fields, a relation $\Delta_{n}=\frac{\sqrt{3}}{2}\pi$ for $n\rightarrow \infty$ was observed in the Scalar-Gauss-Bonnet theory. In the present paper, we extend the discussion by including a Nonzero Scalar field mass. For massive Scalar fields, we show that the relation $\Delta_{n}=\frac{\sqrt{3}}{2}\pi$ for $n\rightarrow \infty$ still holds. We demonstrate this relation with both analytical and numerical methods. The analytical analysis implies that this relation may be a very universal behavior.Comment: 8 pages, 1 figur
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No hair theorem for bound-state massless static Scalar fields outside horizonless Neumann compact stars
'Elsevier BV', 2019Co-Authors: Peng YanAbstract:We study no-hair theorem for horizonless objects, being subject to Neumann boundary conditions. For massive Scalar fields, a no hair theorem for Neumann compact stars was proved by us in a previous paper, where the Nonzero Scalar field mass condition is essential in the proof. In the present work, for massless Scalar fields, we prove a no hair theorem, which claims that bound-state massless static Scalar fields cannot exist outside asymptotically flat horizonless neutral Neumann compact stars.Comment: 7 page
Jian Zhou - One of the best experts on this subject based on the ideXlab platform.
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predicted quantum topological hall effect and noncoplanar antiferromagnetism in k_ 0 5 rho_ 2
Physical Review Letters, 2016Co-Authors: Jian Zhou, Qifeng Liang, Hongming Weng, Y B Chen, Yanfeng Chen, Jinming DongAbstract:: The quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic insulator with a Nonzero Chern number in the presence of spin-orbit coupling (SOC) but in the absence of applied magnetic fields. Associated metallic chiral edge states host dissipationless current transport in electronic devices. This intriguing QAH phase has recently been observed in magnetic impurity-doped topological insulators, albeit, at extremely low temperatures. Based on first-principles density functional calculations, here we predict that layered rhodium oxide K_{0.5}RhO_{2} in the noncoplanar chiral antiferromagnetic state is an unconventional three-dimensional QAH insulator with a large band gap and a Neel temperature of a few tens of Kelvins. Furthermore, this unconventional QAH phase is revealed to be the exotic quantum topological Hall effect caused by Nonzero Scalar spin chirality due to the topological spin structure in the system and without the need of net magnetization and SOC.
