The Experts below are selected from a list of 63 Experts worldwide ranked by ideXlab platform
Yi Liao - One of the best experts on this subject based on the ideXlab platform.
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an explicit construction of the dimension 9 operator basis in the standard model effective field theory
Journal of High Energy Physics, 2020Co-Authors: Yi LiaoAbstract:We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac Matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.
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an explicit construction of the dimension 9 operator basis in the standard model effective field theory
arXiv: High Energy Physics - Phenomenology, 2020Co-Authors: Yi LiaoAbstract:We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac Matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $384|^{\Delta L=\pm 2}_{\Delta B=0}+10|^{\Delta L=0}_{\Delta B=\pm 2}+4|^{\Delta L=\pm3}_{\Delta B=\pm1}+236|^{\Delta L=\mp 1}_{\Delta B=\pm1}$ operators without referring to fermion generations, and $44874|^{\Delta L=\pm 2}_{\Delta B=0}+2862|^{\Delta L=0}_{\Delta B=\pm 2}+486|^{\Delta L=\pm3}_{\Delta B=\pm1}+42234|^{\Delta L=\pm 1}_{\Delta B=\mp1}$ operators when three generations of fermions are referred to, where $\Delta L,~\Delta B$ denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.
Kang Nam-gyu - One of the best experts on this subject based on the ideXlab platform.
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
'Springer Science and Business Media LLC', 2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:We consider the complex eigenvalues of a Wishart type random Matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general $\nu=O(N)$ and $\tau$ we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation $X_1=X_2$ when $\tau=1$. The square root of the complex Wishart eigenvalues, corresponding to the non-zero complex eigenvalues of the Dirac Matrix $\mathcal{D}=\begin{pMatrix} 0 & X_1 \\ X_2^* & 0 \end{pMatrix},$ are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value $\tau_c,$ where the interior of the spectrum splits into two connected components. At multi-criticality we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.Comment: 30 pages, 4 figures, v2: references added, typos correcte
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:We consider the complex eigenvalues of a Wishart type random Matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general $\nu=O(N)$ and $\tau$ we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation $X_1=X_2$ when $\tau=1$. The square root of the complex Wishart eigenvalues, corresponding to the non-zero complex eigenvalues of the Dirac Matrix $\mathcal{D}=\begin{pMatrix} 0 & X_1 \\ X_2^* & 0 \end{pMatrix},$ are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value $\tau_c,$ where the interior of the spectrum splits into two connected components. At multi-criticality we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics we use concentration for the 2D Coulomb gases on Frostman's equilibrium measure, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.Comment: 30 pages, 4 figure
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
'Springer Science and Business Media LLC', 2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:Akemann G, Byun S-S, Kang N-G. A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality. Annales Henri Poincaré . 2020.We consider the complex eigenvalues of a Wishart type random Matrix model X = X1X2*, where two rectangular complex Ginibre matrices X-1,X-2 of size N x (N + nu) are correlated through a non-Hermiticity parameter t is an element of [0, 1]. For general nu = O(N) and tau, we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation X-1 = X-2 when tau = 1. The square root of the complex Wishart eigenvalues, corresponding to the nonzero complex eigenvalues of the Dirac Matrix D = ((0) (X2) (X1)(0)), are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value tc, where the interior of the spectrum splits into two connected components. At multi-criticality, we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane
Michael N Leuenberger - One of the best experts on this subject based on the ideXlab platform.
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giant faraday effect due to pauli exclusion principle in 3d topological insulators
Journal of Physics: Condensed Matter, 2014Co-Authors: Hari P Paudel, Michael N LeuenbergerAbstract:Experiments using ARPES, which is based on the photoelectric effect, show that the surface states in 3D topological insulators (TI) are helical. Here we consider Weyl interface fermions due to band inversion in narrow-bandgap semiconductors, such as Pb1-xSnxTe. The positive and negative energy solutions can be identified by means of opposite helicity in terms of the spin helicity operator in 3D TI as ĥ(TI) = (1/ |p|_ |) β (σ|_ x p|_ ) · z^, where β is a Dirac Matrix and z^ points perpendicular to the interface. Using the 3D Dirac equation and bandstructure calculations we show that the transitions between positive and negative energy solutions, giving rise to electron-hole pairs, obey strict optical selection rules. In order to demonstrate the consequences of these selection rules, we consider the Faraday effect due to the Pauli exclusion principle in a pump-probe setup using a 3D TI double interface of a PbTe/Pb₀.₃₁Sn₀.₆₉Te/PbTe heterostructure. For that we calculate the optical conductivity tensor of this heterostructure, which we use to solve Maxwell's equations. The Faraday rotation angle exhibits oscillations as a function of probe wavelength and thickness of the heterostructure. The maxima in the Faraday rotation angle are of the order of mrds.
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giant faraday effect due to pauli exclusion principle in 3d topological insulators
arXiv: Mesoscale and Nanoscale Physics, 2012Co-Authors: Hari P Paudel, Michael N LeuenbergerAbstract:Experiments using ARPES, which is based on the photoelectric effect, show that the surface states in 3D topological insulators (TI) are helical. Here we consider Weyl interface fermions due to band inversion in narrow-bandgap semiconductors, such as Pb$_{1-x}$Sn$_{x}$Te. The positive and negative energy solutions can be identified by means of opposite helicity in terms of the spin helicity operator in 3D TI as $\hat{h}_{\textrm{TI}}=\left(1/\left|p_{\bot}\right|\right)\beta\left(\boldsymbol{\sigma}_{\perp}\times\boldsymbol{p}_{\perp}\right)\cdot\boldsymbol{\hat{z}}$, where $\beta$ is a Dirac Matrix and $\boldsymbol{\hat{z}}$ points perpendicular to the interface. Using the 3D Dirac equation and bandstructure calculations we show that the transitions between positive and negative energy solutions, giving rise to electron-hole pairs, obey strict optical selection rules. In order to demonstrate the consequences of these selection rules, we consider the Faraday effect due to Pauli exclusion principle in a pump-probe setup using a 3D TI double interface of a PbTe/Pb$_{0.31}$Sn$_{0.69}$Te/PbTe heterostructure. For that we calculate the optical conductivity tensor of this heterostructure, which we use to solve Maxwell's equations. The Faraday rotation angle exhibits oscillations as a function of probe wavelength and thickness of the heterostructure. The maxima in the Faraday rotation angle are of the order of millirads.
Akemann Gernot - One of the best experts on this subject based on the ideXlab platform.
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
'Springer Science and Business Media LLC', 2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:We consider the complex eigenvalues of a Wishart type random Matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general $\nu=O(N)$ and $\tau$ we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation $X_1=X_2$ when $\tau=1$. The square root of the complex Wishart eigenvalues, corresponding to the non-zero complex eigenvalues of the Dirac Matrix $\mathcal{D}=\begin{pMatrix} 0 & X_1 \\ X_2^* & 0 \end{pMatrix},$ are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value $\tau_c,$ where the interior of the spectrum splits into two connected components. At multi-criticality we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.Comment: 30 pages, 4 figures, v2: references added, typos correcte
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:We consider the complex eigenvalues of a Wishart type random Matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general $\nu=O(N)$ and $\tau$ we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation $X_1=X_2$ when $\tau=1$. The square root of the complex Wishart eigenvalues, corresponding to the non-zero complex eigenvalues of the Dirac Matrix $\mathcal{D}=\begin{pMatrix} 0 & X_1 \\ X_2^* & 0 \end{pMatrix},$ are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value $\tau_c,$ where the interior of the spectrum splits into two connected components. At multi-criticality we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics we use concentration for the 2D Coulomb gases on Frostman's equilibrium measure, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.Comment: 30 pages, 4 figure
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A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
'Springer Science and Business Media LLC', 2020Co-Authors: Akemann Gernot, Byun Sung-soo, Kang Nam-gyuAbstract:Akemann G, Byun S-S, Kang N-G. A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality. Annales Henri Poincaré . 2020.We consider the complex eigenvalues of a Wishart type random Matrix model X = X1X2*, where two rectangular complex Ginibre matrices X-1,X-2 of size N x (N + nu) are correlated through a non-Hermiticity parameter t is an element of [0, 1]. For general nu = O(N) and tau, we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation X-1 = X-2 when tau = 1. The square root of the complex Wishart eigenvalues, corresponding to the nonzero complex eigenvalues of the Dirac Matrix D = ((0) (X2) (X1)(0)), are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value tc, where the interior of the spectrum splits into two connected components. At multi-criticality, we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane
Hari P Paudel - One of the best experts on this subject based on the ideXlab platform.
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giant faraday effect due to pauli exclusion principle in 3d topological insulators
Journal of Physics: Condensed Matter, 2014Co-Authors: Hari P Paudel, Michael N LeuenbergerAbstract:Experiments using ARPES, which is based on the photoelectric effect, show that the surface states in 3D topological insulators (TI) are helical. Here we consider Weyl interface fermions due to band inversion in narrow-bandgap semiconductors, such as Pb1-xSnxTe. The positive and negative energy solutions can be identified by means of opposite helicity in terms of the spin helicity operator in 3D TI as ĥ(TI) = (1/ |p|_ |) β (σ|_ x p|_ ) · z^, where β is a Dirac Matrix and z^ points perpendicular to the interface. Using the 3D Dirac equation and bandstructure calculations we show that the transitions between positive and negative energy solutions, giving rise to electron-hole pairs, obey strict optical selection rules. In order to demonstrate the consequences of these selection rules, we consider the Faraday effect due to the Pauli exclusion principle in a pump-probe setup using a 3D TI double interface of a PbTe/Pb₀.₃₁Sn₀.₆₉Te/PbTe heterostructure. For that we calculate the optical conductivity tensor of this heterostructure, which we use to solve Maxwell's equations. The Faraday rotation angle exhibits oscillations as a function of probe wavelength and thickness of the heterostructure. The maxima in the Faraday rotation angle are of the order of mrds.
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giant faraday effect due to pauli exclusion principle in 3d topological insulators
arXiv: Mesoscale and Nanoscale Physics, 2012Co-Authors: Hari P Paudel, Michael N LeuenbergerAbstract:Experiments using ARPES, which is based on the photoelectric effect, show that the surface states in 3D topological insulators (TI) are helical. Here we consider Weyl interface fermions due to band inversion in narrow-bandgap semiconductors, such as Pb$_{1-x}$Sn$_{x}$Te. The positive and negative energy solutions can be identified by means of opposite helicity in terms of the spin helicity operator in 3D TI as $\hat{h}_{\textrm{TI}}=\left(1/\left|p_{\bot}\right|\right)\beta\left(\boldsymbol{\sigma}_{\perp}\times\boldsymbol{p}_{\perp}\right)\cdot\boldsymbol{\hat{z}}$, where $\beta$ is a Dirac Matrix and $\boldsymbol{\hat{z}}$ points perpendicular to the interface. Using the 3D Dirac equation and bandstructure calculations we show that the transitions between positive and negative energy solutions, giving rise to electron-hole pairs, obey strict optical selection rules. In order to demonstrate the consequences of these selection rules, we consider the Faraday effect due to Pauli exclusion principle in a pump-probe setup using a 3D TI double interface of a PbTe/Pb$_{0.31}$Sn$_{0.69}$Te/PbTe heterostructure. For that we calculate the optical conductivity tensor of this heterostructure, which we use to solve Maxwell's equations. The Faraday rotation angle exhibits oscillations as a function of probe wavelength and thickness of the heterostructure. The maxima in the Faraday rotation angle are of the order of millirads.