The Experts below are selected from a list of 84 Experts worldwide ranked by ideXlab platform
Gernot Akemann - One of the best experts on this subject based on the ideXlab platform.
-
random matrix theory of unquenched two colour qcd with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the e-regime of chiral perturbation theory at small μ, where μ2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including Nf = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ.
-
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ . In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the ε -regime of chiral perturbation theory at small μ , where μ ^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including N _ f = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ . On the mathematical side our new results include an analytical formula for the spectral density of real Wishart Eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.
Tilo Wettig - One of the best experts on this subject based on the ideXlab platform.
-
random matrix theory of unquenched two colour qcd with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the e-regime of chiral perturbation theory at small μ, where μ2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including Nf = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ.
-
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ . In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the ε -regime of chiral perturbation theory at small μ , where μ ^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including N _ f = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ . On the mathematical side our new results include an analytical formula for the spectral density of real Wishart Eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.
Elena Panteley - One of the best experts on this subject based on the ideXlab platform.
-
Asymptotic phase synchronization of Kuramoto model with weighted non-symetric interconnections: A case study
2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
-
CDC - Asymptotic phase synchronization of Kuramoto model with weighted non-symmetric interconnections: A case study
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
M J Phillips - One of the best experts on this subject based on the ideXlab platform.
-
random matrix theory of unquenched two colour qcd with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the e-regime of chiral perturbation theory at small μ, where μ2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including Nf = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ.
-
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ . In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the ε -regime of chiral perturbation theory at small μ , where μ ^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including N _ f = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ . On the mathematical side our new results include an analytical formula for the spectral density of real Wishart Eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.
Takuya Kanazawa - One of the best experts on this subject based on the ideXlab platform.
-
random matrix theory of unquenched two colour qcd with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the e-regime of chiral perturbation theory at small μ, where μ2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including Nf = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ.
-
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Journal of High Energy Physics, 2011Co-Authors: Gernot Akemann, Takuya Kanazawa, M J Phillips, Tilo WettigAbstract:We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential μ . In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the ε -regime of chiral perturbation theory at small μ , where μ ^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and μ is unscaled. We give explicit examples for the complex, real, and Imaginary Eigenvalue densities including N _ f = 2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of μ . On the mathematical side our new results include an analytical formula for the spectral density of real Wishart Eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.