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Sanefumi Moriyama - One of the best experts on this subject based on the ideXlab platform.
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superconformal chern simons partition Functions of affine d type quiver from fermi gas
arXiv: High Energy Physics - Theory, 2015Co-Authors: Sanefumi Moriyama, Tomoki NosakaAbstract:We consider the partition Function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition Function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy Function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact expression of the overall constant, which corresponds to the constant map in the topological string theory.
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partition Functions of superconformal chern simons theories from fermi gas approach
arXiv: High Energy Physics - Theory, 2014Co-Authors: Sanefumi Moriyama, Tomoki NosakaAbstract:We study the partition Function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition Function sums up to the Airy Function as $Z(N)=e^{A}C^{-1/3}\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of $B$ for general ${\mathcal N}=4$ theories, a conjectural form of $A$ for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.
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all genus partition Function of the abjm matrix model
International Journal of Modern Physics: Conference Series, 2013Co-Authors: Sanefumi MoriyamaAbstract:We find that, apart from the instanton contributions, the all genus partition Function of the ABJM matrix model sums up to the Airy Function. We present the result, discuss its implication and also summarize some further progress.
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instanton effects in abjm theory from fermi gas approach
arXiv: High Energy Physics - Theory, 2012Co-Authors: Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi OkuyamaAbstract:We study the instanton effects of the ABJM partition Function using the Fermi gas formalism. We compute the exact values of the partition Function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition Function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition Function are expressed in terms of the Airy Function.
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Summing up all genus free energy of ABJM matrix model
Journal of High Energy Physics, 2011Co-Authors: Hiroyuki Fuji, Shinji Hirano, Sanefumi MoriyamaAbstract:The localization technique allows us to compute the free energy of the U( N )_ k × U( N )_− k Chern-Simons-matter theory dual to type IIA strings on AdS _4 × CP ^3 from weak to strong ’t Hooft coupling λ = N / k at finite N , as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large ’t Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up allthe1/ N corrections, apart from the worldsheet instanton contributions. The all genus partition Function takes a remarkably simple form — the Airy Function, $ {\text{Ai}}\left( {{{\left( {{{{\pi {k^2}}} \left/ {{\sqrt {2} }} \right.}} \right)}^{{{2} \left/ {3} \right.}}}{\lambda_{\text{ren}}}} \right) $ , with the renormalized ’t Hooft coupling λ_ren.
A.k. Ganguly - One of the best experts on this subject based on the ideXlab platform.
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numerical simulation of field emission and tunneling a comparison of the wigner Function and transmission coefficient approaches
Journal of Applied Physics, 1993Co-Authors: K.l. Jensen, A.k. GangulyAbstract:Quantum transport through one‐dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or the Wigner distribution Function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each and are compared for (a) calculating current‐field relationships for field‐emission potentials with silicon parameters (and current‐voltage relationships for resonant tunneling diodes), (b) their ability to accommodate scattering, self‐consistency, and time dependence, and for (c) the behavior of their ‘‘particle trajectory’’ interpretations. In making the comparisons, the concern will be on the ability of each method to be incorporated into a larger ensemble‐particle Monte Carlo simulation; it is argued that, in this regard, the WDF approach has significant advantages. Since the TC calculations rely on the Airy Function approach, a detailed comparison of this method is made with the widely used Wentzel–Kramers–Brillouin and Fowler–Nordheim approaches for ...
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numerical simulation of field emission and tunneling a comparison of the wigner Function and transmission coefficient approaches
Journal of Applied Physics, 1993Co-Authors: K.l. Jensen, A.k. GangulyAbstract:Quantum transport through one‐dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or the Wigner distribution Function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each and are compared for (a) calculating current‐field relationships for field‐emission potentials with silicon parameters (and current‐voltage relationships for resonant tunneling diodes), (b) their ability to accommodate scattering, self‐consistency, and time dependence, and for (c) the behavior of their ‘‘particle trajectory’’ interpretations. In making the comparisons, the concern will be on the ability of each method to be incorporated into a larger ensemble‐particle Monte Carlo simulation; it is argued that, in this regard, the WDF approach has significant advantages. Since the TC calculations rely on the Airy Function approach, a detailed comparison of this method is made with the widely used Wentzel–Kramers–Brillouin and Fowler–Nordheim approaches for the general problem of field emission from a material into the vacuum.
David Thomas - One of the best experts on this subject based on the ideXlab platform.
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a phase space approach for propagating field field correlation Functions
New Journal of Physics, 2015Co-Authors: Gabriele Gradoni, Stephen C Creagh, Gregor Tanner, Christopher Smartt, David ThomasAbstract:We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution Function. Our method exploits the connection between correlation Functions and the Wigner Function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-Function type phase space propagators. By exploiting the exact Wigner Function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflection can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as a Function of the distance from the source. The approximations are validated using full-wave simulations of model sources. In particular, results for the reflection of partially coherent sources from flat mirrors are given where the influence of Airy Function corrections can be demonstrated. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility.
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a phase space approach for propagating field field correlation Functions
arXiv: Chaotic Dynamics, 2015Co-Authors: Gabriele Gradoni, Stephen C Creagh, Gregor Tanner, Christopher Smartt, David ThomasAbstract:We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution Function. Our method exploits the connection between correlation Functions and theWigner Function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-Function type phase space propagators. By exploiting the exact Wigner Function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflections can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as Function of the distance from the source. Furthermore, results for the reflection of partially coherent sources from flat mirrors are given. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility.
Christian Jirauschek - One of the best experts on this subject based on the ideXlab platform.
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accuracy of transfer matrix approaches for solving the effective mass schr o dinger equation
arXiv: Mesoscale and Nanoscale Physics, 2011Co-Authors: Christian JirauschekAbstract:The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schr\"{o}dinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schr\"{o}dinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy Function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy Functions.
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accuracy of transfer matrix approaches for solving the effective mass schrodinger equation
IEEE Journal of Quantum Electronics, 2009Co-Authors: Christian JirauschekAbstract:The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrodinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position-dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrodinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy Function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy Functions.
K.l. Jensen - One of the best experts on this subject based on the ideXlab platform.
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numerical simulation of field emission and tunneling a comparison of the wigner Function and transmission coefficient approaches
Journal of Applied Physics, 1993Co-Authors: K.l. Jensen, A.k. GangulyAbstract:Quantum transport through one‐dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or the Wigner distribution Function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each and are compared for (a) calculating current‐field relationships for field‐emission potentials with silicon parameters (and current‐voltage relationships for resonant tunneling diodes), (b) their ability to accommodate scattering, self‐consistency, and time dependence, and for (c) the behavior of their ‘‘particle trajectory’’ interpretations. In making the comparisons, the concern will be on the ability of each method to be incorporated into a larger ensemble‐particle Monte Carlo simulation; it is argued that, in this regard, the WDF approach has significant advantages. Since the TC calculations rely on the Airy Function approach, a detailed comparison of this method is made with the widely used Wentzel–Kramers–Brillouin and Fowler–Nordheim approaches for ...
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numerical simulation of field emission and tunneling a comparison of the wigner Function and transmission coefficient approaches
Journal of Applied Physics, 1993Co-Authors: K.l. Jensen, A.k. GangulyAbstract:Quantum transport through one‐dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or the Wigner distribution Function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each and are compared for (a) calculating current‐field relationships for field‐emission potentials with silicon parameters (and current‐voltage relationships for resonant tunneling diodes), (b) their ability to accommodate scattering, self‐consistency, and time dependence, and for (c) the behavior of their ‘‘particle trajectory’’ interpretations. In making the comparisons, the concern will be on the ability of each method to be incorporated into a larger ensemble‐particle Monte Carlo simulation; it is argued that, in this regard, the WDF approach has significant advantages. Since the TC calculations rely on the Airy Function approach, a detailed comparison of this method is made with the widely used Wentzel–Kramers–Brillouin and Fowler–Nordheim approaches for the general problem of field emission from a material into the vacuum.