The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Tomi Ohtsuki - One of the best experts on this subject based on the ideXlab platform.
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Critical Exponent for the anderson transition in the three dimensional orthogonal universality class
New Journal of Physics, 2014Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:We report a careful finite size scaling study of the metal–insulator transition in Anderson's model of localization. We focus on the estimation of the Critical Exponent ν that describes the divergence of the localization length. We verify the universality of this Critical Exponent for three different distributions of the random potential: box, normal and Cauchy. Our results for the Critical Exponent are consistent with the measured values obtained in experiments on the dynamical localization transition in the quantum kicked rotor realized in a cold atomic gas.
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Critical Exponent FOR THE QUANTUM SPIN HALL TRANSITION IN ℤ2 NETWORK MODEL
arXiv: Disordered Systems and Neural Networks, 2012Co-Authors: Koji Kobayashi, Tomi Ohtsuki, Keith SlevinAbstract:We have estimated the Critical Exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The Critical Exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the Critical Exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov Exponent instead of the smallest positive Lyapunov Exponent. We find a value for the Critical Exponent ν = 2.73 ± 0.02 that is consistent with that for topologically trivial symplectic systems.
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Critical Exponent for the quantum Hall plateau transition
2011Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:In this article we will briefly review our work on estimating the Critical Exponent of the Anderson transition at the centre of a Landau level. We review some basic facts about the quantum Hall effect and briefly describe how the Critical Exponent is measured. We explain why physicists think Critical Exponents are important. We also explain how the Exponent can be estimated numerically and to what extent our current estimate is in agreement with experiments.
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Critical Exponent for the quantum hall transition
Physical Review B, 2009Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:We report an estimate $\ensuremath{\nu}=2.593$ [2.587,2.598] of the Critical Exponent of the Chalker-Coddington model of the integer quantum Hall effect that is significantly larger than previous numerical estimates and in disagreement with experiment. This suggests that models of noninteracting electrons cannot explain the Critical phenomena of the integer quantum Hall effect.
Yuta Wakasugi - One of the best experts on this subject based on the ideXlab platform.
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Critical Exponent for the cauchy problem to the weakly coupled damped wave system
Nonlinear Analysis-theory Methods & Applications, 2014Co-Authors: Kenji Nishihara, Yuta WakasugiAbstract:Abstract In this paper, we consider a system of weakly coupled semilinear damped wave equations. We determine the Critical Exponent for any space dimensions. Our proof of the global existence of solutions for superCritical nonlinearities is based on a weighted energy method, whose multiplier is appropriately modified in the case where one of the Exponent of the nonlinear term is less than the so called Fujita’s Critical Exponent. We also give estimates of the lifespan of solutions from above for subCritical nonlinearities.
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Critical Exponent for the semilinear wave equation with scale invariant damping
arXiv: Analysis of PDEs, 2014Co-Authors: Yuta WakasugiAbstract:In this paper we consider the Critical Exponent problem for the semilinear damped wave equation with time-dependent coefficients. We treat the scale invariant cases. In this case the asymptotic behavior of the solution is very delicate and the size of coefficient plays an essential role. We shall prove that if the power of the nonlinearity is greater than the Fujita Exponent, then there exists a unique global solution with small data, provided that the size of the coefficient is sufficiently large. We shall also prove some blow-up results even in the case that the coefficient is sufficiently small.
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Small data global existence for the semilinear wave equation with space-time dependent damping
Journal of Mathematical Analysis and Applications, 2012Co-Authors: Yuta WakasugiAbstract:In this paper we consider the Critical Exponent problem for the semilinear wave equation with space-time dependent damping. When the damping is effective, it is expected that the Critical Exponent agrees with that of only the space dependent coefficient case. We shall prove that there exists a unique global solution for small data if the power of nonlinearity is larger than the expected Exponent. Moreover, we do not assume that the data are compactly supported. However, it is still open whether there exists a blow-up solution if the power of nonlinearity is smaller than the expected Exponent. © 2012 Elsevier Ltd.
Keith Slevin - One of the best experts on this subject based on the ideXlab platform.
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Critical Exponent for the anderson transition in the three dimensional orthogonal universality class
New Journal of Physics, 2014Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:We report a careful finite size scaling study of the metal–insulator transition in Anderson's model of localization. We focus on the estimation of the Critical Exponent ν that describes the divergence of the localization length. We verify the universality of this Critical Exponent for three different distributions of the random potential: box, normal and Cauchy. Our results for the Critical Exponent are consistent with the measured values obtained in experiments on the dynamical localization transition in the quantum kicked rotor realized in a cold atomic gas.
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Critical Exponent FOR THE QUANTUM SPIN HALL TRANSITION IN ℤ2 NETWORK MODEL
arXiv: Disordered Systems and Neural Networks, 2012Co-Authors: Koji Kobayashi, Tomi Ohtsuki, Keith SlevinAbstract:We have estimated the Critical Exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The Critical Exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the Critical Exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov Exponent instead of the smallest positive Lyapunov Exponent. We find a value for the Critical Exponent ν = 2.73 ± 0.02 that is consistent with that for topologically trivial symplectic systems.
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Critical Exponent for the quantum Hall plateau transition
2011Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:In this article we will briefly review our work on estimating the Critical Exponent of the Anderson transition at the centre of a Landau level. We review some basic facts about the quantum Hall effect and briefly describe how the Critical Exponent is measured. We explain why physicists think Critical Exponents are important. We also explain how the Exponent can be estimated numerically and to what extent our current estimate is in agreement with experiments.
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Critical Exponent for the quantum hall transition
Physical Review B, 2009Co-Authors: Keith Slevin, Tomi OhtsukiAbstract:We report an estimate $\ensuremath{\nu}=2.593$ [2.587,2.598] of the Critical Exponent of the Chalker-Coddington model of the integer quantum Hall effect that is significantly larger than previous numerical estimates and in disagreement with experiment. This suggests that models of noninteracting electrons cannot explain the Critical phenomena of the integer quantum Hall effect.
Chunlei Tang - One of the best experts on this subject based on the ideXlab platform.
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positive solutions for kirchhoff type equations with Critical Exponent in rn
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Jiafeng Liao, Chunlei TangAbstract:Abstract In this paper, we study the following nonlinear Kirchhoff-type equation (0.1) { − ( a + b ∫ R N | ∇ u | 2 d x ) △ u = | u | 2 ⁎ − 2 u + μ h ( x ) , x ∈ R N u ∈ D 1 , 2 ( R N ) , where a ≥ 0 , b > 0 , N ≥ 3 , 2 ⁎ = 2 N N − 2 , μ ≥ 0 and h ∈ L 2 ⁎ 2 ⁎ − 1 ( R N ) \ { 0 } is nonnegative. By using the variational method, we obtain the existence of positive solutions for Eq. (0.1) , under some assumptions on a, b, μ.
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existence and multiplicity of solutions for kirchhoff type problem with Critical Exponent
Communications on Pure and Applied Analysis, 2013Co-Authors: Xingping Wu, Chunlei TangAbstract:In the present paper, the existence and multiplicity of solutions for Kirchhoff type problem involving Critical Exponent with Dirichlet boundary value conditions are obtained via the variational method.
Cesar Gomez - One of the best experts on this subject based on the ideXlab platform.
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landau ginzburg limit of black holeʼs quantum portrait self similarity and Critical Exponent
Physics Letters B, 2012Co-Authors: Gia Dvali, Cesar GomezAbstract:Abstract Recently we have suggested that the microscopic quantum description of a black hole is an overpacked self-sustained Bose-condensate of N weakly-interacting soft gravitons, which obeys the rules of ʼt Hooftʼs large-N physics. In this Letter we derive an effective Landau–Ginzburg Lagrangian for the condensate and show that it becomes an exact description in a semi-classical limit that serves as the black hole analog of ʼt Hooftʼs planar limit. The role of a weakly-coupled Landau–Ginzburg order parameter is played by N. This description consistently reproduces the known properties of black holes in semi-classical limit. Hawking radiation, as the quantum depletion of the condensate, is described by the slow-roll of the field N. In the semi-classical limit, where black holes of arbitrarily small size are allowed, the equation of depletion is self-similar leading to a scaling law for the black hole size with Critical Exponent 1 3 .
