The Experts below are selected from a list of 8256 Experts worldwide ranked by ideXlab platform
Lei Wang - One of the best experts on this subject based on the ideXlab platform.
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continuous matrix product operator approach to finite temperature quantum states
Physical Review Letters, 2020Co-Authors: Wei Tang, Lei WangAbstract:We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without incurring any time discretization error. Moreover, the approach provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions. After verifying the method using the prototypical quantum XXZ chains, we apply it to quantum Ising models with power-law decaying interactions and on the Infinite Cylinder, respectively. The approach offers predictions that are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation rate.
Abner J Salgado - One of the best experts on this subject based on the ideXlab platform.
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finite element approximation of the parabolic fractional obstacle problem
SIAM Journal on Numerical Analysis, 2016Co-Authors: Enrique Otárola, Abner J SalgadoAbstract:We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-Infinite Cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggests a truncation that is suitable for numerical approximation. We discretize the truncation with a backward Euler scheme in time, and, for space, we use first-degree tensor product finite elements. We present an error analysis based on different smoothness assumptions.
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a pde approach to space time fractional parabolic problems
SIAM Journal on Numerical Analysis, 2016Co-Authors: Ricardo H Nochetto, Enrique Otárola, Abner J SalgadoAbstract:We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-Infinite Cylinder in one more spatial dimension. We write our evolution problem as a quasi-stationary elliptic problem with a dynamic boundary condition. We propose and analyze an implicit fully discrete scheme: first-degree tensor product finite elements in space and an implicit finite difference discretization in time. We prove stability and error estimates for this scheme.
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a pde approach to fractional diffusion in general domains a priori error analysis
Foundations of Computational Mathematics, 2015Co-Authors: Ricardo H Nochetto, Enrique Otárola, Abner J SalgadoAbstract:The purpose of this work is to study solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the Dirichlet-to-Neumann map for a degenerate/singular elliptic problem posed on a semi-Infinite Cylinder, which we analyze in the framework of weighted Sobolev spaces. Motivated by the rapid decay of the solution to this problem, we propose a truncation that is suitable for numerical approximation. We discretize this truncation using first degree tensor product finite elements. We derive a priori error estimates in weighted Sobolev spaces. The estimates exhibit optimal regularity but suboptimal order for quasi-uniform meshes. For anisotropic meshes instead, they are quasi-optimal in both order and regularity. We present numerical experiments to illustrate the method's performance.
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a pde approach to fractional diffusion in general domains a priori error analysis
arXiv: Numerical Analysis, 2013Co-Authors: Ricardo H Nochetto, Enrique Otárola, Abner J SalgadoAbstract:The purpose of this work is the study of solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the Dirichlet to Neumann map for a degenerate/singular elliptic problem posed on a semi-Infinite Cylinder, which we analyze in the framework of weighted Sobolev spaces. Motivated by the rapid decay of the solution of this problem, we propose a truncation that is suitable for numerical approximation. We discretize this truncation using first degree tensor product finite elements. We derive a priori error estimates in weighted Sobolev spaces. The estimates exhibit optimal regularity but suboptimal order for quasi-uniform meshes. For anisotropic meshes, instead, they are quasi-optimal in both order and regularity. We present numerical experiments to illustrate the method's performance.
Wei Tang - One of the best experts on this subject based on the ideXlab platform.
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continuous matrix product operator approach to finite temperature quantum states
Physical Review Letters, 2020Co-Authors: Wei Tang, Lei WangAbstract:We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without incurring any time discretization error. Moreover, the approach provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions. After verifying the method using the prototypical quantum XXZ chains, we apply it to quantum Ising models with power-law decaying interactions and on the Infinite Cylinder, respectively. The approach offers predictions that are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation rate.
Frank Pollmann - One of the best experts on this subject based on the ideXlab platform.
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topological characterization of fractional quantum hall ground states from microscopic hamiltonians
Physical Review Letters, 2013Co-Authors: Michael P Zaletel, Roger S K Mong, Frank PollmannAbstract:We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the Infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an Infinite Cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the Infinite density matrix renormalization group. We then show that the wave function obtained on the Infinite Cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an Infinite Cylinder.
Sergey A Denisov - One of the best experts on this subject based on the ideXlab platform.
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on the growth of the support of positive vorticity for 2d euler equation in an Infinite Cylinder
Communications in Mathematical Physics, 2019Co-Authors: Kyudong Choi, Sergey A DenisovAbstract:We consider the incompressible 2D Euler equation in an Infinite Cylinder $${\mathbb{R} \times \mathbb{T}}$$ in the case when the initial vorticity is non-negative, bounded, and compactly supported. We study d(t), the diameter of the support of vorticity, and prove that it allows the following bound: $${d(t) \leqslant Ct^{1/3}{\rm log}^{2}t}$$ when $${t \to \infty}$$ .