| dbo:abstract |
In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies. Mathematically, the problem reduces to solving a Fredholm integral equation of the first kind with an ill-conditioned kernel. As a result, it is an ill-posed inverse problem with no unique solution and where a small noise on the input leads to large errors in the unregularized solution. There are different methods for solving this problem including the maximum entropy method, the average spectrum method and Pade approximation methods. (en) |
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https://spm-lab.github.io/SpM/manual/build/html/index.html https://www.spektra.app https://github.com/CQMP/Maxent |
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dbr:Analytic_continuation dbr:Green's_function_(many-body_theory) dbr:Kramers–Kronig_relations dbr:Linear_response_function dbr:Quantum_Monte_Carlo dbr:Regularization_(mathematics) dbc:Mathematical_physics dbc:Quantum_Monte_Carlo dbr:Boson dbr:Fermion dbr:Fredholm_integral_equation dbr:Inverse_Fourier_transform dbr:Matsubara_frequency dbr:Imaginary_time dbr:Many-body_physics dbr:Analytic_continuation_along_a_curve dbr:Fredholm_integral_equation_of_the_first_kind |
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dbc:Mathematical_physics dbc:Quantum_Monte_Carlo |
| rdfs:comment |
In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies. (en) |
| rdfs:label |
Numerical analytic continuation (en) |
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wikidata:Numerical analytic continuation https://global.dbpedia.org/id/FLTKY |
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wikipedia-en:Numerical_analytic_continuation?oldid=1119164046&ns=0 |
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