The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many-body systems with very high accuracy. Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here, we provide a pedagogical review that elucidates the approach we have developed.

Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo / G. Bertaina, D.E. Galli, E. Vitali. - In: ADVANCES IN PHYSICS: X. - ISSN 2374-6149. - 2:2(2017), pp. 302-323. [10.1080/23746149.2017.1288585]

Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

G. Bertaina
Primo
;
D.E. Galli
;
E. Vitali
Ultimo
2017

Abstract

The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many-body systems with very high accuracy. Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here, we provide a pedagogical review that elucidates the approach we have developed.
Analytic continuation; inverse problems; genetic algorithms; quantum liquids; dynamics; elementary excitations
Settore FIS/03 - Fisica della Materia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/480898
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