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Tesi etd-06272016-100841


Thesis type
Tesi di dottorato di ricerca
Author
GEROLIN GAVEA, JOSE AUGUSTO
URN
etd-06272016-100841
Title
Multi-marginal optimal transport and potential optimization problems for Schrodinger operator
Settore scientifico disciplinare
MAT/05
Corso di studi
MATEMATICA
Commissione
tutor Prof. Buttazzo, Giuseppe
Parole chiave
  • Calculus of Variations
  • Optimal Transprot
  • Density Functional Theory
Data inizio appello
30/07/2016;
Consultabilità
parziale
Data di rilascio
30/07/2019
Riassunto analitico
In the part I: Optimal Transport and Density Functional Theory, we investigate methods to compute the ground state energy for a stationary Schrodinger Equation -∆+V with singular potential V. This is related to Quantum Mechanics or, more precisely, to a computational quantum mechanical modelling, named Density Functional Theory (DFT), which investigates the electronic structure of many-body systems. In a sort of semi-classical regime, the problem to compute the ground state<br>energy for a electronic Schr ̈odinger equation can be seen as a generalized version<br>of a mass-transportation problem.<br><br>In the part II: Optimal Potentials for Schrodinger Operators, we are dealing with stationary Schrodinger operators −∆ + V. Our goal is to study some optimization problems where an optimal potential V ≥ 0 has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.<br>
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