Multiconfigurational Hartree method for many-particle systems

Author(s)

Alex Valerio Andriati

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2022-03-11

Examining board members

Arnaldo Gammal; Tommaso Macri; Caetano Rodrigues Miranda; Monica Andrioli Caracanhas Santarelli; Peter Schmelcher

• Advisor: Arnaldo Gammal

Abstract

In the present thesis, the multiconfigurational time-dependent Hartree method is applied to study flow properties of bosons trapped in annular geometry. This physical system provides a suitable platform to investigate beyond meanfield features, since as one spatial dimensional problem, we can explore different interacting regimes, set a rather large range for parameter values without excessive concern about the computational cost and explore relevant concepts, such as superfluidity. As a very important part of the present thesis, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is carefully described, providing all relevant derivations up to the final equations of motion, as well as a prospectus of the numerical approach. As such, this thesis also deals with topics of numerical analysis due to its method complexity. After the MCTDHB derivation and its numerical implementation are shown, the superfluid properties of a bosonic gas in annular geometry are studied with the most general approach proposed in reference [1], without any assumptions about the condensation status of the system. In addition, the MCTDHBs capability to provide correlation functions is exploited to characterize the loss of superfluid fraction due to a potential barrier. Within the same goal to study bosonic flow properties in a ring, persistent currents are also investigated, with two alternative derivations for the metastability condition as energy local minimum. Besides, the dynamical decay of the current is analyzed after quenching a potential barrier. Fluctuations of the number operator and probabilities are calculated along the time evolution to provide information about the quantum statistical distribution embedded in experimental measures, aiming to spot relevant information on image observation of flowing states. (AU)

• FAPESP's process: 18/02737-4 - Many-body properties of Bose-Einstein condensates from multi configurational time-dependent Hartree method
• Grantee: Alex Valerio Andriati
• Support type: Scholarships in Brazil - Doctorate