Polkuintegraaliperustilamenetelmä

Tutustutaan lyhyesti polkuintegraaliperustilamenetelmään, joka on numeerinen satunnaislukumenetelmä kvanttimekaanisten monihiukkasjärjestelmien ominaisuuksien laskemiseen nollalämpötilassa. Ensiksi käydään läpi menetelmän syntyperä ja suhde muihin samankaltaisiin menetelmiin. Sitten tarkastellaan me...

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Bibliographic Details
Main Author: Kiiskinen, Sampsa
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Fysiikan laitos, University of Jyväskylä, Jyväskylän yliopisto
Format: Bachelor's thesis
Language:fin
Published: 2017
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/57445
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author Kiiskinen, Sampsa
author2 Matemaattis-luonnontieteellinen tiedekunta Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto
author_facet Kiiskinen, Sampsa Matemaattis-luonnontieteellinen tiedekunta Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto Kiiskinen, Sampsa Matemaattis-luonnontieteellinen tiedekunta Fysiikan laitos University of Jyväskylä Jyväskylän yliopisto
author_sort Kiiskinen, Sampsa
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description Tutustutaan lyhyesti polkuintegraaliperustilamenetelmään, joka on numeerinen satunnaislukumenetelmä kvanttimekaanisten monihiukkasjärjestelmien ominaisuuksien laskemiseen nollalämpötilassa. Ensiksi käydään läpi menetelmän syntyperä ja suhde muihin samankaltaisiin menetelmiin. Sitten tarkastellaan menetelmän taustalla vallitsevaa teoriaa lähtien kvanttimekaniikan ja tilastollisen fysiikan perustuksista. Teoriaosuuden pohjalta rakennetaan yksinkertainen mallitoteutus, jonka havainnollistamiseksi lasketaan kvanttiharmonisen oskillaattorin energia ja todennäköisyysjakauma sekä karkea arvio helium-4-nesteen parikorrelaatiofunktiolle. Lopuksi katsotaan vielä muutamia menetelmän olemassaolevia tai mahdollisia käyttökohteita. A short treatise is presented on the path integral ground state method, which is a numerical method for computing the properties of quantum many-body systems at zero temperature. First the origin of the method and its relation to other similar methods is reviewed. Then the underlying theory of the method is presented, starting from the foundations of quantum mechanics and statistical physics. Based on the presentation, a simple sample implementation is constructed and showcased by calculating the energy and probability density function of a quantum harmonic oscillator and a rough estimate for the pair correlation function of liquid helium-4. Finally some of the existing or potential applications of the method are examined.
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spellingShingle Kiiskinen, Sampsa Polkuintegraaliperustilamenetelmä kvanttifysiikka statistinen fysiikka laskennallinen fysiikka Fysiikka
title Polkuintegraaliperustilamenetelmä
title_full Polkuintegraaliperustilamenetelmä
title_fullStr Polkuintegraaliperustilamenetelmä Polkuintegraaliperustilamenetelmä
title_full_unstemmed Polkuintegraaliperustilamenetelmä Polkuintegraaliperustilamenetelmä
title_short Polkuintegraaliperustilamenetelmä
title_sort polkuintegraaliperustilamenetelmä
title_txtP Polkuintegraaliperustilamenetelmä
topic kvanttifysiikka statistinen fysiikka laskennallinen fysiikka Fysiikka
topic_facet Fysiikka kvanttifysiikka laskennallinen fysiikka statistinen fysiikka
url https://jyx.jyu.fi/handle/123456789/57445 http://www.urn.fi/URN:NBN:fi:jyu-201803271854
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