Work statistics in open quantum systems

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School of Science | Doctoral thesis (article-based) | Defence date: 2017-02-13
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Author
Date
2017
Department
Teknillisen fysiikan laitos
Department of Applied Physics
Major/Subject
Mcode
Degree programme
Language
en
Pages
66 + app. 50
Series
Aalto University publication series DOCTORAL DISSERTATIONS, 15/2017
Abstract
Rapid progress in the fabrication and manipulation of micro and nanoscale devices has made it necessary to extend the concepts of thermodynamics to small systems and finally to quantum systems. In such systems the extensive thermodynamic quantities, such as entropy, heat, and work, are not described by their average values alone but by distributions. Remarkably, it has been shown that the stochastic thermodynamic variables often obey fluctuation relations which usually appear in the form of relations between exponential averages. While the two-measurement protocol of thermodynamic variables, especially work, is now well studied in closed quantum systems, there have been conceptual and experimental problems in open quantum systems. In this thesis, we theoretically study work statistics and fluctuation relations in open quantum systems. To calculate the work statistics, we use the quantum jump method and direct master equation calculations. We show that work definitions equivalent in closed systems can lead to mutually different results in the case of open quantum systems due to a different order of approximations. Moreover, we show that the fluctuation relations can be extended to nearly adiabatically driven systems by using the adiabatic renormalization procedure. Last, we focus on how a finite size of the environment affects the dynamics and work statistics of open quantum systems. This is important from the experimental point of view because a finite-size environment allows the detection of heat exchange between the system and the environment. We derive a master equation that takes into account these effects and develop a stochastic model that unravels the master equation. We explicitly show that the finite size of the environment influences the dynamics and the work statistics. We also show that the common fluctuation relations are still valid.

Nopea kehitys pienten komponenttien valmistamisessa on tehnyt tarpeelliseksi laajentaa termodynamiikan konseptit pieniin systeemeihin ja lopulta kvanttimekaanisiin systeemeihin. Näiden systeemien pienen koon takia termodynaamisia suureita, kuten työtä ja lämpöä, ei voida kuvata pelkällä keskiarvolla, vaan koko jakauma täytyy ottaa huomioon. Tässä väitöskirjassa tutkitaan työn statistiikkaa avoimissa kvanttisysteemeissä. Väitöskirjassa näytetään, että työn määritelmät, jotka ovat yhtenevät suljetuille systeemeille, voivat johtaa eri tuloksiin avoimissa kvanttisysteemeissä. Työssä laajennetaan myös työn fluktuaatiorelaatiot lähes adiabaattisesti ajasta riippuviin systeemeihin. Väitöskirjassa kehitetään myös malli, joka ottaa huomioon ympäristön äärellisen koon. Tämä malli mahdollistaa työn mittaamiseen ehdotettujen kokeiden mallintamisen, joissa ympäristön koon täytyy olla pieni lämmönvaihdon mittaamiseksi. Mallille kehitetään myös stokastinen vastine, joka mahdollistaa stokastisen termodynaamikan käytön työn ja lämmön analysoimiseen. Väitöskirjassa kehitetyt menetelmät mahdollistavat termodynamiikan tutkimisen systeemeissä, joita ei tavanomaisilla menetelmillä pystytä tutkimaan.
Description
Supervising professor
Ala-Nissilä, Tapio, Prof., Aalto University, Department of Applied Physics, Finland
Thesis advisor
Ala-Nissilä, Tapio, Prof., Aalto University, Department of Applied Physics, Finland
Keywords
open quantum systems, work fluctuations, stochastic thermodynamics, quantum jump method, finite environment, avoimet kvanttisysteemit, termodynamiikka, stokastinen termodynamiikka, työfluktuaatiot
Other note
Parts
  • [Publication 1]: S. Suomela, P. Solinas, J. P. Pekola, J. Ankerhold, T. Ala-Nissilä. Moments of work in the two-point measurement protocol for a driven open quantum system. Physical Review B, Volume 90, Issue 9, 094304 (8 pages), September 2014.
    DOI: 10.1103/PhysRevB.90.094304 View at publisher
  • [Publication 2]: S. Suomela, J. Salmilehto, I. G. Savenko, T. Ala-Nissilä, and M. Möttönen. Fluctuations of work in a nearly adiabatically driven open quantum system. Physical Review E, Volume 91, Issue 2, 022126 (13 pages), January 2015.
    DOI: 10.1103/PhysRevE.91.022126 View at publisher
  • [Publication 3]: S. Suomela, A. Kutvonen and T. Ala-Nissilä. Quantum jump model for a system with a finite-size environment. Physical Review E, Volume 93, Issue 6, 062106 (7 pages), June 2016.
    DOI: 10.1103/PhysRevE.93.062106 View at publisher
  • [Publication 4]: S. Suomela, R. Sampaio and T. Ala-Nissilä. Comparison between quantum jumps and master equation in the presence of a finite environment. Physical Review E, Volume 94, Issue 4, 032138 (9 pages), September 2016.
    DOI: 10.1103/PhysRevE.94.032138 View at publisher
Citation
Permanent link to this item
https://urn.fi/URN:ISBN:978-952-60-7263-0
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[diss] Perustieteiden korkeakoulu / SCI