Statistics of Work in Quantum Systems under Classical and Quantum Noise

  • Owen Diba

Student thesis: Phd


Quantum thermodynamics aims to build a theory of thermodynamics starting from the theory of quantum mechanics. The natural framework for this formulation of thermodynamics is the theory of open quantum systems. Open quantum system theory concerns the dynamics of a quantum system interacting with a quantum environment. Its techniques are suited to treating the dynamical, nonequilibrium processes that are of central importance to quantum thermodynamics. We give an introduction to the techniques of open quantum systems in \Cref{sec:chapter1}. In quantum thermodynamics, work is an inherently stochastic quantity, and as well as its average behaviour we will look at its fluctuations and the underlying probability distribution that governs the fluctuations. \Cref{sec:chapter2} considers a finite-time quantum Otto engine. To operate at finite-time and simultaneously remove the quantum analogue to friction, a shortcut to adiabaticity protocol is applied. This suppresses nonadiabatic transitions in the system and minimises dissipated work. Any experimental realisation of such a system will be affected by an imperfect control of the driving protocol. We model these fluctuations of the control field with a Gaussian white noise process, and find that the noise is particularly detrimental to performance at short cycle times. At these short cycle times it would appear that it is disadvantageous to use the shortcut protocol. White noise is often an over-simplification of a stochastic process. Noise will generally be correlated with itself at different moments of time - this is referred to as coloured noise. In an extension of the analysis in \Cref{sec:chapter1}, the third chapter is concerned with an isolated work protocol disturbed by coloured Gaussian noise. We find expressions for the first two moments of work for such a system. We then look at a particular model: a stochastic, driven harmonic oscillator and show that the average, non-Markovian dynamics of this model can be calculated exactly. This makes it an excellent test case for the analysis of quantum work in the presence of classical noise. We find non-monotonic behaviour of the work moments with the correlation time of the noise. In the \Cref{sec:chapter4}, we move beyond looking at work moments to calculating the distribution of work itself. We look at a driven two-level system interacting strongly with a heat bath. Most previous studies of work statistics of open systems have considered weakly-coupled systems. We work in a polaron frame which allows us to extend the weak-coupling analysis to the strong-coupling regime. We focus on driving protocols which give near-adiabatic unitary dynamics for the system. We find quantitative and qualitative differences to the weak-coupling theory: an overall broader distribution but with "sharper'' features.
Date of Award1 Aug 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorTobias Galla (Supervisor) & Ahsan Nazir (Supervisor)


  • physics
  • thermodynamics
  • noise

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