About the Project
About the award
This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.
The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.
Please note that of the total number of projects within the competition, up to 15 studentships will be filled.
Location: Streatham Campus, Exeter.
Project Description
Background and aim of PhD project: Thermodynamics is very successful in describing systems consisting of a huge number of constituents with only a few macroscopic parameters. However, most thermodynamical reasoning is based on the key assumptions that the system is in equilibrium and that interactions between the constituents are small. Conceptual problems arise when extending thermodynamic laws to classical and quantum systems that are strongly coupled to their environment. For example, Landauer’s principle of information erasure and the second law of thermodynamics have been questioned in this scenario, and subsequently restored [1]. It was also shown that entanglement, which arises from the strong coupling of quantum systems, can enable the extraction of work from heat [2]. Other recent developments in quantum thermodynamics [3] include resource theory approaches [4].
The aim of the project is to provide new insight into one of the biggest puzzles in quantum thermodynamics: How do the well-studied quantum properties of a few particles translate into a statistical theory from which new macroscopic thermodynamic laws emerge when strong coupling and quantum effects are important?
Recently a stochastic thermodynamics approach has shown that for a classical system that is strongly coupled to a bath the thermodynamic potentials, such as energy, entropy and free energy, differ from the standard definitions in thermodynamics [5]. This approach makes use of the Hamiltonian of mean force, an effective Hamiltonian for classical or quantum systems [6] that accounts for the energy required for the system to be coupled to an environment.
First 6 months: You will learn how thermodynamic quantities, such as heat, work and entropy, are determined in classical thermodynamics and how they transfer to the quantum regime. Following the approaches in [5,6] you will study a global Hamiltonian for a quantum system and a bath of the form H = HS +HB +Vint, and consider different choices for the system Hamiltonian: the “bare” Hamiltonian HS, the Hamiltonian of mean force valid for the system being part of a global equilbrium state [5,6], and the Hamiltonian part in the master equation describing the non-equilbrium dynamics arising from the full Hamiltonian [7]. You will discuss the physical meaning of the associated energy, entropy, heat and work for each of these cases.
PhD project: Following initial literature review you will be guided to understand how the global time-independent Hamiltonian gives rise to a local time-dependent Hamiltonian. You will establish in what situations the notion of a local system Hamiltonian is sensible when the system is strongly coupled and a prescription of how to experimentally confirm its form. For the remaining situations you will be guided in seeking reasons why the association of a system Hamiltonian is in principle impossible for these cases.
Based on these findings you will then be able to reformulate laws of thermodynamics for strongly coupled open systems and identify any differences to standard thermodynamics. The developed theoretical framework will have applications for a number of recent experimental developments that push towards the strongly coupled quantum regime. Controlled nanomechanical oscillators, that are useful as mass sensors for single molecules, are exactly in this regime [8].
Entry Requirements
The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes. If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.
Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.
References
References and further reading:
[1] S. Hilt, S. Shabbir, J. Anders, E. Lutz, Phys. Rev. E 83, 030102(R) (2011)
[2] L. del Rio, J. Aberg, R. Renner, O. Dahlsten, V. Vedral, Nature 474, 61 (2011)
[3] S. Vinjanampathy, J. Anders, Contemporary Physics 57, 545 (2016)
[4] M. Horodecki, J. Oppenheim, Nature Comm. 4, 2059 (2013)
[5] H. Miller, J. Anders, Phys. Rev. E 95, 062123 (2017)
[6] M. Campisi, P. Talkner, P. Hänggi, Phys. Rev. Lett. 102, 210401 (2009)
[7] H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2002)
[8] J. Millen, T. Deesuwan, P. Barker, J. Anders, Nature Nanotechnology 9, 428 (2014)
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