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Jonathan Wise - ​ESR 3,  September 2018 - August 2021

LPMMC, CNRS and Université Grenoble Alpes, France

Master thesis: “Full counting statistics and emptiness formation probability of one-dimensional weakly-interacting Bosons”

In this work we used a path integral approach to access the particle number statistics of weakly-interacting bosons in 1D. After making a small fluctuation approximation we were able to reduce the action to a quadratic form, and hence solve the problem exactly. We considered the spontaneous formation of a region of given size where no particles are present. Despite this being contradictory to the assumption of small density fluctuations, we applied our model beyond its validity and computed the probability of such an event. Qualitative agreement was found with other theoretical works and the non-interacting classical result was recovered.

More quantitative results were obtained for the consideration of small density fluctuations that could be compared directly to data from experiments with ultracold atoms. The results included sub- and super-Poissonian atom number variance (alternatively, anti-bunching and bunching) on different length and temperature scales. It was possible to track the competition between effects amplifying the fluctuations, such as quantum indistinguishability and thermal effects, and effects reducing the fluctuations, such as the weak repulsive interactions. Theoretical Physics, University of Birmingham, UK Supervisor: Dimitri Gangardt

Personal Training Committee

Main Supervisor: Denis Basko, CNRS

Co-supervisor: Wolfgang Belzig, UKON

Mentor: Agnès Henri, EDP Sciences

Planned secondments

At UKON, Germany (February 2019) to learn non-equilibrium Green’s function techniques and (January-March 2021) to study the spatially and temporally resolved heat current noise between two 2-dimensional metallic layers in the Coulomb limit;

At AALTO, Finland (June 2019) to learn experimental specificities and (June 2021) to study the fluctuations of heat current between two reservoirs coupled via a two-level system;

At EDP Sciences (October-November 2020) to get trained in challenges of scientific publishing.

PhD Project

Theory of heat transfer in nanostructures: microscopic and phenomenological approaches

Objectives: Heat may be transferred in materials by a variety of mechanisms. Which method is most significant depends on the geometry of the device. When metallic parts are in direct contact, there is heat conduction by electrons (Figure 1, left), which is well described by the Fourier and Wiedemann-Franz empirical laws. By itself the electron conduction accounts fully for the heat transferred and we needn’t look elsewhere.  When the metallic parts are not in direct contact (Figure 1, right) this conduction is blocked, however there is still mediation of heat by photons through an electromagnetic field. The origin of this is the Coulomb potential between pairs of electrons on either side of the gap. This method of radiant heat transfer may be a cause of unexpected heat leakage even when metallic parts are separated. I intend to explore the dominant mechanisms of heat transfer in a nanostructure, as well as how the properties are affected if one (or many) of the component(s) are superconducting.

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