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Title: Study of full-counting statistics in heat transport in transient and steady state and quantum fluctuation theorems
Keywords: full-counting statistics, thermal transport, fluctuation theorems, nonequilibrium Greens function
Issue Date: 17-Jan-2013
Citation: BIJAY KUMAR AGARWALLA (2013-01-17). Study of full-counting statistics in heat transport in transient and steady state and quantum fluctuation theorems. ScholarBank@NUS Repository.
Abstract: There are very few known universal relations that exists in the field of nonequilibrium statistical physics. Linear response theory is one such example. However it is valid for systems close to equilibrium. It is only in recent times that several other universal relations are discovered for systems driven arbitrarily far-from-equilibrium and they are collectively referred to as the fluctuation theorems. These theorems places condition on the probability distribution for different nonequilibrium observables such as heat, injected work, particle number, generically referred to as entropy production. In this thesis, we study quantum fluctuations of energy flowing through a finite junction connected with multiple reservoirs. Applying non-equilibrium Green's function (NEGF) and two-time quantum measurement technique we first investigate full-counting statistics (FCS) for a phononic lead-junction-lead setup in both transient and steady-state regimes. For harmonic junction we obtain the cumulant generating function (CGF) for heat considering many important aspects which are relevant to the experimental situations. We show that the effect of energy counting is related to shift in time-argument for the self-energy. In the steady state the CGF is given by the famous Levitov-Lesovik formula for phonons satisfying Gallavotti-Cohen fluctuation symmetry. We also analyze FCS for multiterminal lead-lead setup without the junction part and explored transient and steady state fluctuation theorems also known as exchange fluctuation theorem. For general nonlinear junction we develop a formalism to study FCS based on nonequilibrium version of Feynman-Hellmann theorem. The power of this general method is shown by considering an oscillator model with quartic onsite potential. In addition, the methods that we develop for energy counting can be easily extended for the charge counting as shown by an example for non-interacting electrons.
Appears in Collections:Ph.D Theses (Open)

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