We present a consistent thermodynamic theory for the resonant level model in the wide band limit, whose level energy is driven slowly by an external force. The problem of defining 'system' and 'bath' in the strong coupling regime is circumvented by considering as the 'system' everything that is influenced by the externally driven level. The thermodynamic functions that are obtained to first order beyond the quasistatic limit fulfill the first and second law with a positive entropy production, successfully connect to the forces experienced by the external driving, and reproduce the correct weak coupling limit of stochastic thermodynamics.
We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B 89, 161306 (2014), Phys. Rev. B 93, 115318 (2016] have found, for a resonant electronic level interacting with a thermal free electron wide-band bath, that the expectation value for the energy of the interacting subsystem can be correctly calculated by considering a symmetric splitting of the interaction Hamiltonian between the subsystem and the bath. However, the general implications of this approach were questioned [Phys. Rev. B 92, 235440 (2015)]. Here we show that already at equilibrium, such splitting fails to describe the energy fluctuations, as measured here by the second and third central moments (namely width and skewness) of the energy distribution. Furthermore, we find that when the wide-band approximation does not hold, no splitting of the system-bath interaction can describe the system thermodynamics. We conclude that in general no proper division subsystem of the Hamiltonian of the composite system can account for the energy distribution of the subsystem. This also implies that the thermodynamic effects due to local changes in the subsystem cannot in general be described by such splitting.
We develop a Landauer-Büttiker theory of entropy evolution in time-dependent, strongly coupled electron systems. The formalism naturally avoids the problem of the system-bath distinction by defining the entropy current in the attached leads. This current can then be used to infer changes of the entropy of the system which we refer to as the inside-outside duality. We carry out this program in an adiabatic expansion up to first order beyond the quasistatic limit. When combined with particle and energy currents, as well as the work required to change an external potential, our formalism provides a full thermodynamic description, applicable to arbitrary noninteracting electron systems in contact with reservoirs. This provides a clear understanding of the relation between heat and entropy currents generated by time-dependent potentials and their connection to the occurring dissipation.
We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, Q. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum-limited detection (Q → 1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, Q is a monotonously decreasing function of temperature as in the non-interacting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.
We present a field-theoretic treatment of an adiabatic quantum motor. We explicitly discuss a motor called the Thouless motor which is based on a Thouless pump operating in reverse. When a sliding periodic potential is considered to be the motor degree of freedom, a bias voltage applied to the electron channel sets the motor in motion. We investigate a Thouless motor whose electron channel is modeled as a Luttinger liquid. Interactions increase the gap opened by the periodic potential. For an infinite Luttinger liquid the coupling-induced friction is enhanced by electron-electron interactions. When the Luttinger liquid is ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its value for a noninteracting electron system for a constant motor velocity. Our results can also be applied to a motor based on a nanomagnet coupled to a quantum spin Hall edge.
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