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Register a new userNon-equilibrium quantum transport in presence of a defect: the non-interacting case
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We study quantum transport after an inhomogeneous quantum quench in a free fermion lattice system in the presence of a localised defect. Using a new rigorous analytical approach for the calculation of large time and distance asymptotics of physical observables, we derive the exact profiles of particle density and current. Our analysis shows that the predictions of a semiclassical approach that has been extensively applied in similar problems match exactly with the correct asymptotics, except for possible finite distance corrections close to the defect. We generalise our formulas to an arbitrary non-interacting particle-conserving defect, expressing them in terms of its scattering properties.
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We provide systematic analysis on a non-Hermitian PT -symmetric quantum impurity system both in and out of equilibrium, based on exact computations. In order to understand the interplay between non-Hermiticity and Kondo physics, we focus on a prototypical noninteracting impurity system, the resonant level model, with complex coupling constants. Explicitly constructing biorthogonal basis, we study its thermodynamic properties as well as the Loschmidt echo starting from the initially disconnected two free fermion chains. Remarkably, we observe the universal crossover physics in the Loschmidt echo, both in the PT broken and unbroken regimes. We also find that the ground state quantities we compute in the PT broken regime can be obtained by analytic continuation. It turns out that Kondo screening ceases to exist in the PT broken regime, which was also previously predicted in the non-hermitian Kondo model. All the analytical results are corroborated against biorthogonal free fermion numerics.
The impact of bound states in Landauer-Buttiker scattering approach to non-equilibrium quantum transport is investigated. We show that the noise power at frequency $ u$ is sensitive to all bound states with energies $omega_b$ satisfying $|omega_b| < u$. We derive the exact expression of the bound state contribution and compare it to the one produced by the scattering states alone. It turns out that the bound states lead to specific modifications of both space and frequency dependence of the total noise power. The theoretical and experimental consequences of this result are discussed.
We derive the exact n-point current expectation values in the Landauer-Buttiker non-equilibrium steady state of a multi terminal system with star graph geometry and a point-like defect localised in the vertex. The current cumulants are extracted from the connected correlation functions and the cumulant generating function is established. We determine the moments, show that the associated moment problem has a unique solution and reconstruct explicitly the corresponding probability distribution. The basic building blocks of this distribution are the probabilities of particle emission and absorption from the heat reservoirs, driving the system away from equilibrium. We derive and analyse in detail these probabilities, showing that they fully describe the quantum transport problem in the system.
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or line. We study both sudden and slow quenches in a variety of systems including one-dimensional ultracold atoms in an optical lattice, an infinite range ferromagnetic Ising model, and some exactly solvable spin models in one and two dimensions (such as the Kitaev model). We show that quenching leads to the formation of defects whose density has a power-law dependence on the quenching rate; the power depends on the dimensionalities of the system and of the critical surface and on some of the exponents associated with the critical point which is being crossed. We also study the effect of non-linear quenching; the power law of the defects then depends on the degree of non-linearity. Finally, we study some spin-1/2 models to discuss how a qubit can be transferred across a system.
We investigate the quantum transport of anyons in one space dimension. After establishing some universal features of non-equilibrium systems in contact with two heat reservoirs in a generalised Gibbs state, we focus on the abelian anyon solution of the Tomonaga-Luttinger model possessing axial-vector duality. In this context a non-equilibrium representation of the physical observables is constructed, which is the basic tool for a systematic study of the anyon particle and heat transport. We determine the associated Lorentz number and describe explicitly the deviation from the standard Wiedemann-Franz law induced by the interaction and the anyon statistics. The quantum fluctuations generated by the electric and helical currents are investigated and the dependence of the relative noise power on the statistical parameter is established.
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