Interplay between transport and quantum coherences in free fermionic systems

We consider a quantum quench in a non-interacting fermionic one-dimensional field-theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ ($[-L/2,0]$) and $\mathcal{R}$ ($[0,L/2]$), each of them thermalized at two different temperatures, ${T_{L}}$ and ${T_{R}}$ respectively. At a given time the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system ($L\rightarrow \infty$...

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic, non-integrable quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here we show that the confinement of quasi-particles can al...

We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for gene...

For a one-dimensional system of free fermions, we derive a connection between the full counting statistics of domain-wall and alternating occupancy states. We derive linear growth with time at the long times for the even moments in the latter case.

We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the ...

We study macroscopic quantum dynamics of a free domain wall in a quasi-one-dimensional ferromagnet by use of the spin-coherent-state path integral in {\it discrete-time} formalism. Transition amplitudes between typical states are quantitatively discussed by use of {\it stationary-action approximation} with respect to collective degrees of freedom representing the center position and the chirality of the domain wall. It is shown that the chirality may be loosely said to be can...

We study the transport properties of a one-dimensional spinful Fermi gas, after junction of two semi-infinite sub-systems held at different temperatures. The ensuing dynamics is studied by analysing the space-time profiles of local observables emerging at large distances $x$ and times $t$, as a function of $\zeta = x/t$. At equilibrium, the system displays two distinct species of quasi-particles, naturally associated with different physical degrees of freedom. By employing th...

Emergence of hydrodynamics in quantum many-body systems has recently garnered growing interest. The recent experiment of ultracold atoms [J. F. Wienand {\it et al.}, arXiv:2306.11457] studied emergent hydrodynamics in hard-core bosons using a bipartite fluctuation, which quantifies how the particle number fluctuates in a subsystem. In this Letter, we theoretically study the variance of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics starting from ...

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan-Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we compute analytically the profiles of various physical observables in the space-time scaling...

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted dir...