Non-equilibrium steady states of quantum systems on star graphs

Abstract

Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph. Time reversal invariance is spontaneously broken. We study in this general framework the transport properties of the Schrödinger and the Dirac systems on a star graph, modeling a quantum wire junction. The interaction, which drives the system away from equilibrium, is localized in the vertex of the graph. All point-like vertex interactions, giving rise to self-adjoint Hamiltonians possibly involving the minimal coupling to a static electromagnetic field in the ambient space, are considered. In this context we compute the exact electric steady current and the nonequilibrium charge density. We investigate also the heat transport and derive the Casimir energy density away from equilibrium. The appearance of Friedel type oscillations of the charge and energy densities along the edges of the graph is established. We focus finally on the noise power and discuss the non-trivial impact of the point-like interactions on the noise.

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

“…There, under the assumption of quasistationarity, a semiclassical picture applies where the information about the initial state is carried by free stable quasiparticles moving throughout the system. Similar results were obtained in the framework of conformal field theory and Luttinger liquid descriptions [25][26][27][28][29][30][31][32][33][34][35][36][37]. In the presence of interactions the situation was less clear [38][39][40][41][42][43][44][45][46][47], but, eventually, Refs [48,49] have shown that the continuity equations satisfied by the (quasi)local conserved quantities are sufficient to characterize the late-time behavior.…”

Full counting statistics in the free Dirac theory

“…This would be straightforwardly derived by writing down the NESS density operator with taking accounting of the impurity [31]. Another possible generalization could be extending to generic spacial dimensions d. To do so, one should be aware of the different nature of the spinor representation of SO(d, 1) in even and odd dimensions: in odd spatial dimensions there exist Weyl spinors, but this is not the case in even spatial dimensions.…”

Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

“…A particularly simple, yet non-trivial, setting which has been widely investigated is the so-called bipartitioning protocol, where two semi-infinite systems, initially held at different temperatures, are suddenly joined together and left to evolve unitarily under a homogeneous Hamiltonian. While this protocol is of obvious interest for the study of transport, until recently its analytic understanding was limited to the cases of free [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] or conformally invariant models [51][52][53][54][55][56][57][58][59][60][61][62]. A major breakthrough came in Refs.…”