Nonequilibrium-current-induced corrections to the one-particle-correlation function in a wire

Electron gas in a wire connected to two terminals with potential drop is studied with the Schwinger-Keldysh formalism. Recent studies, where the current is enforced to flow with a Lagrange-multiplier term, demonstrated that the current enhances the one-particle-correlation function. We report that in our model, such enhancement is not guaranteed to occur, but conditional both on the potential drop and the positions where we observe the correlation function. That is, under a certain condition, spatially modulated pattern is formed in the wire owing to the nonequilibrium current. PACS codes(keywords): 05.70.Ln (Nonequilibrium thermodynamics, irreversible processes), 72. (Electronic transport in condensed matter), 85.30.Vw (Low-dimensional quantum devices (quantum dots, quantum wires, etc.)) Recently, Antal et al. have reported that nonequilibrium current enhances the one-particlecorrelation function contrary to our naive expectation that nonequilibrium transport would destroy any orders [1, 2, 3]. They utilized a trick with which the nonequilibrium flow is introduced in a frame of equilibrium statistical mechanics. That is, they introduced a Lagrange multiplier λ, and investigated the (equilibrium) ground state of the Hamiltonian given byH−λJ , where H denotes a model Hamiltonian of a wire and J denotes the space integral of the current operator. Namely, the current flow is regarded as an environment variable, which is to be given ad hoc. As for an explicit example of H, they took up the transverse Ising model and the XY model in one dimension, and found that the above-mentioned behavior, namely, the transport-induced correlation enhancement, occurs in these models. Cardy extended their work for a nonintegrable case (a lattice scaler field theory), and confirmed their observation [4]. This enhancement due to nonequilibrium transport had been studied extensively in the field of classical statistical mechanics [5, 6, 7, 8, 9, 10]. It should be noted, however, that the quantum version has an advantage that the (nonequilibrium) dynamics is governed by the Hamiltonian itself, whereas the classical dynamics depends upon the kinetic rules which we implement. In this letter, we investigate the spinless electron gas in a wire, which is connected to two leads with different chemical potentials. Hence, in our case, the current is driven to flow by the potential drop as in actual experimental situations. We stress that we have employed the Schwinger-Keldysh formalism [11, 12], that allows us to treat the transport phenomena driven far out of equilibrium. Thereby, we report that the enhancement due to nonequilibrium flow is not guaranteed to occur, but depends significantly both on the potential drop and the positions where we observe the correlation. As in the previous studies — note that the transverse Ising model and the XY model are equivalent to free-spinless-fermion models — we supposed that the wire electrons are free (quadratic). We believe that the many-body-correlation effect would not change our essential conclusions. Our model Hamiltonian is given by, H = ∑