Charge transfer through nanoscale junctions connecting metallic leads with quantum dots or single molecules is often described within an open system formulation in terms of Redfield theory. Under non-equilibrium conditions, the usually invoked rotating wave approximation is not justified which may lead to unphysical steady state solutions with e.g. negative populations. In this work we explore subtleties and constraints of the approach and thus clarify its applicability in numerical calculations. General findings are illustrated for an analytically solvable case of a molecule with two electronic states.

Transport through molecular contacts with a sluggish intramolecular vibrational mode strongly coupled to excess charges is studied far from equilibrium. A Born-Oppenheimer approximation in steady state reveals voltage-dependent energy surfaces, which cause abrupt conformational changes of the molecular backbone. These are directly related to transitions between current plateaus, which are relatively robust against thermal fluctuations. In a regime accessible in experiments this allows the operation of a molecular junction as a current switch or as a molecular machine in form of a valve controlled by time-dependent bias and gate voltages.

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.

We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions in a magnetic field. Starting from the fully polarized high-field state, we calculate the dispersions of the lowest-lying n-magnon excitations and the saturation field (n=2,3,4). We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of pi except for a small parameter range. We argue that Bose condensation of the bound n magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to n=2 and n=3.

We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.

The spin sector of charge-spin separated single mode quantum wires is studied, accounting for realistic microscopic electron-electron interactions. We utilize the ladder approximation (LA) to the interaction vertex and exploit thermodynamic relations to obtain spin velocities. Down to not too small carrier densities our results compare well with existing quantum Monte Carlo (QMC) data. Analyzing second-order diagrams we identify logarithmically divergent contributions as crucial which the LA includes but which are missed, for example, by the self-consistent Hartree-Fock approximation. Contrary to other approximations the LA yields a nontrivial spin conductance. Its considerably smaller computational effort compared to numerically exact methods, such as the QMC method, enables us to study overall dependences on interaction parameters. We identify the short distance part of the interaction to govern spin sector properties.

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters K-rho and upsilon(sigma) In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density wave to localized in character as the density is lowered. Our results for K-rho are in good agreement with weak-coupling perturbative estimates K-rho(pert) at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. K(rho)(pert)similar ton(1/2) vanishes at small carrier density it, whereas we conjecture that K-rho-->1/2 when n-->0, implying that K-rho should pass through a minimum at an intermediate density. Observation of this nonmonotonic dependence could be used to measure the effective interaction range in a realistic semiconductor quantum wire geometry. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing n. Strong correlation effects make it difficult to obtain fully consistent estimates of upsilon(sigma) from Hartree-Fock calculations. We conjecture that, upsilon(sigma)/upsilon(F)proportional ton/V-0 where V-0 is the interaction strength, in the limit n-->0.