Starting from the usual formulation of nonequilibrium quantum statistical mechanics, the expectation value of an operator A in a steady state nonequilibrium quantum system is shown to have the form {A) ==: Tr{e ~f iiH~Y) A}/Tv{e~p (H~Y) }, where H is the Hamiltonian, p is the inverse of the temperature, and Y is an operator which depends on how the system is driven out of equilibrium. Because {A) is not expressed as a sum of correlation functions integrated over real time, one can now consider performing nonperturbative calculations in interacting nonequilibrium quantum problems.PACS numbers: 72.10. Bg, 05.60,+w Nonequilibrium problems have come under increasing study in condensed matter physics. On the one hand, there exists a growing number of classical systems which undergo a phase transition as one drives them out of equilibrium. On the other hand, with technological advances allowing one to make measurements on smaller samples, it becomes easier to drive systems out of equilibrium. This is particularly true in making resistance measurements on very small (mesoscopic) devices at low temperatures [1], which is an inherently quantum problem. Furthermore, while linear response measurements do probe some equilibrium correlation functions, much more information can be obtained from the nonlinear response, which probes the full nonequilibrium problem. For example, nonlinear current-voltage characteristics in metal-insulator-superconductor tunnel junctions have long been used to determine the superconducting gap and the phonon density of states. In mesoscopic systems similar kinds of information about the density of states can be obtained from nonlinear transport [2][3][4][5].In spite of the experimental importance of studying nonlinear response there are far fewer theoretical techniques available for studying nonequilibrium quantum systems than for studying equilibrium ones. Again using the example of mesoscopic systems, the noninteracting quantum problem may be solved exactly using the scattering states for electrons coming from reservoirs which are at different chemical potentials. This is the essence of the Landauer formula [6] and its subsequent generalizations [7,8]. For an interacting system the nonlinear current-voltage characteristic can be computed by doing perturbation theory in the part of the Hamiltonian which drives the system out of equilibrium, e.g., an electric field or the tunneling between two leads at different chemical potentials. This perturbation theory, which we will call nonequilibrium quantum statistical mechanics, involves summing a set of real time correlation functions for the linear, quadratic, cubic, etc., response to this interaction [9,10].While there are many problems for which a perturbation theory is perfectly satisfactory, there is a large class of problems of current interest for which a nonperturbative approach would be quite useful and perhaps even essential. In the case of mesoscopic systems it is now possible to tunnel through a one-dimensional wire [11], a small quantum...

No abstract

We present an exact solution to the nonequilibrium Kondo problem, based on a special point in the parameter space of the model where both the Hamiltonian and the operator describing the nonequilibrium distribution can be diagonalized simultaneously. Through this solution we are able to compute the differential conductance, spin current, charge-current noise, and magnetization, for arbitrary voltage bias. The differential conductance shows the standard zero-bias anomaly and its splitting under an applied magnetic field. A detailed analysis of the scaling properties at low temperature and voltage is presented. The spin current is independent of the sign of the voltage. Its direction depends solely on the sign of the magnetic field and the asymmetry in the transverse coupling to the left and right leads. The charge-current noise can exceed 2eI c for a large magnetic field, where I c is the charge current. This is not seen in noninteracting quantum problems, but occurs here because of the tunneling of pairs of electrons. The finite-frequency noise spectrum has singularities at ប⍀ϭ Ϯ2 eV, which cannot be explained in terms of noninteracting electrons. These singularities are traced to a different type of pair process involving the simultaneous creation or annihilation of two scattering states. The impurity susceptibility has three characteristic peaks as a function of magnetic field, two of which are due to interlead processes and one is due to intralead processes. Although the solvable point is only one point in the parameter space of the nonequilibrium Kondo problem, we expect it to correctly describe the strong-coupling regime of the model for arbitrary antiferromagnetic coupling constants and to be qualitatively correct as one leaves the strong-coupling regime. ͓S0163-1829͑98͒02442-4͔

No abstract