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This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

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Table Of Integrals Series And Products

비만아 부모의 돌봄 경험: q 방법론

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.

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Magnetic Confinement of Massless Dirac Fermions in Graphene

Experimental and theoretical results for transport through crossed metallic single-wall nanotubes are presented. We observe a zero-bias anomaly in one tube which is suppressed by a current flowing through the other nanotube. The phenomenon is shown to be consistent with the picture of strongly correlated electrons within the Luttinger liquid model. The most relevant coupling between the nanotubes is the electrostatic interaction generated via crossing-induced backscattering processes. Explicit solution of a simplified model is able to describe qualitatively the observed experimental data with only one adjustable parameter.

Evidence for Luttinger-liquid behavior in crossed metallic single-wall nanotubes.

For a general model of a mesoscopic multilevel quantum dot, we determine the necessary conditions for the existence of an anomalous Josephson current with spontaneously broken time-reversal symmetry. They correspond to a finite spin-orbit coupling, a suitably oriented Zeeman field, and the dot being a chiral conductor. We provide analytical expressions for the anomalous supercurrent covering a wide parameter regime.

Anomalous Josephson current through a spin-orbit coupled quantum dot.

Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer–Buttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer’s formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective “Lorentz” force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.

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Current-induced forces in mesoscopic systems: A scattering-matrix approach

We present a detailed comparison of three different methods designed to tackle nonequilibrium quantum transport, namely the functional renormalization group (fRG), the time-dependent density matrix renormalization group (tDMRG), and the iterative summation of real-time path integrals (ISPI). For the nonequilibrium single-impurity Anderson model (including a Zeeman term at the impurity site), we demonstrate that the three methods are in quantitative agreement over a wide range of parameters at the particle-hole symmetric point as well as in the mixed-valence regime. We further compare these techniques with two quantum Monte Carlo approaches and the time-dependent numerical renormalization group method.

Reinhold Egger

Papers

Magnetic Confinement of Massless Dirac Fermions in Graphene

Evidence for Luttinger-liquid behavior in crossed metallic single-wall nanotubes.

Anomalous Josephson current through a spin-orbit coupled quantum dot.

Current-induced forces in mesoscopic systems: A scattering-matrix approach

Comparative study of theoretical methods for nonequilibrium quantum transport