Charge Current Density from the Scattering Matrix

A method to derive the charge current density and its quantum mechanical correlation from the scattering matrix is discussed for quantum scattering systems described by a time-dependent Hamiltonian operator. The current density and charge density are expressed with the help of functional derivatives with respect to the vector potential and the electric potential. A condition imposed by the requirement that these local quantities are gauge invariant is considered. Our formulas lead to a direct relation between the local density of states and the total current density at a given energy. To illustrate the results we consider, as an example, a chiral ladder model.Comment: 4 pages, 1 figur

Local non-equilibrium distribution of charge carriers in a phase-coherent conductor

We use the scattering matrix approach to derive generalized Bardeen-like formulae for the conductances between the contacts of a phase-coherent multiprobe conductor and a tunneling tip which probes its surface. These conductances are proportional to local partial densities of states, called injectivities and emissivities. The current and the current fluctuations measured at the tip are related to an effective local non-equilibrium distribution function. This distribution function contains the quantum-mechanical phase-coherence of the charge carriers in the conductor and is given as products of injectivities and the Fermi distribution functions in the electron reservoirs. The results are illustrated for measurements on ballistic conductors with barriers and for diffusive conductors.Comment: 4 pages, 2 figures, submitted to "Comptes Rendus de l'Academie des Sciences

Survival of Φ0/2\Phi_{0}/2 periodicity in presence of incoherence in asymmetric Aharonov-Bohm rings

Magneto conductance oscillations periodic in flux with periodicity $\Phi_{0}$ and $\Phi_{0}/2$ are seen in asymmetric Aharonov-Bohm rings as a function of density of electrons or Fermi wave vector. Dephasing of these oscillations is incorporated using a simple approach of wave attenuation. In this work we study how the excitation of the $\Phi_{0}/2$ oscillations and the accompanying phase change of $\pi$ are affected by dephasing. Our results show that the $\Phi_{0}/2$ oscillations survive incoherence, i.e., dephasing, albeit with reduced visibility while incoherence is also unable to obliterate the phase change of $\pi$.Comment: 4 pages, 3 figure

Symmetry and environment effects on rectification mechanisms in quantum pumps

We consider a paradigmatic model of quantum pumps and discuss its rectification properties in the framework of a symmetry analysis proposed for ratchet systems. We discuss the role of the environment in breaking time-reversal symmetry and the possibility of a finite directed current in the Hamiltonian limit of annular systems.Comment: To appear as Rapid Communication in PR

Gauge invariance and wave packet simulations in the presence of dipole fields

A method for performing wave packet simulations in dipole fields is presented. Starting from a Hamiltonian with non commuting terms, a gauge transformation leads to a new Hamiltonian which allows to calculate explicitly the evolution operator. In this new gauge, the dipole field is fully included in the {\it vector} potential. The method of Goldberg, Schwartz and Schey based on the Caley form of the evolution operator is then generalized, and the resulting scheme is applied to describe a switching device based on Rabi oscillations. The probability to tunnel in the free region exhibits a plateaux structure as the wave function is emitted by ``bursts'' after each Rabi oscillation has been completed.Comment: 4 pages (Revtex 3.0), figures upon request, LA-UR-94-303

Quantum Nondemolition Measurement of a Kicked Qubit

We propose a quantum nondemolition measurement using a kicked two-state system (qubit). By tuning the waiting time between kicks to be the qubit oscillation period, the kicking apparatus performs a nondemolition measurement. While dephasing is unavoidable, the nondemolition measurement can (1) slow relaxation of diagonal density matrix elements, (2) avoid detector back-action, and (3) allow for a large signal-to-noise ratio. Deviations from the ideal behavior are studied by allowing for detuning of the waiting time, as well as finite-time, noisy pulses. The scheme is illustrated with a double-dot qubit measured by a gate-pulsed quantum point contact.Comment: 7 pages, 1 figur

Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor

We present an analysis of the effect of dephasing on the single channel charge relaxation resistance of a mesoscopic capacitor in the linear low frequency regime. The capacitor consists of a cavity which is via a quantum point contact connected to an electron reservoir and Coulomb coupled to a gate. The capacitor is in a perpendicular high magnetic field such that only one (spin polarized) edge state is (partially) transmitted through the contact. In the coherent limit the charge relaxation resistance for a single channel contact is independent of the transmission probability of the contact and given by half a resistance quantum. The loss of coherence in the conductor is modeled by attaching to it a fictitious probe, which draws no net current. In the incoherent limit one could expect a charge relaxation resistance that is inversely proportional to the transmission probability of the quantum point contact. However, such a two terminal result requires that scattering is between two electron reservoirs which provide full inelastic relaxation. We find that dephasing of a single edge state in the cavity is not sufficient to generate an interface resistance. As a consequence the charge relaxation resistance is given by the sum of one constant interface resistance and the (original) Landauer resistance. The same result is obtained in the high temperature regime due to energy averaging over many occupied states in the cavity. Only for a large number of open dephasing channels, describing spatially homogenous dephasing in the cavity, do we recover the two terminal resistance, which is inversely proportional to the transmission probability of the QPC. We compare different dephasing models and discuss the relation of our results to a recent experiment.Comment: 10 pages, 8 figure

Persistent current magnification in a double quantum-ring system

The electronic transport in a system of two quantum rings side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We derived analytical expressions for the conductance, density of states and the persistent current when the rings are threaded by magnetic fluxes. We found a clear manifestation of the presence of bound states in each one of those physical quantities when either the flux difference or the sum of the fluxes are zero or integer multiples of a quantum of flux. These bound states play an important role in the magnification of the persistent current in the rings. We also found that the persistent current keeps a large amplitude even for strong ring-wire coupling.Comment: 15 pages, 10 figures. Submitted to PR

Magnetic-field symmetries of mesoscopic nonlinear conductance

We examine contributions to the dc-current of mesoscopic samples which are non-linear in applied voltage. In the presence of a magnetic field, the current can be decomposed into components which are odd (antisymmetric) and even (symmetric) under flux reversal. For a two-terminal chaotic cavity, these components turn out to be very sensitive to the strength of the Coulomb interaction and the asymmetry of the contact conductances. For both two- and multi-terminal quantum dots we discuss correlations of current non-linearity in voltage measured at different magnetic fields and temperatures.Comment: 9 pages, 4 figure

dc-Response of a Dissipative Driven Mesoscopic Ring

The behavior of the dc-component of the current along a quantum loop of tight-binding electrons threaded by a magnetic flux that varies linearly in time Phi_M(t)= Phi t is investigated. We analize the electron transport in different kinds of one-dimensional structures bended into a ring geometry: a clean one-dimensional metal, a chain with a two-band structure and a disordered chain. Inelastic scattering events are introduced through the coupling to a particle reservoir. We use a theoretical treatment based in Baym-Kadanoff-Keldysh non-equilibrium Green functions, which allows us to solve the problem exactly.Comment: 10 pages, 9 figures. To appear in PR