Charge Relaxation in the Presence of Shot Noise in Coulomb Coupled Mesoscopic Systems

In the presence of shot noise the charge on a mesoscopic conductor fluctuates. We are interested in the charge fluctuations which arise if the conductor is in the proximity of a gate to which it is coupled by long range Coulomb forces only. Specifically we consider a gate coupled to the edge of a Hall bar subject to a quantizing magnetic field which contains a quantum point contact. The gate is located away from the quantum point contact. We evaluate the charge relaxation resistance for this geometry. The charge relaxation resistance determines the current fluctuations and potential fluctuations induced into the gate. If there is only one edge channel the charge relaxation resistance is determined by transmission and reflection probabilities alone, but in the presence of many channels the density of states of all edge states determines this resistance.Comment: To appear in "Quantum Physics at Mesoscopic Scale" edited by D.C. Glattli, M. Sanquer and J. Tran Thanh Van Editions "Frontieres", 199

Quantum capacitance: a microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.Comment: 7 fig

Irreversibility and Dephasing from Vacuum Fluctuations

We investigate the role of vacuum (zero-point) fluctuations in generating decoherence in a number of simple models. First we discuss a harmonic oscillator coupled to a semi-infinite elastic string and discuss the irreversible nature of such a bath. We investigate the fluctuations in energy of the oscillator and discuss the trace the oscillator leaves in the bath. Most of the work deals with two-level systems coupled to a bosonic bath (a transmission line). For two-level systems with a Hamiltonian that commutes with the total Hamiltonian (system plus coupling plus bath) the ground state is a pure state. The energy of the system is a constant of motion. For the general case, the energy of the two-level system fluctuates, and the ground state is only partially coherent. A particular realization of such a two level system consists of a mesoscopic ring with a quantum dot coupled capacitively to a transmission line. In the presence of an Aharonov-Bohm flux this system exhibits a persistent current. This current is a measure of the coherence of the ground state. As a function of the coupling strength the ground state undergoes a crossover from a state characterized by a time-averaged persistent current which is much larger than its time-averaged mean squared fluctuations to a state characterized by a persistent current with an average amplitude that is much smaller than its mean squared fluctuations.Comment: 27 pages, 6 figures: submitted for "Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations", NATO ASI, Geilo, Norway, April 17-27 (2001) edited by Arne T. Skjeltorp and Tamas Vicsek, (Kluwer, Dordrecht

Reversing the sign of current-current correlations

Current-correlations are a very sensitive probe of the fluctuations of small conductors. For non-interacting particles injected from thermal sources there is a simple connection between the sign of correlations and statistics: current-current correlations of Fermions are negative, intensity-intensity correlations of Bosons can be positive. In contrast to photons, electrons are interacting entities, and we can expect the simple connection between statistics and the sign of current-current correlations to be broken, if interactions play a crucial role. We present a number of examples in which interactions are important. At a voltage probe the potential fluctuates to maintain zero current. It is shown that there are geometries for which these fluctuations lead to positive correlations. Displacement currents at capacitively coupled contacts are also positively correlated if both contacts contribute to screening of the same excess charge fluctuation. Hybrid normal superconducting systems provide another example which permits positive correlations. The conditions for positive correlations differ strongly depending on whether the normal conductor is open and well coupled to the superconductor or is only weakly coupled via a barrier to the superconductor. In latter case, positive correlations result if the partition noise generated by Cooper pairs is overcome by pairs which are broken up and emit one electron into the contacts of interest.Comment: 30 pages, 9 figures, for "Quantum Noise", edited by Yu. V. Nazarov and Ya. M. Blanter (Kluwer

Decoherence from Vacuum Fluctuations

Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to persistent current peaks at values of the gate voltage at which two charge states of the dot have the same free energy. We couple the structure to an external circuit and investigate the effect of the zero-temperature (vacuum fluctuations) on the ground state of the ring. We find that the ground state of the ring undergoes a crossover from a state with an average persistent current much larger than the (time-dependent) mean squared fluctuations to a state with a small average persistent current and large mean squared fluctuations. We discuss the spectral density of charge fluctuations and discuss diffusion rates for angle variables characterizing the ground state in Bloch representation.Comment: 6 pages, 2 figures, submitted for "Electronic Correlations: from meso- to nano-physics", edited by G. Montambaux and T. Martin, Rencontres de Moriond, (unpublished

Wave attenuation to clock sojourn times

The subject of time in quantum mechanics is of perennial interest especially because there is no observable for the time taken by a particle to transmit (or reflect) from a particular region. Several methods have been proposed based on scattering phase shifts and using different quantum clocks, where the time taken is clocked by some external input or indirectly from the phase of the scattering amplitudes. In this work we give a general method for calculating conditional sojourn times based on wave attenuation. In this approach clock mechanism does not couple to the Hamiltonian of the system. For simplicity, specific case of a delta dimer is considered in detail. Our analysis re-affirms recent results based on correcting quantum clocks using optical potential methods, albeit in a much simpler way.Comment: 4 pages, 5 figures. Minor corrections made and journal reference adde

Time-Dependent Transport in Mesoscopic Structures

A discussion of recent work on time-dependent transport in mesoscopic structures is presented. The discussion emphasizes the use of time-dependent transport to gain information on the charge distribution and its collective dynamics. We discuss the RC-time of mesoscopic capacitors, the dynamic conductance of quantum point contacts and dynamic weak localization effects in chaotic cavities. We review work on adiabatic quantum pumping and photon-assisted transport, and conclude with a list which demonstrates the wide range of problems which are of interest

The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

The local Larmor clock is used to derive a hierarchy of local densities of states. At the bottom of this hierarchy are the partial density of states for which represent the contribution to the local density of states if both the incident and outgoing scattering channel are prescribed. On the next higher level is the injectivity which represents the contribution to the local density of states if only the incident channel is prescribed regardless of the final scattering channel. The injectivity is related by reciprocity to the emissivity of a point into a quantum channel. The sum of all partial density of states or the sum of all injectivities or the sum of all emissivities is equal to the local density of states. The use of the partial density of states is illustrated for a number of different electron transport problems in mesoscopic physics: The transmission from a tunneling tip into a mesoscopic conductor, the discussion of inelastic or phase breaking scattering with a voltage probe, and the ac-conductance of mesoscopic conductors. The transition from a capacitive response (positive time-delay) to an inductive response (negative time-delay) for a quantum point contact is used to illustrate the difficulty in associating time-scales with a linear response analysis. A brief discussion of the off-diagonal elements of a partial density of states matrix is presented. The off-diagonal elements permit to investigate carrier fluctuations away from the average carrier density. The work concludes with a discussion of the relation between the partial density of states matrix and the Wigner-Smith delay time matrix

Charge Relaxation Resistances and Charge Fluctuations in Mesoscopic Conductors

A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We discuss the charge relaxation resistance for mesoscopic capacitors, quantum point contacts, chaotic cavities, ballistic wires and for transport along edge channels in the quantized Hall regime. At equilibrium the charge relaxation resistance also determines via the fluctuation-dissipation theorem the spontaneous fluctuations of charge on the conductor. Of particular interest are the charge fluctuations in the presence of transport in a regime where the conductor exhibits shot noise. At low frequencies and voltages charge relaxation is determined by a nonequilibrium charge relaxation resistance

Shot noise induced charge and potential fluctuations of edge states in proximity of a gate

We evaluate the RC-time of edge states capacitively coupled to a gate located away from a QPC which allows for partial transmission of an edge channel. At long times or low frequencies the RC-time governs the relaxation of charge and current and governs the fluctuations of the equilibrium electrostatic potential. The RC-time in mesoscopic structures is determined by an electrochemical capacitance which depends on the density of states of the edge states and a charge relaxation resistance. In the non-equilibrium case, in the presence of transport, the shot noise leads to charge fluctuations in proximity of the gate which are again determined by the equilibrium electrochemical capacitance but with a novel resistance. The case of multiple edge states is discussed and the effect of a dephasing voltage probe on these resistances is investigated. The potential fluctuations characterized by these capacitances and resistances are of interest since they determine the dephasing rate in Coulomb coupled mesoscopic conductors.Comment: To appear in the Proceedings of the XVI Sitges Conference, Statistical and Dynamical Aspects of Mesoscopic Systems, (Lecture Notes in Physics, Springer