545 research outputs found

### 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

### 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

### 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

### 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

### 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
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### 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

### 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

### 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

### 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

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