2,589 research outputs found
Exponential decay in a spin bath
We show that the coherence of an electron spin interacting with a bath of
nuclear spins can exhibit a well-defined purely exponential decay for special
(`narrowed') bath initial conditions in the presence of a strong applied
magnetic field. This is in contrast to the typical case, where spin-bath
dynamics have been investigated in the non-Markovian limit, giving
super-exponential or power-law decay of correlation functions. We calculate the
relevant decoherence time T_2 explicitly for free-induction decay and find a
simple expression with dependence on bath polarization, magnetic field, the
shape of the electron wave function, dimensionality, total nuclear spin I, and
isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices
with extensive technical details, version to appear in Phys. Rev. B
Singlet-triplet decoherence due to nuclear spins in a double quantum dot
We have evaluated hyperfine-induced electron spin dynamics for two electrons
confined to a double quantum dot. Our quantum solution accounts for decay of a
singlet-triplet correlator even in the presence of a fully static nuclear spin
system, with no ensemble averaging over initial conditions. In contrast to an
earlier semiclassical calculation, which neglects the exchange interaction, we
find that the singlet-triplet correlator shows a long-time saturation value
that differs from 1/2, even in the presence of a strong magnetic field.
Furthermore, we find that the form of the long-time decay undergoes a
transition from a rapid Gaussian to a slow power law () when
the exchange interaction becomes nonzero and the singlet-triplet correlator
acquires a phase shift given by a universal (parameter independent) value of
at long times. The oscillation frequency and time-dependent phase
shift of the singlet-triplet correlator can be used to perform a precision
measurement of the exchange interaction and Overhauser field fluctuations in an
experimentally accessible system. We also address the effect of orbital
dephasing on singlet-triplet decoherence, and find that there is an optimal
operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure
Free-induction decay and envelope modulations in a narrowed nuclear spin bath
We evaluate free-induction decay for the transverse components of a localized
electron spin coupled to a bath of nuclear spins via the Fermi contact
hyperfine interaction. Our perturbative treatment is valid for special
(narrowed) bath initial conditions and when the Zeeman energy of the electron
exceeds the total hyperfine coupling constant : . Using one unified
and systematic method, we recover previous results reported at short and long
times using different techniques. We find a new and unexpected modulation of
the free-induction-decay envelope, which is present even for a purely isotropic
hyperfine interaction without spin echoes and for a single nuclear species. We
give sub-leading corrections to the decoherence rate, and show that, in
general, the decoherence rate has a non-monotonic dependence on electron Zeeman
splitting, leading to a pronounced maximum. These results illustrate the
limitations of methods that make use of leading-order effective Hamiltonians
and re-exponentiation of short-time expansions for a strongly-interacting
system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure
Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
We have performed a systematic calculation for the non-Markovian dynamics of
a localized electron spin interacting with an environment of nuclear spins via
the Fermi contact hyperfine interaction. This work applies to an electron in
the s -type orbital ground state of a quantum dot or bound to a donor impurity,
and is valid for arbitrary polarization p of the nuclear spin system, and
arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and
I=1/2, the Born approximation of our perturbative theory recovers the exact
electron spin dynamics. We have found the form of the generalized master
equation (GME) for the longitudinal and transverse components of the electron
spin to all orders in the electron spin--nuclear spin flip-flop terms. Our
perturbative expansion is regular, unlike standard time-dependent perturbation
theory, and can be carried-out to higher orders. We show this explicitly with a
fourth-order calculation of the longitudinal spin dynamics. In zero magnetic
field, the fraction of the electron spin that decays is bounded by the
smallness parameter \delta=1/p^{2}N, where N is the number of nuclear spins
within the extent of the electron wave function. However, the form of the decay
can only be determined in a high magnetic field, much larger than the maximum
Overhauser field. In general the electron spin shows rich dynamics, described
by a sum of contributions with non-exponential decay, exponential decay, and
undamped oscillations. There is an abrupt crossover in the electron spin
asymptotics at a critical dimensionality and shape of the electron envelope
wave function. We propose a scheme that could be used to measure the
non-Markovian dynamics using a standard spin-echo technique, even when the
fraction that undergoes non-Markovian dynamics is small.Comment: 22 pages, 8 figure
Vacancy assisted arsenic diffusion and time dependent clustering effects in silicon
We present results of kinetic lattice Monte Carlo (KLMC) simulations of
substitutional arsenic diffusion in silicon mediated by lattice vacancies.
Large systems are considered, with 1000 dopant atoms and long range \textit{ab
initio} interactions, to the 18th nearest lattice neighbor, and the diffusivity
of each defect species over time is calculated. The concentration of vacancies
is greater than equilibrium concentrations in order to simulate conditions
shortly after ion implantation. A previously unreported time dependence in the
applicability of the pair diffusion model, even at low temperatures, is
demonstrated. Additionally, long range interactions are shown to be of critical
importance in KLMC simulations; when shorter interaction ranges are considered
only clusters composed entirely of vacancies form. An increase in arsenic
diffusivity for arsenic concentrations up to is
observed, along with a decrease in arsenic diffusivity for higher arsenic
concentrations, due to the formation of arsenic dominated clusters. Finally,
the effect of vacancy concentration on diffusivity and clustering is studied,
and increasing vacancy concentration is found to lead to a greater number of
clusters, more defects per cluster, and a greater vacancy fraction within the
clusters.Comment: 22 pages, 16 figure
Lepton-mediated electroweak baryogenesis
We investigate the impact of the tau and bottom Yukawa couplings on the
transport dynamics for electroweak baryogenesis in supersymmetric extensions of
the Standard Model. Although it has generally been assumed in the literature
that all Yukawa interactions except those involving the top quark are
negligible, we find that the tau and bottom Yukawa interaction rates are too
fast to be neglected. We identify an illustrative "lepton-mediated electroweak
baryogenesis" scenario in which the baryon asymmetry is induced mainly through
the presence of a left-handed leptonic charge. We derive analytic formulae for
the computation of the baryon asymmetry that, in light of these effects, are
qualitatively different from those in the established literature. In this
scenario, for fixed CP-violating phases, the baryon asymmetry has opposite sign
compared to that calculated using established formulae.Comment: 26 pages, 5 figure
Rigorous Born Approximation and beyond for the Spin-Boson Model
Within the lowest-order Born approximation, we present an exact calculation
of the time dynamics of the spin-boson model in the ohmic regime. We observe
non-Markovian effects at zero temperature that scale with the system-bath
coupling strength and cause qualitative changes in the evolution of coherence
at intermediate times of order of the oscillation period. These changes could
significantly affect the performance of these systems as qubits. In the biased
case, we find a prompt loss of coherence at these intermediate times, whose
decay rate is set by , where is the coupling strength
to the environment. We also explore the calculation of the next order Born
approximation: we show that, at the expense of very large computational
complexity, interesting physical quantities can be rigorously computed at
fourth order using computer algebra, presented completely in an accompanying
Mathematica file. We compute the corrections to the long time
behavior of the system density matrix; the result is identical to the reduced
density matrix of the equilibrium state to the same order in . All
these calculations indicate precision experimental tests that could confirm or
refute the validity of the spin-boson model in a variety of systems.Comment: Greatly extended version of short paper cond-mat/0304118.
Accompanying Mathematica notebook fop5.nb, available in Source, is an
essential part of this work; it gives full details of the fourth-order Born
calculation summarized in the text. fop5.nb is prepared in arXiv style
(available from Wolfram Research
Hall effect in quasi one-dimensional organic conductors
We study the Hall effect in a system of weakly coupled Luttinger Liquid
chains, using a Memory function approach to compute the Hall constant in the
presence of umklapp scattering along the chains. In this approximation, the
Hall constant decomposes into two terms: a high-frequency term and a Memory
function term. For the case of zero umklapp scattering, where the Memory
function vanishes, the Hall constant is simply the band value, in agreement
with former results in a similar model with no dissipation along the chains.
With umklapp scattering along the chains, we find a power-law temperature
dependance of the Hall constant. We discuss the applications to quasi 1D
organic conductors at high temperatures.Comment: Proceedings of the ISCOM conference "Sixth International Symposium on
Crystalline Organic Metals, Superconductors, and Ferromagnets", Key West,
Florida, USA (Sept. 2005), to be plublished in the Journal of Low Temperature
Physic
Vergleichendes Wörterbuch der indogermanischen Sprachen (Vol. 1)
First published 1870, PDF-file is the 4th editio
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