189 research outputs found
Low-temperature asymptotics of integrable systems in an external field
An asymptotic low-temperature expansion is performed for an integrable
bosonic lattice model and for the critical spin-1/2 Heisenberg chain in a
magnetic field. The results apply to the integrable Bose gas as well. We also
comment on a high-temperature expansion of the bosonic lattice model.Comment: 17 pages, 2 figure
Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic -chain at finite temperatures
We evaluate numerically certain multiple integrals representing nearest and
next-nearest neighbor correlation functions of the spin-1/2 Heisenberg
infinite chain at finite temperatures.Comment: 22 pages, 6 figure
Exact dynamics in the inhomogeneous central-spin model
We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by
inhomogeneous Heisenberg couplings including a central magnetic field. This
central-spin model describes decoherence in quantum bit systems. An exact
formula for the dynamics of the central spin is presented, based on the Bethe
ansatz. This formula is evaluated explicitly for initial conditions such that
the bath spins are completely polarized at the beginning. For this case we
find, after an initial decay, a persistent oscillatory behaviour of the central
spin. For a large number of bath spins , the oscillation frequency is
proportional to , whereas the amplitude behaves like , to leading
order. No asymptotic decay due to the non-uniform couplings is observed, in
contrast to some recent studies.Comment: 7 pages, 3 figure
Dynamics and decoherence in the central spin model using exact methods
The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a
bath of nuclear spins via hyperfine interactions in a quantum dot is studied.
We show how exact results from the integrable solution can be used to
understand the dynamic behavior of the qubit. It is possible to predict the
main frequency contributions and their broadening for relatively general
initial states analytically, leading to an estimate of the corresponding decay
times. Furthermore, for a small bath polarization, a new low-frequency time
scale is observed.Comment: 4 pages, 2 figures. Published version. See also
http://www.physik.uni-kl.de/eggert/papers/index.htm
Spin- and entanglement-dynamics in the central spin model with homogeneous couplings
We calculate exactly the time-dependent reduced density matrix for the
central spin in the central-spin model with homogeneous Heisenberg couplings.
Therefrom, the dynamics and the entanglement entropy of the central spin are
obtained. A rich variety of behaviors is found, depending on the initial state
of the bath spins. For an initially unpolarized unentangled bath, the
polarization of the central spin decays to zero in the thermodynamic limit,
while its entanglement entropy becomes maximal. On the other hand, if the
unpolarized environment is initially in an eigenstate of the total bath spin,
the central spin and the entanglement entropy exhibit persistent monochromatic
large-amplitude oscillations. This raises the question to what extent
entanglement of the bath spins prevents decoherence of the central spin.Comment: 8 pages, 2 figures, typos corrected, published versio
Dynamics and decoherence in the central spin model using exact methods
The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a
bath of nuclear spins via hyperfine interactions in a quantum dot is studied.
We show how exact results from the integrable solution can be used to
understand the dynamic behavior of the qubit. It is possible to predict the
main frequency contributions and their broadening for relatively general
initial states analytically, leading to an estimate of the corresponding decay
times. Furthermore, for a small bath polarization, a new low-frequency time
scale is observed.Comment: 4 pages, 2 figures. Published version. See also
http://www.physik.uni-kl.de/eggert/papers/index.htm
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