239 research outputs found
Maximizing nearest neighbour entanglement in finitely correlated qubit--chains
We consider translationally invariant states of an infinite one dimensional
chain of qubits or spin-1/2 particles. We maximize the entanglement shared by
nearest neighbours via a variational approach based on finitely correlated
states. We find an upper bound of nearest neighbour concurrence equal to
C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a
completely different procedure. The obtained state maximizing nearest neighbour
entanglement seems to approximate the maximally entangled mixed states (MEMS).
Further we investigate in detail several other properties of the so obtained
optimal state.Comment: 12 pages, 4 figures, 2nd version minor change
Fractal dimension of transport coefficients in a deterministic dynamical system
In many low-dimensional dynamical systems transport coefficients are very
irregular, perhaps even fractal functions of control parameters. To analyse
this phenomenon we study a dynamical system defined by a piece-wise linear map
and investigate the dependence of transport coefficients on the slope of the
map. We present analytical arguments, supported by numerical calculations,
showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of
the graphs of these functions is 1 with a logarithmic correction, and find that
the exponent controlling this correction is bounded from above by 1 or
2, depending on some detailed properties of the system. Using numerical
techniques we show local self-similarity of the graphs. The local
self-similarity scaling transformations turn out to depend (irregularly) on the
values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2,
corrected typos, etc.
Phasic, nonsynaptic GABA-A receptor-mediated inhibition entrains thalamocortical oscillations.
GABA-A receptors (GABA-ARs) are typically expressed at synaptic or nonsynaptic sites mediating phasic and tonic inhibition, respectively. These two forms of inhibition conjointly control various network oscillations. To disentangle their roles in thalamocortical rhythms, we focally deleted synaptic, γ2 subunit-containing GABA-ARs in the thalamus using viral intervention in mice. After successful removal of γ2 subunit clusters, spontaneous and evoked GABAergic synaptic currents disappeared in thalamocortical cells when the presynaptic, reticular thalamic (nRT) neurons fired in tonic mode. However, when nRT cells fired in burst mode, slow phasic GABA-AR-mediated events persisted, indicating a dynamic, burst-specific recruitment of nonsynaptic GABA-ARs. In vivo, removal of synaptic GABA-ARs reduced the firing of individual thalamocortical cells but did not abolish slow oscillations or sleep spindles. We conclude that nonsynaptic GABA-ARs are recruited in a phasic manner specifically during burst firing of nRT cells and provide sufficient GABA-AR activation to control major thalamocortical oscillations
Karhunen-Lo\`eve expansion for a generalization of Wiener bridge
We derive a Karhunen-Lo\`eve expansion of the Gauss process , , where is a
standard Wiener process and is a twice continuously
differentiable function with and . This
process is an important limit process in the theory of goodness-of-fit tests.
We formulate two special cases with the function
, , and , ,
respectively. The latter one corresponds to the Wiener bridge over from
to .Comment: 25 pages, 1 figure. The appendix is extende
Elucidating the Ultrafast Dynamics of Photoinduced Charge Separation in Metalloporphyrin-Fullerene Dyads Across the Electromagnetic Spectrum
Metalloporphyrins are prominent building blocks in the synthetic toolbox of advanced photodriven molecular devices. When the central ion is paramagnetic, the relaxation pathways within the manifold of excited states are highly intricate so that unravelling the intramolecular energy and electron transfer processes is usually a very complex task. This fact is critically hampering the development of applications based on the enhanced coupling offered by the electronic exchange interaction. In this work, the dynamics of charge separation in a copper porphyrin-fullerene are studied with several complementary spectroscopic tools across the electromagnetic spectrum (from near-infrared to X-ray wavelengths), each of them providing specific diagnostics. Correlating the various rates clearly demonstrates that the lifetime of the photoinduced charge-separated state exceeds by about 10-fold that of the isolated photoexcited CuII porphyrin. As revealed by the spectral modifications in the XANES region, this stabilization is accompanied by a transient change in covalency around the CuII center, which is induced by an enhanced interaction with the C60 moiety. This experimental finding is further confirmed by state-of-the art calculations using DFT and TD-DFT including dispersion effects that explain the electrostatic and structural origins of this interaction, as the CuIIP cation becomes ruffled and approaches closer to the fullerene in the charge-separated state. From a methodological point of view, these results exemplify the potential of multielectron excitation features in transient X-ray spectra as future diagnostics of subfemtosecond electronic dynamics. From a practical point of view, this work is paving the way for elucidating out-of-equilibrium electron transfer events coupled to magnetic interaction processes on their intrinsic time-scales
Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole-magnetic dipole interaction
We study the gravitational radiation reaction in compact binary systems
composed of neutron stars with spin and huge magnetic dipole moments
(magnetars). The magnetic dipole moments undergo a precessional motion about
the respective spins. At sufficiently high values of the magnetic dipole
moments, their interaction generates second post-Newtonian order contributions
both to the equations of motion and to the gravitational radiation escaping the
system. We parametrize the radial motion and average over a radial period in
order to find the secular contributions to the energy and magnitude of the
orbital angular momentum losses, in the generic case of \textit{eccentric}
orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole
interactions, here too we deduce the secular evolution of the relative
orientations of the orbital angular momentum and spins. These equations,
supplemented by the evolution equations for the angles characterizing the
orientation of the dipole moments form a first order differential system, which
is closed. The circular orbit limit of the energy loss agrees with Ioka and
Taniguchi's earlier result
Spin effects in gravitational radiation backreaction III. Compact binaries with two spinning components
The secular evolution of a spinning, massive binary system in eccentric orbit
is analyzed, expanding and generalizing our previous treatments of the
Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin
effects up to the 3/2 post-Newtonian order are considered, both in the
equations of motion and in the radiative losses. The description of the orbit
in terms of the true anomaly parametrization provides a simple averaging
technique, based on the residue theorem, over eccentric orbits. The evolution
equations of the angle variables characterizing the relative orientation of the
spin and orbital angular momenta reveal a speed-up effect due to the
eccentricity. The dissipative evolutions of the relevant dynamical and angular
variables is presented in the form of a closed system of differential
equations.Comment: 10 pages, 1 figur
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