35,889 research outputs found
Superdiffusive nonequilibrium motion of an impurity in a Fermi sea
We treat the nonequilibrium motion of a single impurity atom in a
low-temperature single-species Fermi sea, interacting via a contact
interaction. In the nonequilibrium regime, the impurity does a superdiffusive
geometric random walk where the typical distance traveled grows with time as
for the -dimensional system with . For nonzero
temperature , this crosses over to diffusive motion at long times with
diffusivity . These results apply also to a nonzero
concentration of impurity atoms as long as they remain dilute and
nondegenerate.Comment: 5 pages, 1 figure, to appear in Phys. Rev.
Ballistic spreading of entanglement in a diffusive nonintegrable system
We study the time evolution of the entanglement entropy of a one-dimensional
nonintegrable spin chain, starting from random nonentangled initial pure
states. We use exact diagonalization of a nonintegrable quantum Ising chain
with transverse and longitudinal fields to obtain the exact quantum dynamics.
We show that the entanglement entropy increases linearly with time before
finite-size saturation begins, demonstrating a ballistic spreading of the
entanglement, while the energy transport in the same system is diffusive. Thus
we explicitly demonstrate that the spreading of entanglement is much faster
than the energy diffusion in this nonintegrable system.Comment: 7 pages, 7 figures. Published version. Supplementary material adde
Thermalization of entanglement
We explore the dynamics of the entanglement entropy near equilibrium in
highly-entangled pure states of two quantum-chaotic spin chains undergoing
unitary time evolution. We examine the relaxation to equilibrium from initial
states with either less or more entanglement entropy than the equilibrium
value, as well as the dynamics of the spontaneous fluctuations of the
entanglement that occur in equilibrium. For the spin chain with a
time-independent Hamiltonian and thus an extensive conserved energy, we find
slow relaxation of the entanglement entropy near equilibration. Such slow
relaxation is absent in a Floquet spin chain with a Hamiltonian that is
periodic in time and thus has no local conservation law. Therefore, we argue
that slow diffusive energy transport is responsible for the slow relaxation of
the entanglement entropy in the Hamiltonian system.Comment: 6 pages, 6 figures; as in journa
Entanglement spreading in a many-body localized system
Motivated by the findings of logarithmic spreading of entanglement in a
many-body localized system, we more closely examine the spreading of
entanglement in the fully many-body localized phase, where all many-body
eigenstates are localized. Performing full diagonalizations of an XXZ spin
model with random longitudinal fields, we identify two factors contributing to
the spreading rate: the localization length (), which depends on the
disorder strength, and the final value of entanglement per spin (),
which primarily depends on the initial state. We find that the entanglement
entropy grows with time as , providing support
for the phenomenology of many-body localized systems recently proposed by Huse
and Oganesyan [arXiv:1305.4915v1].Comment: 7 pages, 5 figure
The Relationship of the value of the Dollar, and the Prices of Gold and Oil: A Tale of Asset Risk
This paper investigates the relationship between the value of the dollar and the prices of two commodities, gold and oil. Granger causality is used on monthly data from January of 1970 through July of 2008. The empirical results show that the hypothesis that there is no causal relation between the value of the dollar and the prices of gold and oil is not supported by the evidence. There are causal relations between each of the prices, and there is a negative relation between the value of the dollar and the price of each of the commodities, as predicted by standard economic theory. Also consistent with the predictions of classical economic theory is that there is a positive statistical association between the prices of gold and oil. The implication is that gold and oil represent safe havens from fluctuations in the value of the dollar.Dollar, Gold, Oil, Exchange Rates, Commodity Prices, Granger Causality
Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a
strong sense: in the limit of an infinite system, {\it every} eigenstate is
thermal. We examine expectation values of few-body operators in highly-excited
many-body eigenstates and search for `outliers', the eigenstates that deviate
the most from ETH. We use exact diagonalization of two one-dimensional
nonintegrable models: a quantum Ising chain with transverse and longitudinal
fields, and hard-core bosons at half-filling with nearest- and
next-nearest-neighbor hopping and interaction. We show that even the most
extreme outliers appear to obey ETH as the system size increases, and thus
provide numerical evidences that support ETH in this strong sense. Finally,
periodically driving the Ising Hamiltonian, we show that the eigenstates of the
corresponding Floquet operator obey ETH even more closely. We attribute this
better thermalization to removing the constraint of conservation of the total
energy.Comment: 9 pages, 6 figures. Updated references and clarified some argument
Heat and spin transport in a cold atomic Fermi gas
Motivated by recent experiments measuring the spin transport in ultracold
unitary atomic Fermi gases (Sommer et al., 2011; Sommer et al., 2011), we
explore the theory of spin and heat transport in a three-dimensional
spin-polarized atomic Fermi gas. We develop estimates of spin and thermal
diffusivities and discuss magnetocaloric effects, namely the the spin Seebeck
and spin Peltier effects. We estimate these transport coefficients using a
Boltzmann kinetic equation in the classical regime and present experimentally
accessible signatures of the spin Seebeck effect. We study an exactly solvable
model that illustrates the role of momentum-dependent scattering in the
magnetocaloric effects.Comment: 18 pages, 6 figures, slight notation changes from previous versio
Non-Gaussianity in Axion N-flation Models
We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter fNL may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation
Identifiability and parameter estimation of the single particle lithium-ion battery model
This paper investigates the identifiability and estimation of the parameters
of the single particle model (SPM) for lithium-ion battery simulation.
Identifiability is addressed both in principle and in practice. The approach
begins by grouping parameters and partially non-dimensionalising the SPM to
determine the maximum expected degrees of freedom in the problem. We discover
that, excluding open circuit voltage, there are only six independent
parameters. We then examine the structural identifiability by considering
whether the transfer function of the linearised SPM is unique. It is found that
the model is unique provided that the electrode open circuit voltage functions
have a known non-zero gradient, the parameters are ordered, and the electrode
kinetics are lumped into a single charge transfer resistance parameter. We then
demonstrate the practical estimation of model parameters from measured
frequency-domain experimental electrochemical impedance spectroscopy (EIS)
data, and show additionally that the parametrised model provides good
predictive capabilities in the time domain, exhibiting a maximum voltage error
of 20 mV between model and experiment over a 10 minute dynamic discharge.Comment: 16 pages, 9 figures, pre-print submitted to the IEEE Transactions on
Control Systems Technolog
Dark matter haloes in modified gravity and dark energy: interaction rate, small-, and large-scale alignment
We study the properties of dark matter haloes in a wide range of modified
gravity models, namely, , DGP, and interacting dark energy models. We
study the effects of modified gravity and dark energy on the internal
properties of haloes, such as the spin and the structural parameters. We find
that gravity enhance the median value of the Bullock spin parameter, but
could not detect such effects for DGP and coupled dark energy. also
yields a lower median sphericity and oblateness, while coupled dark energy has
the opposite effect. However, these effects are very small. We then study the
interaction rate of haloes in different gravity, and find that only strongly
coupled dark energy models enhance the interaction rate. We then quantify the
enhancement of the alignment of the spins of interacting halo pairs by modified
gravity. Finally, we study the alignment of the major axes of haloes with the
large-scale structures. The alignment of the spins of interacting pairs of
haloes in DGP and coupled dark energy models show no discrepancy with GR, while
shows a weaker alignment. Strongly coupled dark energy shows a stronger
alignment of the halo shape with the large-scale structures.Comment: 11 pages, 6 figures, MNRAS Accepte
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