9,410 research outputs found
Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph
This paper considers the leader-follower control problem for a linear
multi-agent system with directed communication topology and linear nonidentical
uncertain coupling subject to integral quadratic constraints (IQCs). A
consensus-type control protocol is proposed based on each agent's states
relative to its neighbors and leader's state relative to agents which observe
the leader. A sufficient condition is obtained by overbounding the cost
function. Based on this sufficient condition, a computational algorithm is
introduced to minimize the proposed guaranteed bound on tracking performance,
which yields a suboptimal bound on the system consensus control and tracking
performance. The effectiveness of the proposed method is demonstrated using a
simulation example.Comment: Accepted for presentation at the 2013 Australian Control conferenc
FFLO correlation and free fluids in the one-dimensional attractive Hubbard model
In this Rapid Communication we show that low energy macroscopic properties of
the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound
pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations
of the model, we first determine the low temperature phase diagram and
analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing
correlation function for the partially-polarized phase. We then show that for
such a FFLO-like state in the low density regime the effective chemical
potentials of bound pairs and unpaired fermions behave like two free fluids.
Consequently, the susceptibility, compressibility and specific heat obey simple
additivity rules, indicating the `free' particle nature of interacting fermions
on a 1D lattice. In contrast to the continuum Fermi gases, the correlation
critical exponents and thermodynamics of the attractive Hubbard model
essentially depend on two lattice interacting parameters. Finally, we study
scaling functions, the Wilson ratio and susceptibility which provide universal
macroscopic properties/dimensionless constants of interacting fermions at low
energy.Comment: In this Letter we analytically study FFLO pairing correlation and the
universal nature of the FFLO-like state. More detailed studies of this model
will be presented in arXiv:1710.08742 and arXiv:1708.0778
Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model
We study the long-distance asymptotic behavior of various correlation
functions for the one-dimensional (1D) attractive Hubbard model in a partially
polarized phase through the Bethe ansatz and conformal field theory approaches.
We particularly find the oscillating behavior of these correlation functions
with spatial power-law decay, of which the pair (spin) correlation function
oscillates with a frequency (). Here is the mismatch in the Fermi surfaces of
spin-up and spin-down particles. Consequently, the pair correlation function in
momentum space has peaks at the mismatch , which has been
observed in recent numerical work on this model. These singular peaks in
momentum space together with the spatial oscillation suggest an analog of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The
parameter representing the lattice effect becomes prominent in critical
exponents which determine the power-law decay of all correlation functions. We
point out that the backscattering of unpaired fermions and bound pairs within
their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.Comment: 26 pages, 4 figures, published version, a series of study on the 1D
attractive Hubbard model, few typos were corrected, references were added,
also see arXiv:1708.07784 and arXiv:1708.0777
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