968 research outputs found

### Orbital selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

We study the asymmetric Hubbard model at half-filling as a generic model to
describe the physics of two species of repulsively interacting fermionic cold
atoms in optical lattices. We use Dynamical Mean Field Theory to obtain the
paramagnetic phase diagram of the model as function of temperature, interaction
strength and hopping asymmetry. A Mott transition with a region of two
coexistent solutions is found for all nonzero values of the hopping asymmetry.
At low temperatures the metallic phase is a heavy Fermi-liquid, qualitatively
analogous to the Fermi liquid state of the symmetric Hubbard model. Above a
coherence temperature, an orbital-selective crossover takes place, wherein one
fermionic species effectively localizes, and the resulting bad metallic state
resembles the non-Fermi liquid state of the Falicov-Kimball model. We compute
observables relevant to cold atom systems such as the double occupation, the
specific heat and entropy and characterize their behavior in the different
phases

### Weak coupling study of decoherence of a qubit in disordered magnetic environments

We study the decoherence of a qubit weakly coupled to frustrated spin baths.
We focus on spin-baths described by the classical Ising spin glass and the
quantum random transverse Ising model which are known to have complex
thermodynamic phase diagrams as a function of an external magnetic field and
temperature. Using a combination of numerical and analytical methods, we show
that for baths initally in thermal equilibrium, the resulting decoherence is
highly sensitive to the nature of the coupling to the environment and is
qualitatively different in different parts of the phase diagram. We find an
unexpected strong non-Markovian decay of the coherence when the random
transverse Ising model bath is prepared in an initial state characterized by a
finite temperature paramagnet. This is contrary to the usual case of
exponential decay (Markovian) expected for spin baths in finite temperature
paramagnetic phases, thereby illustrating the importance of the underlying
non-trivial dynamics of interacting quantum spinbaths.Comment: 12 pages, 18 figure

### Phase diagram of the asymmetric Hubbard model and an entropic chromatographic method for cooling cold fermions in optical lattices

We study the phase diagram of the asymmetric Hubbard model (AHM), which is
characterized by different values of the hopping for the two spin projections
of a fermion or equivalently, two different orbitals. This model is expected to
provide a good description of a mass-imbalanced cold fermionic mixture in a 3D
optical lattice. We use the dynamical mean field theory to study various
physical properties of this system. In particular, we show how
orbital-selective physics, observed in multi-orbital strongly correlated
electron systems, can be realized in such a simple model. We find that the
density distribution is a good probe of this orbital selective crossover from a
Fermi liquid to a non-Fermi liquid state.
Below an ordering temperature $T_o$, which is a function of both the
interaction and hopping asymmetry, the system exhibits staggered long range
orbital order. Apart from the special case of the symmetric limit, i.e.,
Hubbard model, where there is no hopping asymmetry, this orbital order is
accompanied by a true charge density wave order for all values of the hopping
asymmetry. We calculate the order parameters and various physical quantities
including the thermodynamics in both the ordered and disordered phases. We find
that the formation of the charge density wave is signaled by an abrupt increase
in the sublattice double occupancies. Finally, we propose a new method,
entropic chromatography, for cooling fermionic atoms in optical lattices, by
exploiting the properties of the AHM. To establish this cooling strategy on a
firmer basis, we also discuss the variations in temperature induced by the
adiabatic tuning of interactions and hopping parameters.Comment: 16 pages, 19 fig

### Methane Flow through Organic-Rich Nanopores : The Key Role of Atomic-Scale Roughness

We perform a detailed study of methane flow through nanoporous kerogen. Using molecular dynamics and modeling the kerogen pore with an amorphous carbon nanotube (a-CNT), we show that the reported flow enhancement over Hagen−Poisseuile flow is mainly due to the smoothness, on an atomic scale, of the CNTs. It acts in two ways: first, it helps the mobility of the adsorbed layer; second, and even more important for the flow enhancement, it prevents the dependency on the inverse of the channel length (L) from developing. While the former can incrementally contribute to the flow, the latter effect can explain the orders of magnitude found in comparison to macroscopic results.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

### Polynomial evaluation over finite fields: new algorithms and complexity bounds

An efficient evaluation method is described for polynomials in finite fields.
Its complexity is shown to be lower than that of standard techniques when the
degree of the polynomial is large enough. Applications to the syndrome
computation in the decoding of Reed-Solomon codes are highlighted.Comment: accepted for publication in Applicable Algebra in Engineering,
Communication and Computing. The final publication will be available at
springerlink.com. DOI: 10.1007/s00200-011-0160-

### Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete
Fourier transforms (DFT) of a continuous function $g(t)$ given by its values
$g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes
of elements of finite adjoint order $N$ in the fundamental region $F$ of
compact semisimple Lie groups. The present implementation of the method is for
the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for
$SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case
turns out to result in a transform known as discrete cosine transform (DCT),
which is often considered to be simply a specific type of the standard DFT.
Here we show that the DCT is very different from the standard DFT when the
properties of the continuous extensions of these two discrete transforms from
the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are
considered. (A) Unlike the continuous extension of the DFT, the continuous
extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$
between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT
converges to the derivative of $g(t)$. And (C), for CEDCT the principle of
locality is valid. Finally, we use the continuous extension of 2-dimensional
DCT to illustrate its potential for interpolation, as well as for the data
compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's
Repor

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