1,783 research outputs found
Weak-coupling phase diagrams of bond-aligned and diagonal doped Hubbard ladders
We study, using a perturbative renormalization group technique, the phase
diagrams of bond-aligned and diagonal Hubbard ladders defined as sections of a
square lattice with nearest-neighbor and next-nearest-neighbor hopping. We find
that for not too large hole doping and small next-nearest-neighbor hopping the
bond-aligned systems exhibit a fully spin-gapped phase while the diagonal
systems remain gapless. Increasing the next-nearest-neighbor hopping typically
leads to a decrease of the gap in the bond-aligned ladders, and to a transition
into a gapped phase in the diagonal ladders. Embedding the ladders in an
antiferromagnetic environment can lead to a reduction in the extent of the
gapped phases. These findings suggest a relation between the orientation of
hole-rich stripes and superconductivity as observed in LSCO.Comment: Published version. The set of RG equations in the presence of
magnetization was corrected and two figures were replace
Dilations of unitary tuples
We study the space of all -tuples of unitaries using
dilation theory and matrix ranges. Given two -tuples and generating
C*-algebras and , we seek the minimal dilation
constant such that , by which we mean that is a
compression of some -isomorphic copy of . This gives rise to a metric on the set of equivalence classes of
-isomorphic tuples of unitaries. We also consider the metric and we show the inequality Let be the universal unitary tuple satisfying
, where
is a real antisymmetric matrix. We find that . From this we recover the result of
Haagerup-Rordam and Gao that there exists a map such that and Of special
interest are: the universal -tuple of noncommuting unitaries ,
the -tuple of free Haar unitaries , and the universal -tuple of
commuting unitaries . We obtain the bounds From this, we recover Passer's upper
bound for the universal unitaries . In the
case we obtain the new lower bound
improving on the previously known lower bound .Comment: 30 page
The Container Selection Problem
We introduce and study a network resource management problem that is a special case of non-metric k-median, naturally arising in cross platform scheduling and cloud computing. In the continuous d-dimensional container selection problem, we are given a set C of input points in d-dimensional Euclidean space, for some d >= 2, and a budget k. An input point p can be assigned to a "container point" c only if c dominates p in every dimension. The assignment cost is then equal to the L1-norm of the container point. The goal is to find k container points in the d-dimensional space, such that the total assignment cost for all input points is minimized. The discrete variant of the problem has one key distinction, namely, the container points must be chosen from a given set F of points.
For the continuous version, we obtain a polynomial time approximation scheme for any fixed dimension d>= 2. On the negative side, we show that the problem is NP-hard for any d>=3. We further show that the discrete version is significantly harder, as it is NP-hard to approximate without violating the budget k in any dimension d>=3. Thus, we focus on obtaining bi-approximation algorithms. For d=2, the bi-approximation guarantee is (1+epsilon,3), i.e., for any epsilon>0, our scheme outputs a solution of size 3k and cost at most (1+epsilon) times the optimum. For fixed d>2, we present a (1+epsilon,O((1/epsilon)log k)) bi-approximation algorithm
Hydrodynamic singularities and clustering in a freely cooling inelastic gas
We employ hydrodynamic equations to follow the clustering instability of a
freely cooling dilute gas of inelastically colliding spheres into a
well-developed nonlinear regime. We simplify the problem by dealing with a
one-dimensional coarse-grained flow. We observe that at a late stage of the
instability the shear stress becomes negligibly small, and the gas flows solely
by inertia. As a result the flow formally develops a finite time singularity,
as the velocity gradient and the gas density diverge at some location. We argue
that flow by inertia represents a generic intermediate asymptotic of unstable
free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure
Close-packed floating clusters: granular hydrodynamics beyond the freezing point?
Monodisperse granular flows often develop regions with hexagonal close
packing of particles. We investigate this effect in a system of inelastic hard
spheres driven from below by a "thermal" plate. Molecular dynamics simulations
show, in a wide range of parameters, a close-packed cluster supported by a
low-density region. Surprisingly, the steady-state density profile, including
the close-packed cluster part, is well described by a variant of Navier-Stokes
granular hydrodynamics (NSGH). We suggest a simple explanation for the success
of NSGH beyond the freezing point.Comment: 4 pages, 5 figures. To appear in Phys. Rev. Let
Theory of the vortex matter transformations in high Tc superconductor YBCO
Flux line lattice in type II superconductors undergoes a transition into a
"disordered" phase like vortex liquid or vortex glass, due to thermal
fluctuations and random quenched disorder. We quantitatively describe the
competition between the thermal fluctuations and the disorder using the
Ginzburg -- Landau approach. The following T-H phase diagram of YBCO emerges.
There are just two distinct thermodynamical phases, the homogeneous and the
crystalline one, separated by a single first order transitions line. The line
however makes a wiggle near the experimentally claimed critical point at 12T.
The "critical point" is reinterpreted as a (noncritical) Kauzmann point in
which the latent heat vanishes and the line is parallel to the T axis. The
magnetization, the entropy and the specific heat discontinuities at melting
compare well with experiments.Comment: 4 pages 3 figure
Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns
We analyze a recent experiment of Sharon \textit{et al.} (2003) on the
coarsening, due to surface tension, of fractal viscous fingering patterns
(FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw
model, a natural model for that experiment, belongs to the same universality
class as model B of phase ordering. Two series of numerical simulations with
model B are performed, with the FVFPs grown in the experiment, and with
Diffusion Limited Aggregates, as the initial conditions. We observed
Lifshitz-Slyozov scaling at intermediate distances and very slow
convergence to this scaling at small distances. Dynamic scale invariance breaks
down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.
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