192 research outputs found
Metastable nonconfining states in SU(3) lattice gauge theory with sextet fermions
We study the SU(3) lattice gauge theory, with two flavors of sextet
Wilson-clover fermions, near its finite-temperature phase transition. We find
metastable states that have Wilson line expectation values whose complex phases
are near 2pi/3 or pi. The true equilibrium phase at these couplings and
temperatures has its Wilson line oriented only towards the positive real axis,
in agreement with perturbation theory.Comment: 14 pages, 9 figures; added a referenc
Universal Dimer in a Collisionally Opaque Medium: Experimental Observables and Efimov Resonances
A universal dimer is subject to secondary collisions with atoms when formed
in a cloud of ultracold atoms via three-body recombination. We show that in a
collisionally opaque medium, the value of the scattering length that results in
the maximum number of secondary collisions may not correspond to the Efimov
resonance at the atom-dimer threshold and thus can not be automatically
associated with it. This result explains a number of controversies in recent
experimental results on universal three-body states and supports the emerging
evidence for the significant finite range corrections to the first excited
Efimov energy level.Comment: 5 pages, 2 figure
On the density of honest subrecursive classes
The relation of honest subrecursive classes to the computational complexity of the functions they contain is briefly reviewed. It is shown that the honest subrecursive classes are dense under the partial ordering of set inclusion. In fact, any countable partial ordering can be embedded in the gap between an effective increasing sequence of honest subrecursive classes and an honest subrecursive class which is properly above the sequence (or in the gap between an eflective decreasing sequence and a class which is properly below the sequence). Information is obtained about the possible existence of least upper bounds (greater lower bounds) of increasing (decreasing) sequences of honest subrecursive classes. Finally it is shown that for any two honest subrecursive classes, one properly containing the other, there exists a pair of incomparable honest subrecursive classes such that the greatest lower bound of the pair is the smaller of the first two classes and the least upper bound of the pair is the larger of the first two classes
Minimal pairs of polynomial degrees with subexponential complexity
AbstractThe goal of extending work on relative polynomial time computability from computations relative to sets of natural numbers to computations relative to arbitrary functions of natural numbers is discussed. The principal techniques used to prove that the honest subrecursive classes are a lattice are then used to construct a minimal pair of polynomial degrees with subexponential complexity; that is two sets computable by Turing machines in subexponential time but not in polynomial time are constructed such that any set computable from both in polynomial time can be computed directly in polynomial time
Three-body recombination at vanishing scattering lengths in an ultracold Bose gas
We report on measurements of three-body recombination rates in an ultracold
gas of Li atoms in the extremely nonuniversal regime where the two-body
scattering length vanishes. We show that the rate is well defined and can be
described by two-body parameters only: the scattering length and the
effective range . We find the rate to be energy independent, and, by
connecting our results with previously reported measurements in the universal
limit, we cover the behavior of the three-body recombination in the whole range
from weak to strong two-body interactions. We identify a nontrivial magnetic
field value in the nonuniversal regime where the rate should be strongly
reduced.Comment: Version with enhanced supplemental material
Honest elementary degrees and degrees of relative provability without the cupping property
An element a of a lattice cups to an element b>ab>a if there is a c<bc<b such that a∪c=ba∪c=b. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary degrees that do not have the cupping property, which answers a question of Kristiansen, Schlage-Puchta, and Weiermann. In fact, we show that if b is a sufficiently large honest elementary degree, then b has the anti-cupping property, which means that there is an a with 0<Ea<Eb0<Ea<Eb that does not cup to b. For comparison, we also modify a result of Cai to show, in several versions of the degrees of relative provability that are closely related to the honest elementary degrees, that in fact all non-zero degrees have the anti-cupping property, not just sufficiently large degrees
Spectrum of orientifold QCD in the strong coupling and hopping expansion approximation
We use the strong coupling and hopping parameter expansions to calculate the
pion and rho meson masses for lattice Yang-Mills gauge theories with fermions
in irreducible two-index representations, namely the adjoint, symmetric and
antisymmetric. The results are found to be consistent with orientifold planar
equivalence, and leading order 1/N corrections are calculated in the lattice
phase. An estimate of the critical bare mass, for which the pion is massless,
is obtained as a function of the bare coupling. A comparison to data from the
two-flavour SU(2) theory with adjoint fermions gives evidence for a bulk phase
transition at beta~2, separating a pure lattice phase from a phase smoothly
connected to the continuum.Comment: 16 page
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