30 research outputs found
The rank of variants of nilpotent pseudovarieties
We investigate the rank of pseudovarieties defined by several of the variants
of nilpotency conditions for semigroups in the sense of Mal'cev. For several of
them, we provide finite bases of pseudoidentities. We also show that the
Neumann-Taylor variant does not have finite rank.Comment: 41 page
Cooling of a Nanomechanical Resonator in the Presence of a Single Diatomic Molecule
We propose a theoretical scheme for coupling a nanomechanical resonator to a
single diatomic molecule via microwave cavity mode of a driven LC resonator. We
describe the diatomic molecule by a Morse potential and find the corresponding
equations of motion of the hybrid system by using Fokker-Planck formalism.
Analytical expressions for the effective frequency and the effective damping of
the nanomechanical resonator are obtained. We analyze the ground state cooling
of the nanomechanical resonator in presence of the diatomic molecule. The
results confirm that presence of the molecule improves the cooling process of
the mechanical resonator. Finally, the effect of molecule's parameters on the
cooling mechanism is studied.Comment: 10 pages, 8 figure
A description of a class of finite semigroups that are near to being Malcev nilpotent
In this paper we continue the investigations on the algebraic structure of a
finite semigroup that is determined by its associated upper non-nilpotent
graph . The vertices of this graph are the elements of and
two vertices are adjacent if they generate a semigroup that is not nilpotent
(in the sense of Malcev). We introduce a class of semigroups in which the
Mal'cev nilpotent property lifts through ideal chains. We call this the class
of \B\ semigroups. The definition is such that the global information that a
semigroup is not nilpotent induces local information, i.e. some two-generated
subsemigroups are not nilpotent. It turns out that a finite monoid (in
particular, a finite group) is \B\ if and only if it is nilpotent. Our main
result is a description of \B\ finite semigroups in terms of their
associated graph . In particular, has a largest nilpotent
ideal, say , and is a 0-disjoint union of its connected components
(adjoined with a zero) with at least two elements
Generating quantum discord between two distant Bose-Einstein condensates with Bell-like detection
We propose a technique that enables the creation of quantum discord between
two distant nodes, each containing a cavity consist of the Bose-Einstein
condensate, by applying a non-ideal Bell-like detection on the output modes of
optical cavities. We find the covariance matrix of the system after the
non-ideal Bell-like detection, showing explicitly that one enables manipulation
of the quantum correlations, and particularly quantum discord, between remote
Bose-Einstein condensates. We also find that the non-ideal Bell-like detection
can create entanglement between distant Bose-Einstein condensates at the two
remote site