4,030 research outputs found
Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
We study a model describing identical bosonic atoms trapped in a
double-well potential together with a single impurity atom, comparing and
contrasting it throughout with the Dicke model. As the boson-impurity coupling
strength is varied, there is a symmetry-breaking pitchfork bifurcation which is
analogous to the quantum phase transition occurring in the Dicke model. Through
stability analysis around the bifurcation point, we show that the critical
value of the coupling strength has the same dependence on the parameters as the
critical coupling value in the Dicke model. We also show that, like the Dicke
model, the mean-field dynamics go from being regular to chaotic above the
bifurcation and macroscopic excitations of the bosons are observed. Overall,
the boson-impurity system behaves like a poor man's version of the Dicke model.Comment: 17 pages, 16 figure
Dicke-type phase transition in a multimode optomechanical system
We consider the "membrane in the middle" optomechanical model consisting of a
laser pumped cavity which is divided in two by a flexible membrane that is
partially transmissive to light and subject to radiation pressure. Steady state
solutions at the mean-field level reveal that there is a critical strength of
the light-membrane coupling above which there is a symmetry breaking
bifurcation where the membrane spontaneously acquires a displacement either to
the left or the right. This bifurcation bears many of the signatures of a
second order phase transition and we compare and contrast it with that found in
the Dicke model. In particular, by studying limiting cases and deriving
dynamical critical exponents using the fidelity susceptibility method, we argue
that the two models share very similar critical behaviour. For example, the
obtained critical exponents indicate that they fall within the same
universality class. Away from the critical regime we identify, however, some
discrepancies between the two models. Our results are discussed in terms of
experimentally relevant parameters and we evaluate the prospects for realizing
Dicke-type physics in these systems.Comment: 14 pages, 6 figure
General pure multipartite entangled states and the Segre variety
In this paper, we construct a measure of entanglement by generalizing the
quadric polynomial of the Segre variety for general multipartite states. We
give explicit expressions for general pure three-partite and four-partite
states. Moreover, we will discuss and compare this measure of entanglement with
the generalized concurrence.Comment: 5 page
Noncommutative geometrical structures of entangled quantum states
We study the noncommutative geometrical structures of quantum entangled
states. We show that the space of a pure entangled state is a noncommutative
space. In particular we show that by rewritten the conifold or the Segre
variety we can get a -deformed relation in noncommutative geometry. We
generalized our construction into a multi-qubit state. We also in detail
discuss the noncommutative geometrical structure of a three-qubit state.Comment: 7 page
Topological quantum gate entangler for a multi-qubit state
We establish a relation between topological and quantum entanglement for a
multi-qubit state by considering the unitary representations of the Artin braid
group. We construct topological operators that can entangle multi-qubit state.
In particular we construct operators that create quantum entanglement for
multi-qubit states based on the Segre ideal of complex multi-projective space.
We also in detail discuss and construct these operators for two-qubit and
three-qubit states.Comment: 6 page
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Developing transferable management skills through Action Learning
There has been increasing criticism of the relevance of the Master of Business Administration (MBA) in developing skills and competencies. Action learning, devised to address problem-solving in the workplace, offers a potential response to such criticism. This paper offers an insight into one university’s attempt to integrate action learning into the curriculum. Sixty-five part-time students were questioned at two points in their final year about their action learning experience and the enhancement of relevant skills and competencies. Results showed a mixed picture. Strong confirmation of the importance of selected skills and competencies contrasted with weaker agreement about the extent to which these were developed by action learning. There was, nonetheless, a firm belief in the positive impact on the learning process. The paper concludes that action learning is not a panacea but has an important role in a repertoire of educational approaches to develop relevant skills and competencies
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