4,698 research outputs found
Approximate and pseudo-amenability of various classes of Banach algebras
We continue the investigation of notions of approximate amenability that were
introduced in work of the second and third authors. It is shown that every
boundedly approximately contractible Banach algebra has a bounded approximate
identity.
Among our other results, it is shown that the Fourier algebra of the free
group on two generators is not approximately amenable. Further examples are
obtained of -semigroup algebras which are approximately amenable but
not amenable; using these, we show that bounded approximate amenability need
not imply sequential approximate amenability. Results are also given for Segal
subalgebras of , where is a locally compact group, and the algebras
of -pseudofunctions on a discrete group (of which
the reduced -algebra is a special case).Comment: 35 pages, revision of Jan '08 preprint. Abstract and MSC added;
bibliograpy updated; slight tweaks to Section 4; and correction of a few
typos. The final version is to appear in J. Funct. Ana
Dissipative production of a maximally entangled steady state
Entangled states are a key resource in fundamental quantum physics, quantum
cryp-tography, and quantum computation [1].To date, controlled unitary
interactions applied to a quantum system, so-called "quantum gates", have been
the most widely used method to deterministically create entanglement [2]. These
processes require high-fidelity state preparation as well as minimizing the
decoherence that inevitably arises from coupling between the system and the
environment and imperfect control of the system parameters. Here, on the
contrary, we combine unitary processes with engineered dissipation to
deterministically produce and stabilize an approximate Bell state of two
trapped-ion qubits independent of their initial state. While previous works
along this line involved the application of sequences of multiple
time-dependent gates [3] or generated entanglement of atomic ensembles
dissipatively but relied on a measurement record for steady-state entanglement
[4], we implement the process in a continuous time-independent fashion,
analogous to optical pumping of atomic states. By continuously driving the
system towards steady-state, the entanglement is stabilized even in the
presence of experimental noise and decoherence. Our demonstration of an
entangled steady state of two qubits represents a step towards dissipative
state engineering, dissipative quantum computation, and dissipative phase
transitions [5-7]. Following this approach, engineered coupling to the
environment may be applied to a broad range of experimental systems to achieve
desired quantum dynamics or steady states. Indeed, concurrently with this work,
an entangled steady state of two superconducting qubits was demonstrated using
dissipation [8].Comment: 25 pages, 5 figure
On the equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei
The present paper establishes a link between pairing correlations in rotating
nuclei and collective vortical modes in the intrinsic frame. We show that the
latter can be embodied by a simple S-type coupling a la Chandrasekhar between
rotational and intrinsic vortical collective modes. This results from a
comparison between the solutions of microscopic calculations within the HFB and
the HF Routhian formalisms. The HF Routhian solutions are constrained to have
the same Kelvin circulation expectation value as the HFB ones. It is shown in
several mass regions, pairing regimes, and for various spin values that this
procedure yields moments of inertia, angular velocities, and current
distributions which are very similar within both formalisms. We finally present
perspectives for further studies.Comment: 8 pages, 4 figures, submitted to Phys. Rev.
Vortex avalanches and self organized criticality in superconducting niobium
In 1993 Tang proposed [1] that vortex avalanches should produce a self
organized critical state in superconductors, but conclusive evidence for this
has heretofore been lacking. In the present paper, we report extensive
micro-Hall probe data from the vortex dynamics in superconducting niobium,
where a broad distribution of avalanche sizes scaling as a power-law for more
than two decades is found. The measurements are combined with magneto-optical
imaging, and show that over a widely varying magnetic landscape the scaling
behaviour does not change, hence establishing that the dynamics of
superconducting vortices is a SOC phenomenon.Comment: 3 pages + 4 figures, a reference added, citation typos fixe
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