1,871 research outputs found
Some remarks on the strong limit-point condition of second-order linear differential expressions
On open quantum systems, effective Hamiltonians and device characterization
High fidelity models, which support accurate device characterization and
correctly account for environmental effects, are crucial to the engineering of
scalable quantum technologies. As it ensures positivity of the density matrix,
one preferred model for open systems describes the dynamics with a master
equation in Lindblad form. The Linblad operators are rarely derived from first
principles, resulting in dynamical models which miss those additional terms
that must generally be added to bring the master equation into Lindblad form,
together with concomitant other terms that must be assimilated into an
effective Hamiltonian. In first principles derivations such additional terms
are often cancelled (countered), frequently in an ad hoc manner. In the case of
a Superconducting Quantum Interference Device (SQUID) coupled to an Ohmic bath,
the resulting master equation implies the environment has a significant impact
on the system's energy. We discuss the prospect of keeping or cancelling this
impact; and note that, for the SQUID, measuring the magnetic susceptibility
under control of the capacitive coupling strength and the externally applied
flux, results in experimentally measurable differences between models. If this
is not done correctly, device characterization will be prone to systemic
errors.Comment: 5 pages, 3 figure
On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole
For any real limit- th-order selfadjoint linear differential
expression on , Titchmarsh- Weyl matrices
can be defined. Two matrices of particu lar interest are the
matrices and assoc iated respectively with
Dirichlet and Neumann boundary conditions at . These satisfy
. It is known that when these matrices
have poles (which can only lie on the real axis) the existence of valid HELP
inequalities depends on their behaviour in the neighbourhood of these poles. We
prove a conjecture of Bennewitz and use it, together with a new algorithm for
computing the Laurent expansion of a Titchmarsh-Weyl matrix in the
neighbourhood of a pole, to investigate the existence of HELP inequalities for
a number of differential equations which have so far proved awkward to analys
Fast algorithm for detecting community structure in networks
It has been found that many networks display community structure -- groups of
vertices within which connections are dense but between which they are sparser
-- and highly sensitive computer algorithms have in recent years been developed
for detecting such structure. These algorithms however are computationally
demanding, which limits their application to small networks. Here we describe a
new algorithm which gives excellent results when tested on both
computer-generated and real-world networks and is much faster, typically
thousands of times faster than previous algorithms. We give several example
applications, including one to a collaboration network of more than 50000
physicists.Comment: 5 pages, 4 figure
Persistent entanglement in two coupled SQUID rings in the quantum to classical transition - A quantum jumps approach
We explore the quantum-classical crossover of two coupled, identical,
superconducting quantum interference device (SQUID) rings. The motivation for
this work is based on a series of recent papers. In ~[1] we showed that the
entanglement characteristics of chaotic and periodic (entrained) solutions of
the Duffing oscillator differed significantly and that in the classical limit
entanglement was preserved only in the chaotic-like solutions. However, Duffing
oscillators are a highly idealised toy system. Motivated by a wish to explore
more experimentally realisable systems we extended our work in [2,3] to an
analysis of SQUID rings. In [3] we showed that the two systems share a common
feature. That is, when the SQUID ring's trajectories appear to follow (semi)
classical orbits entanglement persists. Our analysis in[3] was restricted to
the quantum state diffusion unravelling of the master equation - representing
unit efficiency heterodyne detection (or ambi-quadrature homodyne detection).
Here we show that very similar behaviour occurs using the quantum jumps
unravelling of the master equation. Quantum jumps represents a discontinuous
photon counting measurement process. Hence, the results presented here imply
that such persistent entanglement is independent of measurement process and
that our results may well be quite general in nature.Comment: 6 pages, 3 figures. Published as part of a special issue for the 11th
International Conference on Squeezed States and Uncertainty Relations/4th
Feynman festival in Olomouc 2009 (This paper extends the results presented in
arXiv:0909.4488
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