3,571 research outputs found
Entanglement in quantum catastrophes
We classify entanglement singularities for various two-mode bosonic systems
in terms of catastrophe theory. Employing an abstract phase-space
representation, we obtain exact results in limiting cases for the entropy in
cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical
results to extract the scaling of the entropy with the non-linearity parameter,
and discuss the role of mixing entropies in more complex systems.Comment: 7 pages, 3 figure
Truncation method for Green's functions in time-dependent fields
We investigate the influence of a time dependent, homogeneous electric field
on scattering properties of non-interacting electrons in an arbitrary static
potential. We develop a method to calculate the (Keldysh) Green's function in
two complementary approaches. Starting from a plane wave basis, a formally
exact solution is given in terms of the inverse of a matrix containing
infinitely many 'photoblocks' which can be evaluated approximately by
truncation. In the exact eigenstate basis of the scattering potential, we
obtain a version of the Floquet state theory in the Green's functions language.
The formalism is checked for cases such as a simple model of a double barrier
in a strong electric field. Furthermore, an exact relation between the
inelastic scattering rate due to the microwave and the AC conductivity of the
system is derived which in particular holds near or at a metal-insulator
transition in disordered systems.Comment: to appear in Phys. Rev. B., 21 pages, 3 figures (ps-files
Non-equilibrium correlations and entanglement in a semiconductor hybrid circuit-QED system
We present a theoretical study of a hybrid circuit-QED system composed of two
semiconducting charge-qubits confined in a microwave resonator. The qubits are
defined in terms of the charge states of two spatially separated double quantum
dots (DQDs) which are coupled to the same photon mode in the microwave
resonator. We analyze a transport setup where each DQD is attached to
electronic reservoirs and biased out-of-equilibrium by a large voltage, and
study how electron transport across each DQD is modified by the coupling to the
common resonator. In particular, we show that the inelastic current through
each DQD reflects an indirect qubit-qubit interaction mediated by off-resonant
photons in the microwave resonator. As a result of this interaction, both
charge qubits stay entangled in the steady (dissipative) state. Finite shot
noise cross-correlations between currents across distant DQDs are another
manifestation of this nontrivial steady-state entanglement.Comment: Final versio
Entanglement and the Phase Transition in Single Mode Superradiance
We consider the entanglement properties of the quantum phase transition in
the single-mode superradiance model, involving the interaction of a boson mode
and an ensemble of atoms. For infinite system size, the atom-field entanglement
of formation diverges logarithmically with the correlation length exponent.
Using a continuous variable representation, we compare this to the divergence
of the entropy in conformal field theories, and derive an exact expression for
the scaled concurrence and the cusp-like non-analyticity of the momentum
squeezing.Comment: 4 pages, 2 figue
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Noise enhancement due to quantum coherence in coupled quantum dots
We show that the intriguing observation of noise enhancement in the charge
transport through two vertically coupled quantum dots can be explained by the
interplay of quantum coherence and strong Coulomb blockade. We demonstrate that
this novel mechanism for super-Poissonian charge transfer is very sensitive to
decoherence caused by electron-phonon scattering as inferred from the measured
temperature dependence.Comment: 4 pages, 3 figures, corrected version (Figs.2 and 3
Finite-Size Scaling Exponents in the Dicke Model
We consider the finite-size corrections in the Dicke model and determine the
scaling exponents at the critical point for several quantities such as the
ground state energy or the gap. Therefore, we use the Holstein-Primakoff
representation of the angular momentum and introduce a nonlinear transformation
to diagonalize the Hamiltonian in the normal phase. As already observed in
several systems, these corrections turn out to be singular at the transition
point and thus lead to nontrivial exponents. We show that for the atomic
observables, these exponents are the same as in the Lipkin-Meshkov-Glick model,
in agreement with numerical results. We also investigate the behavior of the
order parameter related to the radiation mode and show that it is driven by the
same scaling variable as the atomic one.Comment: 4 pages, published versio
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