955 research outputs found
Quantum Hall Physics - hierarchies and CFT techniques
The fractional quantum Hall effect, being one of the most studied phenomena
in condensed matter physics during the past thirty years, has generated many
groundbreaking new ideas and concepts. Very early on it was realized that the
zoo of emerging states of matter would need to be understood in a systematic
manner. The first attempts to do this, by Haldane and Halperin, set an agenda
for further work which has continued to this day. Since that time the idea of
hierarchies of quasiparticles condensing to form new states has been a pillar
of our understanding of fractional quantum Hall physics. In the thirty years
that have passed since then, a number of new directions of thought have
advanced our understanding of fractional quantum Hall states, and have extended
it in new and unexpected ways. Among these directions is the extensive use of
topological quantum field theories and conformal field theories, the
application of the ideas of composite bosons and fermions, and the study of
nonabelian quantum Hall liquids. This article aims to present a comprehensive
overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure
Emergent complex quantum networks in continuous-variables non-Gaussian states
Large multipartite quantum systems tend to rapidly reach extraordinary levels
of complexity as their number of constituents and entanglement links grow. Here
we use complex network theory to study a class of continuous variables quantum
states that present both multipartite entanglement and non-Gaussian statistics.
In particular, the states are built from an initial imprinted cluster state
created via Gaussian entangling operations according to a complex network
structure. To go beyond states that can be easily simulated via classical
computers we engender non-Gaussian statistics via multiple photon subtraction
operations. We then use typical networks measures, the degree and clustering,
to characterize the emergent complex network of photon-number correlations
after photon subtractions. We show that, in contrast to regular clusters, in
the case of imprinted complex network structures the emergent correlations are
strongly affected by photon subtraction. On the one hand, we unveil that photon
subtraction universally increases the average photon-number correlations,
regardless of the imprinted network structure. On the other hand, we show that
the shape of the distributions in the emergent networks after subtraction is
greatly influenced by the structure of the imprinted network, as witnessed by
their higher-moments. Thus for the field of network theory, we introduce a new
class of networks to study. At the same time for the field of continuous
variable quantum states, this work presents a new set of practical tools to
benchmark systems of increasing complexity.Comment: 25 pages (incl. appendix), 17 figure
Order out of Randomness : Self-Organization Processes in Astrophysics
Self-organization is a property of dissipative nonlinear processes that are
governed by an internal driver and a positive feedback mechanism, which creates
regular geometric and/or temporal patterns and decreases the entropy, in
contrast to random processes. Here we investigate for the first time a
comprehensive number of 16 self-organization processes that operate in
planetary physics, solar physics, stellar physics, galactic physics, and
cosmology. Self-organizing systems create spontaneous {\sl order out of chaos},
during the evolution from an initially disordered system to an ordered
stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical
resonances, or gyromagnetic resonances. The internal driver can be gravity,
rotation, thermal pressure, or acceleration of nonthermal particles, while the
positive feedback mechanism is often an instability, such as the
magneto-rotational instability, the Rayleigh-B\'enard convection instability,
turbulence, vortex attraction, magnetic reconnection, plasma condensation, or
loss-cone instability. Physical models of astrophysical self-organization
processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra
equation systems.Comment: 61 pages, 38 Figure
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