350 research outputs found
A Survey of Quantum Lyapunov Control Methods
The condition of a quantum Lyapunov-based control which can be well used in a
closed quantum system is that the method can make the system convergent but not
just stable. In the convergence study of the quantum Lyapunov control, two
situations are classified: non-degenerate cases and degenerate cases. In this
paper, for these two situations, respectively, the target state is divided into
four categories: eigenstate, the mixed state which commutes with the internal
Hamiltonian, the superposition state, and the mixed state which does not
commute with the internal Hamiltonian state. For these four categories, the
quantum Lyapunov control methods for the closed quantum systems are summarized
and analyzed. Especially, the convergence of the control system to the
different target states is reviewed, and how to make the convergence conditions
be satisfied is summarized and analyzed.Comment: 1
Stochastic population growth in spatially heterogeneous environments: The density-dependent case
This work is devoted to studying the dynamics of a structured population that
is subject to the combined effects of environmental stochasticity, competition
for resources, spatio-temporal heterogeneity and dispersal. The population is
spread throughout patches whose population abundances are modelled as the
solutions of a system of nonlinear stochastic differential equations living on
.
We prove that , the stochastic growth rate of the total population in the
absence of competition, determines the long-term behaviour of the population.
The parameter can be expressed as the Lyapunov exponent of an associated
linearized system of stochastic differential equations. Detailed analysis shows
that if , the population abundances converge polynomially fast to a unique
invariant probability measure on , while when , the
population abundances of the patches converge almost surely to
exponentially fast. This generalizes and extends the results of Evans et al
(2014 J. Math. Biol.) and proves one of their conjectures.
Compared to recent developments, our model incorporates very general
density-dependent growth rates and competition terms. Furthermore, we prove
that persistence is robust to small, possibly density dependent, perturbations
of the growth rates, dispersal matrix and covariance matrix of the
environmental noise. Our work allows the environmental noise driving our system
to be degenerate. This is relevant from a biological point of view since, for
example, the environments of the different patches can be perfectly correlated.
As an example we fully analyze the two-patch case, , and show that the
stochastic growth rate is a decreasing function of the dispersion rate. In
particular, coupling two sink patches can never yield persistence, in contrast
to the results from the non-degenerate setting treated by Evans et al.Comment: 43 pages, 1 figure, edited according to the suggestion of the
referees, to appear in Journal of Mathematical Biolog
Research Advances in Chaos Theory
The subject of chaos has invaded practically every area of the natural sciences. Weather patterns are referred to as chaotic. There are chemical reactions and chaotic evolution of insect populations. Atomic and molecular physics have also seen the emergence of the study of chaos in these microscopic domains. This book examines the issue of chaos in nonlinear and dynamical systems, quantum mechanics, biology, and economics
Renormalization: an advanced overview
We present several approaches to renormalization in QFT: the multi-scale
analysis in perturbative renormalization, the functional methods \`a la
Wetterich equation, and the loop-vertex expansion in non-perturbative
renormalization. While each of these is quite well-established, they go beyond
standard QFT textbook material, and may be little-known to specialists of each
other approach. This review is aimed at bridging this gap.Comment: Review, 130 pages, 33 figures; v2: misprints corrected, refs. added,
minor improvements; v3: some changes to sect. 5, refs. adde
Dynamics Days Latin America and the Caribbean 2018
This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics
Hybrid quantum-classical modeling of quantum dot devices
The design of electrically driven quantum dot devices for quantum optical
applications asks for modeling approaches combining classical device physics
with quantum mechanics. We connect the well-established fields of
semi-classical semiconductor transport theory and the theory of open quantum
systems to meet this requirement. By coupling the van Roosbroeck system with a
quantum master equation in Lindblad form, we introduce a new hybrid
quantum-classical modeling approach, which provides a comprehensive description
of quantum dot devices on multiple scales: It enables the calculation of
quantum optical figures of merit and the spatially resolved simulation of the
current flow in realistic semiconductor device geometries in a unified way. We
construct the interface between both theories in such a way, that the resulting
hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics.
We show that our approach guarantees the conservation of charge, consistency
with the thermodynamic equilibrium and the second law of thermodynamics. The
feasibility of the approach is demonstrated by numerical simulations of an
electrically driven single-photon source based on a single quantum dot in the
stationary and transient operation regime
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