851 research outputs found
Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions
a b s t r a c t This paper deals with the stability analysis of a class of uncertain switched systems on nonuniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuous-time subsystem and an uncertain discrete-time subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on non-uniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leader-follower consensus problem under intermittent information transmissions
Uniform global stability of switched nonlinear systems in the Koopman operator framework
In this paper, we provide a novel solution to an open problem on the global
uniform stability of switched nonlinear systems. Our results are based on the
Koopman operator approach and, to our knowledge, this is the first theoretical
contribution to an open problem within that framework. By focusing on the
adjoint of the Koopman generator in the Hardy space on the polydisk (or on the
real hypercube), we define equivalent linear (but infinite-dimensional)
switched systems and we construct a common Lyapunov functional for those
systems, under a solvability condition of the Lie algebra generated by the
linearized vector fields. A common Lyapunov function for the original switched
nonlinear systems is derived from the Lyapunov functional by exploiting the
reproducing kernel property of the Hardy space. The Lyapunov function is shown
to converge in a bounded region of the state space, which proves global uniform
stability of specific switched nonlinear systems on bounded invariant sets.Comment: 29 pages, 3 figure
Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
The properties of the isotropic incompressible fractional quantum
Hall (FQH) state are described by a paired state of composite fermions in zero
(effective) magnetic field, with a uniform pairing order parameter,
which is a non-Abelian topological phase with chiral Majorana and charge modes
at the boundary. Recent experiments suggest the existence of a proximate
nematic phase at . This finding motivates us to consider an
inhomogeneous paired state - a pair-density-wave (PDW) - whose
melting could be the origin of the observed liquid-crystalline phases. This
state can viewed as an array of domain and anti-domain walls of the
order parameter. We show that the nodes of the PDW order parameter, the
location of the domain walls (and anti-domain walls) where the order parameter
changes sign, support a pair of symmetry-protected counter-propagating Majorana
modes. The coupling behavior of the domain wall Majorana modes crucially
depends on the interplay of the Fermi energy and the PDW pairing energy
. The analysis of this interplay yields a rich set of
topological states. The pair-density-wave order state in paired FQH system
provides a fertile setting to study Abelian and non-Abelian FQH phases - as
well as transitions thereof - tuned by the strength of the paired liquid
crystalline order.Comment: 27 pages, 11 figures; Published versio
Real Algebraic Geometry With A View Toward Systems Control and Free Positivity
New interactions between real algebraic geometry, convex optimization and free non-commutative geometry have recently emerged, and have been the subject of numerous international meetings. The aim of the workshop was to bring together experts, as well as young researchers, to investigate current key questions at the interface of these fields, and to explore emerging interdisciplinary applications
Controlling and observing nonseparability of phonons created in time-dependent 1D atomic Bose condensates
We study the spectrum and entanglement of phonons produced by temporal
changes in homogeneous one-dimensional atomic condensates. To characterize the
experimentally accessible changes, we first consider the dynamics of the
condensate when varying the radial trapping frequency, separately studying two
regimes: an adiabatic one and an oscillatory one. Working in momentum space, we
then show that in situ measurements of the density-density correlation function
can be used to assess the nonseparability of the phonon state after such
changes. We also study time-of-flight (TOF) measurements, paying particular
attention to the role played by the adiabaticity of opening the trap on the
nonseparability of the final state of atoms. In both cases, we emphasize that
commuting measurements can suffice to assess nonseparability. Some recent
observations are analyzed, and we make proposals for future experiments.Comment: 26 pages, 17 figure
Random-matrix theory of Majorana fermions and topological superconductors
I. Introduction (What is new in RMT, Superconducting quasiparticles,
Experimental platforms)
II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana
zero-modes, Phase transition beyond mean-field)
III. Fundamental symmetries (Particle-hole symmetry, Majorana representation,
Time-reversal and chiral symmetry)
IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy
level repulsion)
V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering,
Circular ensembles, Topological quantum numbers)
VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes,
Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise
of Majorana edge modes)
VII. Thermal conduction (Topological phase transitions, Super-universality,
Heat transport by Majorana edge modes, Thermopower and time-delay matrix,
Andreev billiard with chiral symmetry)
VIII. Josephson junctions (Fermion parity switches, 4{\pi}-periodic Josephson
effect, Discrete vortices)
IX. ConclusionComment: V1: 18 pages, 16 figures; pre-submission version, for feedback; V2:
33 pages, 31 figures; greatly expanded in response to feedback, thank you!;
V3: minor corrections, version to be published in Reviews of Modern Physic
Periodic-orbit theory of universal level correlations in quantum chaos
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate
universal behaviour of the two-point correlator of the density of levels for
quantum systems whose classical limit is fully chaotic. We go beyond previous
work in establishing the full correlator such that its Fourier transform, the
spectral form factor, is determined for all times, below and above the
Heisenberg time. We cover dynamics with and without time reversal invariance
(from the orthogonal and unitary symmetry classes). A key step in our reasoning
is to sum the periodic-orbit expansion in terms of a matrix integral, like the
one known from the sigma model of random-matrix theory.Comment: 44 pages, 11 figures, changed title; final version published in New
J. Phys. + additional appendices B-F not included in the journal versio
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