4,576 research outputs found
Fourier-Domain Electromagnetic Wave Theory for Layered Metamaterials of Finite Extent
The Floquet-Bloch theorem allows waves in infinite, lossless periodic media
to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is
challenged under the realistic constraints of loss and finite extent. In this
work, we mathematically reveal the existence of Floquet-Bloch modes in the
electromagnetic fields sustained by lossy, finite periodic layered media using
Maxwell's equations alone without invoking the Floquet-Bloch theorem. Starting
with a transfer-matrix representation of the electromagnetic field in a generic
layered medium, we apply Fourier transformation and a series of mathematical
manipulations to isolate a term explicitly dependent on Floquet-Bloch modes.
Fourier-domain representation of the electromagnetic field can be reduced into
a product of the Floquet-Bloch term and two other matrix factors: one governed
by reflections from the medium boundaries and another dependent on layer
composition. Electromagnetic fields in any finite, lossy, layered structure can
now be interpreted in the Fourier-domain by separable factors dependent on
distinct physical features of the structure. The developed theory enables new
methods for analyzing and communicating the electromagnetic properties of
layered metamaterials.Comment: 10 pages, 3 figure
A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter
Many systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as linear time-invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a linear periodically time- varying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground
Periodic orbits from Δ-modulation of stable linear systems
The �-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c �Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the �-modulated orbit
Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies
The statistical mechanics of periodically driven ("Floquet") systems in
contact with a heat bath exhibits some radical differences from the traditional
statistical mechanics of undriven systems. In Floquet systems all quasienergies
can be placed in a finite frequency interval, and the number of near
degeneracies in this interval grows without limit as the dimension N of the
Hilbert space increases. This leads to pathologies, including drastic changes
in the Floquet states, as N increases. In earlier work these difficulties were
put aside by fixing N, while taking the coupling to the bath to be smaller than
any quasienergy difference. This led to a simple explicit theory for the
reduced density matrix, but with some major differences from the usual time
independent statistical mechanics. We show that, for weak but finite coupling
between system and heat bath, the accuracy of a calculation within the
truncated Hilbert space spanned by the N lowest energy eigenstates of the
undriven system is limited, as N increases indefinitely, only by the usual
neglect of bath memory effects within the Born and Markov approximations. As we
seek higher accuracy by increasing N, we inevitably encounter quasienergy
differences smaller than the system-bath coupling. We therefore derive the
steady state reduced density matrix without restriction on the size of
quasienergy splittings. In general, it is no longer diagonal in the Floquet
states. We analyze, in particular, the behavior near a weakly avoided crossing,
where quasienergy near degeneracies routinely appear. The explicit form of our
results for the denisty matrix gives a consistent prescription for the
statistical mechanics for many periodically driven systems with N infinite, in
spite of the Floquet state pathologies.Comment: 31 pages, 3 figure
Spectroscopic probes of isolated nonequilibrium quantum matter: Quantum quenches, Floquet states, and distribution functions
We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor
tunneling, and ARPES as probes of isolated out-of-equilibrium quantum systems,
and examine the crucial role played by the nonequilibrium distribution
function. As an example, we focus on the induced topological time-periodic
(Floquet) phase in a 2D superfluid, following an instantaneous quench of
the coupling strength. The post-quench Cooper pairs occupy a linear combination
of "ground" and "excited" Floquet states, with coefficients determined by the
distribution function. While the Floquet bandstructure exhibits a single
avoided crossing relative to the equilibrium case, the distribution function
shows a population inversion of the Floquet bands at low energies. For a
realization in ultracold atoms, these two features compensate, producing a bulk
average rf signal that is well-captured by a quasi-equilibrium approximation.
In particular, the rf spectrum shows a robust gap. The single crossing occurs
because the quench-induced Floquet phase belongs to a particular class of
soliton dynamics for the BCS equation. The population inversion is a
consequence of this, and ensures the conservation of the pseudospin winding
number. As a comparison, we compute the rf signal when only the lower Floquet
band is occupied; in this case, the gap disappears for strong quenches. The
tunneling signal in a solid state realization is ignorant of the distribution
function, and can show wildly different behaviors. We also examine rf,
tunneling, and ARPES for weak quenches, such that the resulting topological
steady-state is characterized by a constant nonequilibrium order parameter. In
a system with a boundary, tunneling reveals the Majorana edge states. However,
the local rf signal due to the edge states is suppressed by a factor of the
inverse system size, and is spatially deconfined throughout the bulk of the
sample.Comment: 22 pages, 15 figures. v2: Added calculated ARPES spectr
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