1,426 research outputs found
Nonlinear normal modes and spectral submanifolds: Existence, uniqueness and use in model reduction
We propose a unified approach to nonlinear modal analysis in dissipative
oscillatory systems. This approach eliminates conflicting definitions, covers
both autonomous and time-dependent systems, and provides exact mathematical
existence, uniqueness and robustness results. In this setting, a nonlinear
normal mode (NNM) is a set filled with small-amplitude recurrent motions: a
fixed point, a periodic orbit or the closure of a quasiperiodic orbit. In
contrast, a spectral submanifold (SSM) is an invariant manifold asymptotic to a
NNM, serving as the smoothest nonlinear continuation of a spectral subspace of
the linearized system along the NNM. The existence and uniqueness of SSMs turns
out to depend on a spectral quotient computed from the real part of the
spectrum of the linearized system. This quotient may well be large even for
small dissipation, thus the inclusion of damping is essential for firm
conclusions about NNMs, SSMs and the reduced-order models they yield.Comment: To appear in Nonlinear Dynamic
Excitations with projected entangled pair states using the corner transfer matrix method
We present an extension of a framework for simulating single quasiparticle or
collective excitations on top of strongly correlated quantum many-body ground
states using infinite projected entangled pair states, a tensor network ansatz
for two-dimensional wave functions in the thermodynamic limit. Our approach
performs a systematic summation of locally perturbed states in order to obtain
excited eigenstates localized in momentum space, using the corner transfer
matrix method, and generalizes the framework to arbitrary unit cell sizes, the
implementation of global Abelian symmetries and fermionic systems. Results for
several test cases are presented, including the transverse Ising model, the
spin- Heisenberg model and a free fermionic model, to demonstrate
the capability of the method to accurately capture dispersions. We also provide
insight into the nature of excitations at the point of the
Heisenberg model.Comment: 13 pages, 10 figure
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