2,863 research outputs found
Universal properties of distorted Kerr-Newman black holes
We discuss universal properties of axisymmetric and stationary configurations
consisting of a central black hole and surrounding matter in Einstein-Maxwell
theory. In particular, we find that certain physical equations and inequalities
(involving angular momentum, electric charge and horizon area) are not
restricted to the Kerr-Newman solution but can be generalized to the situation
where the black hole is distorted by an arbitrary axisymmetric and stationary
surrounding matter distribution.Comment: 7 page
Surmounting collectively oscillating bottlenecks
We study the collective escape dynamics of a chain of coupled, weakly damped
nonlinear oscillators from a metastable state over a barrier when driven by a
thermal heat bath in combination with a weak, globally acting periodic
perturbation. Optimal parameter choices are identified that lead to a drastic
enhancement of escape rates as compared to a pure noise-assisted situation. We
elucidate the speed-up of escape in the driven Langevin dynamics by showing
that the time-periodic external field in combination with the thermal
fluctuations triggers an instability mechanism of the stationary homogeneous
lattice state of the system. Perturbations of the latter provided by incoherent
thermal fluctuations grow because of a parametric resonance, leading to the
formation of spatially localized modes (LMs). Remarkably, the LMs persist in
spite of continuously impacting thermal noise. The average escape time assumes
a distinct minimum by either tuning the coupling strength and/or the driving
frequency. This weak ac-driven assisted escape in turn implies a giant speed of
the activation rate of such thermally driven coupled nonlinear oscillator
chains
Periodic and compacton travelling wave solutions of discrete nonlinear Klein-Gordon lattices
We prove the existence of periodic travelling wave solutions for general
discrete nonlinear Klein-Gordon systems, considering both cases of hard and
soft on-site potentials. In the case of hard on-site potentials we implement a
fixed point theory approach, combining Schauder's fixed point theorem and the
contraction mapping principle. This approach enables us to identify a ring in
the energy space for non-trivial solutions to exist, energy (norm) thresholds
for their existence and upper bounds on their velocity. In the case of soft
on-site potentials, the proof of existence of periodic travelling wave
solutions is facilitated by a variational approach based on the Mountain Pass
Theorem. The proof of the existence of travelling wave solutions satisfying
Dirichlet boundary conditions establishes rigorously the presence of compactons
in discrete nonlinear Klein-Gordon chains. Thresholds on the averaged kinetic
energy for these solutions to exist are also derived.Comment: 21 pages, 1 figur
Bulk and surface magnetoinductive breathers in binary metamaterials
We study theoretically the existence of bulk and surface discrete breathers
in a one-dimensional magnetic metamaterial comprised of a periodic binary array
of split-ring resonators. The two types of resonators differ in the size of
their slits and this leads to different resonant frequencies. In the framework
of the rotating-wave approximation (RWA) we construct several types of breather
excitations for both the energy-conserved and the dissipative-driven systems by
continuation of trivial breather solutions from the anticontinuous limit to
finite couplings. Numerically-exact computations that integrate the full model
equations confirm the quality of the RWA results. Moreover, it is demonstrated
that discrete breathers can spontaneously appear in the dissipative-driven
system as a results of a fundamental instability.Comment: 10 pages, 16 figure
The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation
While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a “continuous dependence” on their initial data in the and metrics. The most striking relevance of the analytical results is that small amplitude solutions of the Ablowitz-Ladik system persist in the Discrete Nonlinear Schrödinger one. It is shown that the closeness results are also valid in higher dimensional lattices, as well as, for generalised nonlinearities. For illustration of the applicability of the approach, a brief numerical study is included, showing that when the 1-soliton solution of the Ablowitz-Ladik system is initiated in the Discrete Nonlinear Schrödinger system with cubic or saturable nonlinearity, it persists for long-times. Thereby, excellent agreement of the numerical findings with the theoretical predictions is obtained.Regional Government of Andalusia and EU (FEDER program) project P18-RT-3480Regional Government of Andalusia and EU (FEDER program) project US-1380977MICINN, AEI and EU (FEDER program) project PID2019-110430GB-C21MICINN, AEI and EU (FEDER program) project PID2020-112620GB-I0
Dissipative localised structures for the complex Discrete Ginzburg-Landau equation
The discrete complex Ginzburg-Landau equation is a fundamental model for the
dynamics of nonlinear lattices incorporating competitive dissipation and energy
gain effects. Such mechanisms are of particular importance for the study of
survival/destruction of localised structures in many physical situations. In
this work, we prove that in the discrete complex Ginzburg-Landau equation
dissipative solitonic waveforms persist for significant times by introducing a
dynamical transitivity argument. This argument is based on a combination of the
notions of ``inviscid limits'' and of the ``continuous dependence of solutions
on their initial data'', between the dissipative system and its Hamiltonian
counterparts. Thereby, it establishes closeness of the solutions of the
Ginzburg-Landau lattice to those of the conservative ideals described by the
Discrete Nonlinear Schr\"odinger and Ablowitz-Ladik lattices. Such a closeness
holds when the initial conditions of the systems are chosen to be sufficiently
small in the suitable metrics and for small values of the dissipation or gain
strengths. Our numerical findings are in excellent agreement with the
analytical predictions for the dynamics of the dissipative bright, dark or even
Peregrine-type solitonic waveforms.Comment: 20 pages, 10 figures. To appear in Journal of Nonlinear Scienc
On smoothness of Black Saturns
We prove smoothness of the domain of outer communications (d.o.c.) of the
Black Saturn solutions of Elvang and Figueras. We show that the metric on the
d.o.c. extends smoothly across two disjoint event horizons with topology R x
S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the
Komar angular momentum of the spherical component of the horizon vanishes, and
present numerical evidence for stable causality in general.Comment: 47 pages, 5 figure
Directed current in the Holstein system
We propose a mechanism to rectify charge transport in the semiclassical
Holstein model. It is shown that localised initial conditions, associated with
a polaron solution, in conjunction with a nonreversion symmetric static
electron on-site potential constitute minimal prerequisites for the emergence
of a directed current in the underlying periodic lattice system. In particular,
we demonstrate that for unbiased spatially localised initial conditions,
violation of parity prevents the existence of pairs of counter-propagating
trajectories, thus allowing for a directed current despite the
time-reversibility of the equations of motion. Occurrence of long-range
coherent charge transport is demonstrated
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