Related papers: Concentration of Quasimodes for Perturbed Harmonic…
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures…
We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds on the resolvent near the real axis when no geometric control…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible…
We consider the possible concentration in phase space of a sequence of eigenfunctions (or, more generally, a quasimode) of an operator whose principal symbol has completely integrable Hamilton flow. The semiclassical wavefront set $WF_h$ of…
In this article we study the semiclassical asymptotics of the Martinet sub-Laplacian on the flat toroidal cylinder $M = \mathbb{R} \times \mathbb{T}^2$. We describe the asymptotic distribution of sequences of eigenfunctions oscillating at…
We construct quasimodes for some non-selfadjoint semiclassical operators at the boundary of the pseudo-spectrum using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is…
Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in optomechanical systems. In this Letter, we…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic"…
We study properties of the nodal sets of high frequency eigenfunctions and quasimodes for radial perturbations of the Harmonic Oscillator. In particular, we consider nodal sets on spheres of large radius (in the classically forbidden…
In this work, we wish to address the question -- whether the quasi-normal modes, the characteristic frequencies associated with perturbed black hole spacetimes, central to the stability of these black holes, are themselves stable. Though…
We consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
Fluid dynamics induced by periodically forced flow around a cylinder is analyzed computationally for the case when the forcing frequency is much lower than the von K{\'a}rm{\'a}n vortex shedding frequency corresponding to the constant flow…
We study a transverse electron-hole focusing effect in a normal-superconductor system. The spectrum of the quasiparticles is calculated both quantum mechanically and in semiclassical approximation, showing an excellent agreement. A…
We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some…
Periodic disturbances composed of harmonics typically occur during periodic operations, impairing performance of mechanical and electrical systems. To improve the performance, control of periodic-disturbance suppression has been studied,…
Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically…
Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a non-Hermitian differential operator. They hold crucial significance in the physics of black holes. The analysis of quasinormal modes of black holes in…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…