Related papers: Airy wavepackets are Perelomov coherent states
Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A…
We consider wave packets of free particles with a general energy-momentum dispersion relation $E(p)$. The spreading of the wave packet is determined by the velocity $v = \p_p E$. The position-velocity uncertainty relation $\Delta x \Delta v…
The concept of nonlinear quantum-beat pump-probe Auger spectroscopy is introduced by discussing a relatively simple four-level model system. We consider a coherent wave packet involving two low-lying states that was prepared by an…
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…
Space-time wave packets are propagation-invariant pulsed beams that travel in free space without diffraction or dispersion by virtue of tight correlations introduced into their spatio-temporal spectrum. Such correlations constitute an…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
The entangled states that include every physical properties of particles would be important for both theoretical and applied physics. However, the existence and properties of such entangled states are unclear at present. Here we…
A lossless beam-splitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the…
We present a geometrical way of understanding the dynamics of wavefunctions in a free space, using the phase-space formulation of quantum mechanics. By visualizing the Wigner function, the spreading, shearing, the so-called "negative…
We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive…
The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisonless plasma, and the BGK waves are its famous exact steady solutions. They play an important role on the long time dynamics of a…
We study the quantum evolution in dimension three of a system composed by a test particle interacting with an environment made of $N$ harmonic oscillators. At time zero the test particle is described by a spherical wave, i.e. a highly…
We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension (1D) for both positive and negative signs of the nonlinear term, as…
A generalization of the Chirikov-Taylor model is introduced to study the dynamics of a charged particle in the field of an electrostatic wave packet with an arbitrary but finite number of harmonics.
According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
In previous works [4, 5], existence and uniqueness of travelling waves for the nonlinear Schr\"odinger equations have been shown for speeds close to the speed of sound. Furthermore, it has been proved that a chain of dark solitons of…
We consider wavepackets composed of two modulated carrier Bloch waves with opposite group velocities in the one dimensional periodic Nonlinear Schroedinger/Gross-Pitaevskii equation. These can be approximated by first order coupled mode…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
Counterpropagating Alfv\'en waves are ubiquitously observed in many astrophysical environments, such as a star surface and a planetary foreshock. We discuss an efficient particle acceleration mechanism in two counterpropagating circularly…