Related papers: Sub-Planck scale structures in the P{\"o}schl-Tell…
A set of quasi-exactly solvable quantum mechanical potentials associated with the Poeschl-Teller potential, the generalized Poeschl-Teller potential, the Scarf potential, and the harmonic oscillator potential have been studied. Solutions of…
Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study…
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to…
Schr\"{o}dinger operators of the form $\Delta - W$ on $L^2_{\text{rad}}(\mathbb{R}^3)$, the space of radially symmetric square integrable functions are relevant in a variety of physical contexts. The potential $W$ is taken to be radially…
We discuss vacuum structure and vacuum stability in classically scale-invariant renormalizable models with a scalar dark matter multiplet of global O(N) symmetry together with an electroweak singlet scalar mediator. Our conformally…
General forms of the K\"ahler and superpotenials that lead to consistent low energy broken Supersymmetry originating from $N=1$ Supergravity have been classified and used for model building since more than three decades. We point out the…
GUT scale threshold corrections in minimal SU(5) supergravity grand unification are discussed. It is shown that predictions may be made despite uncertainties associated with the high energy scale. A bound relating the strong coupling…
Exact solvability (typically, of harmonic oscillators) in quantum mechanics usually implies an elementary form of the spectrum while in all the "next-to-solvable" models, the energies E are only available in an implicit form (typically, as…
2nd-order conformal superintegrable systems in $n$ dimensions are Laplace equations on a manifold with an added scalar potential and $2n - 1$ independent 2nd order conformal symmetry operators. They encode all the information about…
In the study of Planck-scale ("quantum-gravity induced") violations of Lorentz symmetry, an important role was played by the deformed-electrodynamics model introduced by Myers and Pospelov. Its reliance on conventional effective quantum…
Oscillons are localized, non-singular, time-dependent, spherically-symmetric solutions of nonlinear scalar field theories which, although unstable, are extremely long-lived. We show that they naturally appear during the collapse of…
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
The quasilinear theory of the Wigner-Poisson system in one spatial dimension is examined. Conservation laws and properties of the stationary solutions are determined. Quantum effects are shown to manifest themselves in transient periodic…
Self-assembly into target structures is an efficient material design strategy. Combining analytical calculations and computational techniques of evolutionary and Monte Carlo types, we report about a remarkable structural variability of…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
Black hole quasinormal modes are known to exhibit spectral instability under ultraviolet perturbations of the effective potential. In the present work, we investigate the sensitivity of the fundamental mode to different types of localized…
This talk discusses the relation between spacetime-dependent scalars, such as couplings or fields, and the violation of Lorentz symmetry. A specific cosmological supergravity model demonstrates how scalar fields can acquire time-dependent…
This paper is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite square-well and also in P\"oschl-Teller…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…