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The points where diffraction orders emerge or vanish in the propagating spectrum of periodic non-Hermitian systems are referred to as scattering thresholds. Close to these branch points, resonances from different Riemann sheets can…
Hyperpolarized nuclear spins in molecules exhibit high magnetization that is unachievable by classical polarization techniques, making them widely used as sensors in physics, chemistry, and medicine. The state of a hyperpolarized material,…
Extensive theoretical and experimental investigations on multipartite systems close to an avoided energy-level crossing reveal interesting features such as the extremisation of entanglement. Conventionally, the estimation of entanglement…
An experimental method for obtaining quantum interference signal in atomic ensemble using a bi-chromatic field is discussed. Here, the quantum interference signal is obtained by scanning the magnetic field rather than conventional method of…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
Light-matter interacting quantum systems manifest strong correlations that lead to distinct cooperative spontaneous emissions of subradiance or superradiance. To demonstrate the essence of long-range correlations in such systems, we…
We show that low-energy inelastic cross sections can decrease as well as increase in the vicinity of a zero-energy Feshbach resonance. When an external field is used to tune across such a resonance, the real and imaginary parts of the…
A simple two-atom model is shown to describe a Bose-Einstein condensate of alkali atoms subjected to external magnetic field ramps near a Feshbach resonance. The implications uncovered for two atoms in a trap can be applied at least…
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…
The increasing precision of cosmology data in the modern era is calling for methods to allow the extraction of non-Gaussian information using tools beyond two-point statistics. The marked power spectrum has the potential to extract beyond…
For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The paper studies the question of existence of polynomials with given roots over associative non-commutative rings with identity. It is shown that in the case of an associative division ring for arbitrary n elements of this ring there…
We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy…
Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical…
We describe two different modes for electronically detecting an adsorbed molecule using a nanoscale transistor. The attachment of an ionic molecular target shifts the threshold voltage through modulation of the depletion layer…
We study properties of two different atoms at a single optical lattice site at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum, the efficiency of rf association and the lifetime as a function of magnetic field…
Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitray number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted…
Inelastic tunneling through magnetically anisotropic molecules is studied theoretically in the presence of a strong magnetic field. Since the molecular orientation is not well controlled in tunneling experiments, we consider arbitrary…