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Let $(M,\omega)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are…
The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a…
Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser…
The mesoscopic spin system formed by the 10E4-10E6 nuclear spins in a semiconductor quantum dot offers a unique setting for the study of many-body spin physics in the condensed matter. The dynamics of this system and its coupling to…
An electron within a mesoscopic (quantum-coherent) spintronic structure is described by a single wave function which, in the presence of both charge scattering and spin-orbit coupling, encodes an information about {\em entanglement} of its…
Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,\omega)$. We prove the existence of an action integral around loops in $\text{Ham(M)}$, and determine the value of this…
We obtain a microscopic description of the interaction between electron spins in bulk semiconductors and in pairs of semiconductor quantum dots. Treating the k.p band mixing and the Coulomb interaction on the same footing, we obtain in the…
The interplay of electric charge, spin, and orbital polarizations, coherently driven by picosecond long oscillations of light fields in spin-orbit coupled systems, is the foundation of emerging terahertz spintronics and orbitronics. The…
We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
The usual theoretical model for synchrotron radiation in circular accelerators (synchrotrons and storage rings) is to treat a single electron moving in a horizontal circle in a uniform vertical magnetic field, but the true situation in real…
We revisit the problem of electron transport through mesoscopic rings with spin-orbit (SO) interaction. In the well-known path-integral approach, the scattering states for a quasi-1D ring with quasi-1D leads can be expressed in terms of…
Recent studies identified spin-order-driven phenomena such as spin-charge interconversion without relying on the relativistic spin-orbit interaction. Those physical properties can be prominent in systems containing light magnetic atoms due…
High-index surfaces of silicon with adsorbed gold can reconstruct to form highly ordered linear step arrays. These steps take the form of a narrow strip of graphitic silicon. In some cases - specifically, for Si(553)-Au and Si(557)-Au - a…
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
In a previous paper, second- and fourth-order explicit symplectic integrators were designed for a Hamiltonian of the Schwarzschild black hole. Following this work, we continue to trace the possibility of the construction of explicit…
Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds…
In this work, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical…
In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface where the symplectic volume goes either to infinity or to zero…