Tight focusing of partially polarized vortex beams has been studied. Compact form of the coherence matrix has been derived for polarized vortex beams. Effects of topological charge and polarization distribution of the incident beam on intensity distribution, degree of polarization, and coherence have been investigated.

The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a global quantum quench. While the dynamics of the bipartite entanglement and spin fluctuations are already known to provide insights into the nature of the manybody localized phases, we discuss the relevance of these quantities in the context of the localization transition. In particular, we observe that near the transition the long time limits of both quantities show behavior similar to divergent thermodynamic fluctuations.

The geometry of the generalized Bloch sphere Ω ₃ , the state space of a qutrit, is studied. Closed form expressions for Ω ₃ , its boundary ∂Ω ₃ , and the set of extremals are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω ₃ into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T _d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU (3), the symmetry underlying Ω ₃ , into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T _d .

We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S\left(t\right)\sim lnt$ and the saturated entanglement entropy scales with system size $L$ as $S(L,t\to \infty )\sim lnL$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.

Non-equilibrium processes which convert chemical energy into mechanical motion enable the motility of organisms. Bundles of inextensible filaments driven by energy transduction of molecular motors form essential components of micron-scale motility engines like cilia and flagella. The mimicry of cilia-like motion in recent experiments on synthetic active filaments supports the idea that generic physical mechanisms may be sufficient to generate such motion. Here we show, theoretically, that the competition between the destabilising effect of hydrodynamic interactions induced by force-free and torque-free chemomechanically active flows and the stabilising effect of nonlinear elasticity, provides a generic route to spontaneous oscillations in active filaments. These oscillations, reminiscent of prokaryotic and eukaryotic flagellar motion, are obtained without having to invoke structural complexity or biochemical regulation. This minimality implies that biomimetic oscillations, previously observed only in complex bundles of active filaments, can be replicated in simple chains of generic chemomechanically active beads.

Unconventional systems that adopt the concept of ghost schemes have led to advancements in some imaging applications. However, their application in quantitative phase imaging remains a challenge. Here, we introduce a basis for quantitative phase imaging with ghost diffraction and demonstrate ghost diffraction holographic microscopy for complex-valued imaging. We achieve this by introducing an off-axis holography approach in the modified ghost diffraction system. We also realize a correlation hologram in the cross-correlation of intensities from two detectors in the modified ghost diffraction setup and digitally process the correlation hologram to image complex-valued objects. To generate experiment results, we use a modified interferometer setup and exploit the spatial statistics of the scattered field from a time-frozen pseudothermal light source. Finally, we evaluate the efficacy of the approach by simulation and follow that with experiments that demonstrate imaging of pure phase objects, planar transparencies, and resolution test targets, among others.