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In this survey article we describe some geometric results in the theory of noncommutative rings and, more generally, in the theory of abelian categories. Roughly speaking and by analogy with the commutative situation, the category of graded…
The non-Abelian geometric phase possesses the capability of enabling robust and fault-resilient unitary transformations, making it a cornerstone of holonomic quantum computation. This "all-geometric" approach has successfully advanced the…
Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…
We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and…
Specific features of nonlinear interference processes at quantum transitions in near- and fully-resonant optically-dense Doppler-broadened medium are studied. The feasibility of overcoming of the fundamental limitation on a…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
Electromagnetic wave propagation in three-dimensional space typically suffers omnidirectional scattering when encountering obstacles. In this study, we employed Chern vectors to construct a topological heterostructure, where large-volume…
Creating materials with time-variant properties is critical for breaking reciprocity that imposes fundamental limitations to wave propagation. However, it is challenging to realize efficient and ultrafast temporal modulation in a photonic…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non- Hermitian time-Floquet systems are capable of non-reciprocal operations…
In this paper, we extend the result of [Andreas Fring et al J. Phys. A 43, 345401 (2010)] in noncommutative phase-space (NCPS). We compute the non-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a new P T-symmetry in…
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the…
Based on transformation optics, a strategy is proposed to expose the inner one-dimensional space of a wave field inside a beam volume to the surface of the propagation medium and extend the space from one-dimensional to two-dimensional,…
Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties, but realizing them has remained a daunting experimental task. This is because non-Hermiticity is often associated…
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…
Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate…
The extraordinary properties of resonant four-wave mixing of backward waves in doped negative-index materials are investigated. The feasibility of independent engineering of negative refractive index and nonlinear optical response as well…
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems, and is embodied in the time-reversal mirror. A time-reversal mirror…
Access to the transverse spin of light has unlocked new regimes in topological photonics and optomechanics. To achieve the transverse spin of nonzero longitudinal fields, various platforms that derive transversely confined waves based on…
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…