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Two different formalisms for the homogenization of composite materials containing oriented ellipsoidal particles of isotropic dielectric materials are being named after Bruggeman. Numerical studies reveal clear differences between the two…
Theory of exciton fine structure in semiconductor quantum dots and its dependence on quantum dot anisotropy and external lateral electric field is presented. The effective exciton Hamiltonian including long range electron-hole exchange…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
Two active dielectric materials may be blended together to realize a homogenized composite material (HCM) which exhibits more gain than either component material. Likewise, two dissipative dielectric materials may be blended together to…
Expressions arising from the Bruggeman approach for the homogenization of dielectric-magnetic composite materials, without ignoring the sizes of the spherical particles, are presented. These expressions exhibit the proper limit behavior.…
A dielectric columnar thin film (CTF), characterized macroscopically by a relative permittivity dyadic, was investigated theoretically with the assumption that, on the nanoscale, it is an assembly of parallel, identical, elongated…
Using numerical techniques and asymptotic expansions we obtain the phase diagram of a paradigmatic model of Coulomb frustrated phase separation in systems with negative short-range compressibility. The transition from the homogeneous phase…
Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT-symmetry is respected, and in that case an equivalent Hermitian description exists via the so-called Dyson map.…
The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $\beta=2$, the field theory is free. Correlation functions are calculated and a perturbation theory is discussed for…
The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Within the framework of quantum electrodynamics (QED), vacuum is a nonlinear medium which can be linearized for a rapidly time-varying electromagnetic field with a small amplitude subjected to a magnetostatic field. The linearized QED…
We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies…
We have developed a numerical method for calculating the second harmonic generation (SHG) generated by an anisotropic material whose optical properties present an arbitrary modulation in one dimension. The method is based on the Berreman…
In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and…
Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a…
The pseudomode method for open quantum systems, also known as the mesoscopic leads approach, consists in replacing a structured environment by a set of auxiliary "pseudomodes" subject to local damping that approximate the environment's…
Providing quantitative interpretation of coherent nonlinear microscopy images, such as third-harmonic generation (THG), is generally hampered by the complex phase-matching conditions, especially in the presence of sample linear…
We suggest a new approach for analyzing spatial anisotropy of acoustooptic figure of merit (AOFM). The relations for the effective elastooptic coefficients and the AOFM are derived for all possible types of acoustooptic (AO) interactions in…
Nonlinear optics is crucial for shaping the spatial structure of shortwave light and its interactions with matter, but achieving this through simple harmonic generation with a single pump is challenging. This study demonstrates nonlinear…