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We develop a universal approach enabling the study of any multimode quantum optical system evolving under a quadratic Hamiltonian. Our strategy generalizes the standard symplectic analysis and permits the treatment of multimode systems even…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For {\it isolated} systems, a hydrodynamic theory explains the origin and spreading of entanglement via…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
In this work we propose a general theoretical approach to the modelling of complex dispersion characteristics of leaky optical modes operating in photonic crystal slab composed of two high-index contrast gratings, beyond the protection of…
We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
We analyze enhanced optical transmission through subwavelength apertures using a modal formulation for the two fundamental polarizations, transverse electric (TE) and transverse magnetic (TM). Within this framework, the fields inside the…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to…
We study the propagation of high-frequency electromagnetic waves in randomly heterogeneous bianisotropic media with dissipative properties. For that purpose we consider randomly fluctuating optical responses of such media with correlation…
Absorption and emission in inorganic bipolar solar cells based on low dimensional structures exhibiting the effects of quantum confinement is investigated in the framework of a comprehensive microscopic theory of the optical and electronic…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
We show that an open fermionic system coupled to continuous environment with unitary system-environment evolution can be exactly mapped onto an auxiliary system consisting of the physical fermion system and a set of discrete fermionic modes…
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this…
Amplification/attenuation of light waves in artificial materials with a gain/loss modulation on the wavelength scale can be sensitive to the propagation direction. We give a numerical proof of the high anisotropy of the gain/loss in two…
Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian…
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schr\"odinger operator $-\Delta+V(x)$ in $R^n$ with periodic potential near the edges of the spectrum. A well known conjecture says that…
The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. While describing the dynamics of systems with few resonances is a relatively well understood problem,…