相关论文: Relations between Projected Emittances and Eigenem…
Recent progress in manipulating quantum states of light and matter brings quantum-enhanced measurements closer to prospective applications. The current challenge is to make quantum metrologic strategies robust against imperfections.
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
Given an arbitrary field K and non-zero scalars a and b, we give necessary and sufficient conditions for a matrix A in M_n(K) to be a linear combination of two idempotents with coefficients a and b. This extends results previously obtained…
The problem of the measurability of the electromagnetic field is investigated 1) in the framework of the abstract restricted-path-integral method, and 2) by explicitly accounting the action of the field onto the meter and its back reaction.…
In order to reduce light pollution we have to reduce the overall amount of artificial light emissions. This is a consequence of the basic rules governing the propagation of light in the terrestrial environment. In this work I revisit the…
The general expression with the physical significance and positive definite condition of the eigenvalues of $4\times 4$ Hermitian and trace-one matrix are obtained. This implies that the eigenvalue problem of the $4\times 4$ density matrix…
Our focus is upon {\it irreducible} nonnegative $n$-by-$n$ matrix realizations of nonnegatively realizable spectra or, equivalently, characteristic polynomials. After giving some general background, we make some useful new observations and…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…
We describe applications of two-dimensional subwavelength quantum emitter arrays as efficient optical elements in the linear regime. For normally incident light, the cooperative optical response, stemming from emitter-emitter dipole…
The semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may…
In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…
The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our…
It is known that the two eigen plane waves incident to the generalized soft-and-hard/DB (GSHDB) boundary are reflected as from the PEC or PMC boundary, i.e., with reflection coefficients $-1$ or $+1$, for any angle of incidence. The present…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
In this lecture we introduce from basic principles the main concepts of beam focusing and transport in modern accelerators using the beam envelope equationas a convenient mathematical tool. Matching conditions suitable for preserving beam…
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…
The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective…
We show how two level atoms can be used to build microscopic models for mirrors and beamsplitters. The mirrors can have arbitrary shape allowing closed cavities to be built. It is possible to build networks or mirrors and beamsplitters and…
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the…