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This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…
We revisit the backgrounds of type IIB on manifolds with $SU(4)$-structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex…
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss…
The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances,…
We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the…
Reciprocity is when the scattering amplitude of wave propagation satisfies a symmetry property, connecting a scattering process with an appropriate reversed one. We report on an experiment using nuclear resonance scattering of synchrotron…
We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…
We use a relative Fourier-Mukai transform on elliptic K3 surfaces $X$ to describe mirror symmetry. The action of this Fourier-Mukai transform on the cohomology ring of $X$ reproduces relative T-duality and provides an infinitesimal isometry…
We reveal how to exploit joint spatial-electromagnetic duality symmetries to obtain invariant scattering properties (including extinction, scattering, absorption) of self-dual scattering systems for incident waves of arbitrary…
A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; either the reflected beam is displaced (spatial shift) and/or travels in a different…
A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using…
It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
A structure is proposed for the mass matrices of the quarks and leptons that arises in a natural way from the assumption that the breaking of SO(10) gauge symmetry is achieved by the smallest possible set of vacuum expectation values. This…
The signal registered by a plane photodetector placed behind an optically inhomogeneous object irradiated by two coherent Gaussian beams intersecting inside the object at small angle to each other is calculated in the single-scattering…
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…