Related papers: A variational characterization of Einstein-Brillou…

We investigate the Schr\"odinger (non-relativistic) and the Dirac (``relativistic") billiards in the universal regime. The study is based on a non-ideal quantum resonant scattering numerical simulation. We show universal results that reveal…

The focus of these lectures is on the quantum vacuum subjected to classical electromagnetic fields. To this end we explicitly derive the renowned Heisenberg-Euler effective action in constant electromagnetic fields in a rather pedagogical…

We characterise the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns…

Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is the abstract statement of Schanuel's Conjecture, and an adapted form of existential closure. Here we show that if…

We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number…

The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…

Let E and E' be elliptic curves over Q with complex multiplication by the ring of integers of an imaginary quadratic field K and let Y=Kum(ExE') be the minimal desingularisation of the quotient of ExE' by the action of -1. We study the…

We consider the semiclassical quantization of the Sinai billiard for disk radii R small compared to the wave length 2 pi/k. Via the application of the periodic orbit theory of diffraction we derive the semiclassical spectral determinant.…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a…

We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.

We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ ring homomorphisms into an algebraic closure from an \'etale extension of…

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…

Let $1\leq q\leq (n-1)$. We first show that a necessary condition for a Hankel operator on $(0,q-1)$-forms on a convex domain to be compact is that its symbol is holomorphic along $q$-dimensional analytic varieties in the boundary. Because…

We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is…

Let $q \ge 3$ be a period. There are at least two $(1,q)$-periodic trajectories inside any smooth strictly convex billiard table, and all of them have the same length when the table is an ellipse or a circle. We quantify the chaotic…

We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequivalent irreducibles. This is the BKK bound of the corresponding…

We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.

We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of…

This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a…