Related papers: Quantum Unique Ergodicity for Eisenstein Series in…
The main new result is the computation of the degeneration of l-adic Eisenstein classes at the cusps. This is done by relating it to the degeneration of the elliptic polylog. These classes come from K-theory and their Hodge regulator can…
For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $\Sigma$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $\Sigma$, realized using…
We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However…
We prove an asymptotic formula expressing the regularized fourth moment of all newform Eisenstein series of primitive nebentypus as a mean value of $L$-functions. This is an analogue of the recent work of Djankovi\'c and Khan in the…
A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories,…
In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…
Quantum gravitational corrections to the effective potential, at one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity ---which is taken as an effective theory for quantum…
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
In this paper, we compute for odd fundamental discriminants $D>1$ the Fourier expansion of non-holomorphic elliptic Eisenstein series for $\Gamma_0(D)$ with quadratic nebentypus character $\chi_D$ satisfying a certain plus space condition.…
We define new objects called 'horizontal $p$-adic $L$-functions' associated to $L$-values of twists of elliptic curves over $\mathbb{Q}$ by characters of $p$-power order and conductor prime to $p$. We study the fundamental properties of…
We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a Bruggeman-Kuznetsov formula for newforms…
In this paper, we develop a general homogenization theory for elliptic equations with coefficients that oscillate periodically at infinitely many scales $\varepsilon = (\varepsilon_1, \varepsilon_2, \cdots) \in (0,1)^\infty$, with…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
Piecewise $\alpha$-stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Euler-Maruyama (EM) scheme more difficult to analyze. We…
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
We consider an infinite dimensional diffusion on $T^{\mathbb Z^d}$, where $T$ is the circle, defined by an infinitesimal generator of the form $L=\sum_{i\in\mathbb Z^d}\left(\frac{a_i(\eta)}{2}\partial^2_i +b_i(\eta)\partial_i\right)$, with…