Related papers: Modular weights of wave functions on magnetized to…
In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action…
In this paper, continuing the discussion about Species Quantum Mechanics, we investigate quantum mechanics in moduli spaces using a mini-superspace approach. From this perspective, moduli-dependent functions can be viewed as operators, and…
In the scalar setting, the power functions $|x|^{\gamma}$, for $-1 < \gamma<1$, are the canonical examples of $A_2$ weights. In this paper, we study two types of power functions in the matrix setting, with the goal of obtaining canonical…
We complete several generating functions to non-holomorphic modular forms in two variables. For instance, we consider the generating function of a natural family of meromorphic modular forms of weight two. We then show that this generating…
We present a new method for computing the wave function in the presence of constraints. As an explicit example we compute the wave function for the many electrons problem in coupled metallic rings in the presence of external magnetic…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the Boolean algebra generated by intervals with non--positive rational ends, with values in analytic functions…
Mock modular forms, which give the theoretical framework for Ramanujan's enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular parameterizations of elliptic curves $E/\mathbb{Q}$. We…
Stationary electromagnetic waves display aspects that are shared with massive particles, since the energy and momentum contained in a volume of sides equal to the wavelengths form a non-zero energy-momentum invariant. The parallel can be…
The recent increasing interest in detecting gravitational waves (GWs) by lunar seismic measurement urges us to have a clear understanding of the response of the moon to passing GWs. In this paper, we clarify the relationship between two…
On a basis of extensive analytical and numerical studies we show that a linear-polarized microwave field creates a stationary magnetization in mesoscopic ballistic quantum dots with two-dimensional electron gas being at a thermal…
We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the…
Elliptic modular graph forms (eMGFs) are non-holomorphic modular forms depending on a modular parameter $\tau$ of a torus and marked points $z$ thereon. Traditionally, eMGFs are constructed from nested lattice sums over the discrete momenta…
Transition-metal dichalcogenides (TMDs) are promising for two-dimensional (2D) semiconducting devices and novel phenomena. For 2D applications, their work function, ionization energy, and electron affinity are required as a function of…
We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus $T^2$ and toroidal orbifolds $T^2/\mathbb{Z}_N$ ($N=2,3,4,6$) with a background homogeneous magnetic field. As is well-known, magnetic flux…
We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients…
Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an…
Let $E$ be a level 1, vector valued Eisenstein series of half-integral weight, normalized so that the coefficients are all in $\mathbb{Z}$. We show that there is a level one vector valued cusp form $f$ with the same weight as $E$ and with…
In this article our main object of investigation is the simple modular density ideals $\mathcal{Z}_g(f)$ introduced in [Bose et al., Indag. math., 2018] where $g$ is a weight function, more precisely, $g\in G$, $G=\{g:\omega \to…
Stationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw's dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a…