Related papers: The semi-classical approximation for modular opera…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy estimates on derivatives. As an application, we use Donnelly…
We propose a new approximate series solution of the semiclassical Wigner equation by uniformization of WKB approximations of the Schr\"odinger eigenfunctions.
In this article, a class of Fourier Integral Operators which converge to the unitary group of the Schr\"odinger equation in semiclassical limit $\epsilon\to 0$ is constructed. The convergence is in the uniform operator norm and allows for a…
A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…
We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state…
An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact…
We present new theoretical results on the spectrum of the quantum field theory of the Double Sine Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained…
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this…
We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^{\kappa}\hat{K}$, where…
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…
We present a formalism that enables the analytic calculation of the interaction of a spin-half particle with a polychromatic electromagnetic field. This powerful new approach provides a clear physical picture even for cases with highly…
We study the spectral properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, if $M$ carries an…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
Modular operads are an extension of operads. In the same way that operads, as dendroidal sets, can be considered as presheaves over the category of trees, so can modular operads be considered as presheaves over a category of graphs. This…
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
The semiclassical approximation of coherent state path integrals is employed to study the dynamics of the Jaynes-Cummings model. Decomposing the Hilbert space into subspaces of given excitation quanta above the ground state, the…
Recent progress in experimental techniques has made the quantum regime in plasmonics accessible. Since plasmons correspond to collective electron excitations, the electron-electron interaction plays an essential role in their theoretical…