相关论文: The semi-classical approximation for modular opera…
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
Let R be a complete discrete valuation ring, S=R[[u]] and n a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S^d. As S is not principal, it…
We study the survival probability associated with a semi-classical matrix Shr\"odinger operator that models the predissociation of a general molecule in the Born-Oppenheimer approximation. We show that it is given by its usual…
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving…
It is well-known in physics that the limit of large quantum spin $S$ should be understood as a semiclassical limit. This raises the question of whether such emergent classicality facilitates the approximation of computationally hard quantum…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a semi-classical framework. The concept of Coherent Internal States is used in the formulation of the semiclassical approximation from…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano-Regge type of asymptotic of…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
We characterize the set of semiclassical measures corresponding to sequences of eigenfunctions of the attractive Coulomb operator $\widehat{H}_{\hbar}:=-\frac{\hbar^2}{2}\Delta_{\mathbb{R}^3}-\frac{1}{|x|}$. In particular, any Radon…
In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…
We study sampling of Fourier Integral Operators $A$ at rates $sh$ with $s$ fixed and $h$ a small parameter. We show that the Nyquist sampling limit of $Af$ and $f$ are related by the canonical relation of $A$ using semiclassical analysis.…
The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…