Related papers: The real-time Feynman path integral for step poten…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs)…
We consider the backreaction of a quantum system $q$ on an effectively classical degree of freedom $C$ that is interacting with it. The backreaction equation based on the standard path integral formalism gives the so-called `in-out'…
Schr\"odinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
We investigate spontaneous photon emission and absorption processes of two two-level atoms trapped close to the focal points of an ellipsoidal cavity, thereby taking into account the full multimode scenario. In particular, we calculate the…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong…
The restricted Feynman path integrals (RFPIs) have been proposed to study continuous quantum measurements in physics. The RFPIs are heuristically determined in terms of the usual probability amplitude multiplied by weight for each path,…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may…
This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical…
A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological…
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the…