Related papers: Instantonic Methods for Quantum Tunneling in Finit…

The paper contains description of the path integrals in the action-angle phase space. It allows to split the action and angle degrees of freedom and to show that the angular quantum corrections cancel each other if the classical classical…

We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…

We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric…

Semi-classical analysis is used to investigate synchronous quantum tunneling in a multidimensional potential energy surface (PES) characterized by four degenerate minima, serving as a foundational model for coupled vibrational modes. The…

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, then instantons are necessarily complexified. These fuzzy instantons can have various physical applications. In slow-roll inflation models, fuzzy…

We investigate oscillating instanton solutions of a self-gravitating scalar field between degenerate vacua. We show that there exist O(4)-symmetric oscillating solutions in a de Sitter background. The geometry of this solution is finite and…

Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…

We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with…

To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…

We study the quantum-mechanical tunneling phenomenon in models which include the existence of non-equivalent vacua. For such a purpose we evaluate the euclidean propagator between two minima of the potential at issue in terms of the…

The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.

We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…

We present an analytical solution for the tunneling process in a piecewise linear and quadratic potential which does not make use of the thin-wall approximation. A quadratic potential allows for smooth attachment of various slopes exiting…

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing ``momentum'') at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely;…

Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is…

The worldline formalism offers an alternative framework to the standard diagrammatic approach in quantum field theory, grounded in first-quantized relativistic path integrals. Over recent decades, this formalism has attracted growing…

A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…

Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…

The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…