Related papers: On Exact Evaluation of Path Integrals
In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from…
A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree…
Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method, originally proposed by Takahashi and Imada, is…
We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to…
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…
The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for…
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis.…
Correction to Annals of Applied Probability 17 (2007) 781--808 [doi:10.1214/105051607000000032].
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…
A comment on a misleading statement contained in [Phys. Rev. A 97, 062115 (2018)]. v2: a typo corrected
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure"…
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $V(x) = \frac{1}{2} \omega^2 x^2 + g x^4$ is presented. Using a path integral formalism, the exact…
Timelike Liouville field theory (also known as imaginary Liouville theory or imaginary Gaussian multiplicative chaos) is expected to describe two-dimensional quantum gravity in a positive-curvature regime, but its path integral is not a…
We have performed analytically the transverse momentum integrations in the real corrections to the longitudinal \gamma^*_L impact factor and carried out numerically the remaining integrations. I outline the analytical integration and…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
We compute the depth of powers of edge ideals of integrally closed edge-weighted paths.
This note corrects some serious errors in the first-order perturbation analysis of singular vectors as published by G.W. Stewart in his book "Matrix Algorithms Volume II: Eigensystems", SIAM, 2001.