Related papers: Feynman path integrals for discrete-variable syste…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for…
Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete…
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main…
We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolations indexed by forests, in the fashion of constructive…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one…
In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges. We consider the walks with coins that are one-parameter continuous deformation…
The Feynman path integral is defined over the space $\mathbb{R}^T$ of all possible paths; it has been a powerful tool to develop Quantum Mechanics. The absolute value of Feynman's integrand is not integrable, then Lebesgue integration…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…