Related papers: Quantum Feynman-Kac perturbations
A concept of quantum stochastic convolution cocycle is introduced and studied in two different contexts -- purely algebraic and operator space theoretic. A quantum stochastic convolution cocycle is a quantum stochastic process on a…
Functionals of a stochastic process Y(t) model many physical time-extensive observables, e.g. particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
In this work, we developed an efficient quantum algorithm for the simulation of non-Markovian quantum dynamics, based on the Feynman path integral formulation. The algorithm scales polynomially with the number of native gates and the number…
Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin…
We derive Feynman-Kac formulas for Dirichlet realizations of Pauli-Fierz operators generating the dynamics of nonrelativistic quantum mechanical matter particles, which are minimally coupled to both classical and quantized radiation fields…
In the context of the Feynman's derivation of electrodynamics, we show that noncommutativity allows other particle dynamics than the standard formalism of electrodynamics.
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
For many practical purposes, it is convenient to formulate unbroken non-abelian gauge theories like QCD in a color-flow basis. We present a new derivation of SU(N) interactions in the color-flow basis by extending the gauge group to…
In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…
The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional…
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In…