相关论文: Feynman-Kac perturbation of $C^*$ quantum stochast…
The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over…
This paper is devoted to the study of propagation of chaos and mean-field limits for systems of indistinguable particles, undergoing collision processes. The prime examples we will consider are the many-particle jump processes of Kac and…
Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop…
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm…
Henry Stapp has made many significant contributions in quantum physics and its use in trying to understand the mind-matter relationship. I have been influenced by his use of the notion of {\em process} to bring more clarity to understand…
We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.
In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's master equation)…
Acausal features of quantum electrodynamic processes are discussed. While these processes are not present for the classical electrodynamic theory, in the quantum electrodynamic theory, acausal processes are well known to exist. For example,…
It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of…
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…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…
We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists…
We re-use some original ideas of de~Broglie, Schr\"odiger, Dirac and Feynman to revise the ensemble interpretation of wave function in quantum mechanics. To this end we introduce coherence (auto-concordance) of ensembles of quantum…
New applications of Feynman disentangling method in quantum mechanics are studied and the time-dependent singular oscillator problem is solved in this approach. The important role of representation group theory is discussed in this context.
The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time Markov processes. This connection allows for the creation of numerical schemes for…
An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…
The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator…