Related papers: Bessel Process and Conformal Quantum Mechanics
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is…
Tensor universality often implies that multi-partite quantum-state processing is determined by what happens in totally disentangled cases. In independent systems relative time direction for the parts is arbitrary. This hints that time may…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Aiming at providing an objective picture for the collapse process of wave function during measurement, further analysis about the quantum discontinuous motion is presented, when considering general relativity we show that the new motion is…
The conceptuality interpretation of quantum mechanics proposes that quantum entities have a conceptual nature, interacting with the material world through processes that are the physical counterpart of the meaning-based processes which…
Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
Relational Quantum Mechanics (RQM) is an interpretation of quantum theory based on the idea of abolishing the notion of absolute states of systems, in favor of states of systems relative to other systems. Such a move is claimed to solve the…
The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…
Numerous models have been proposed to describe the Bose-Einstein correlations in multiple particle production processes. In the present paper we describe a generalization, which includes many previous models as special cases and, therefore,…
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back…
We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal…
The O'Connell process is a softened version (a geometric lifting with a parameter $a>0$) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…