相关论文: A Generalized Rule For Non-Commuting Operators in …

The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…

We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…

In 1929 Heisenberg and Pauli laid the foundations of QFT by quantizing the fields (method of canonical quantization). This general theory of quantized fields has remained undisputed up to now. We show how the unmodified Heisenberg-Pauli…

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which…

Any quantum communication task requires a common reference frame (i.e. phase, coordinate system). In particular, Quantum Key Distribution requires different bases for preparation and measurements of states which are obviously based on the…

The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…

We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…

In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…

The origin of the algebra of the non-commuting operators of quantum mechanics is explained in the general Fenyes-Nelson stochastic models in which the diffusion constant is a free parameter. This is achieved by continuing the diffusion…

The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the…

We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…

Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…

The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally…

We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…

Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a…

Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…

A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At…

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…