Related papers: Quantum Mechanics as a Classical Theory XVI: Posit…
We delve into the in-in formalism and derive general expressions for the computation of n-point functions for a self-interacting scalar field by means of a probability density functional (PDF). Even though in typical situations these…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is "when phase space measurements are performed". We introduce the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…
The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to…
Using the basis of Hermite-Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive the practical constraints for a function and its Fourier transform to be both positive. We propose a constructive method…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
Density-functional theory is used to study the electronic structure of quantum dots in a magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…