Related papers: Fermions from classical statistics
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
Statistical properties of Fermionic Molecular Dynamics are studied. It is shown that, although the centroids of the single--particle wave--packets follow classical trajectories in the case of a harmonic oscillator potential, the equilibrium…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We consider the quantum evolution of a fermion-hole pair in a d-dimensional gas of non-interacting fermions in the presence of random phase scattering. This system is mapped onto an effective Ising model, which enables us to show rigorously…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
The quantum or quantum field theory concept of a complex wave function is useful for understanding the information transport in classical statistical generalized Ising models. We relate complex conjugation to the discrete transformations…
A new category of phenomena is predicted in which fermions of different flavours can transmute into one another, for example $e \to \mu$ or $e \to \tau$, as a consequence of the `rotating' mass matrix due to renormalization. As examples,…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…