Related papers: Obtaining the Probability Vector Current Density i…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where 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…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The…
The fact that certain "extraordinary" probabilistic phenomena--in particular, macroscopic violations of the second law of thermodynamics--have never been observed to occur can be accounted for by taking hard preclusion as a basic physical…
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
This paper explores the generalization of the concept of a "probability current", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated…
We investigate the backflow effect in elementary quantum mechanics - the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schr\"odinger equation.…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
The density fluctuations of quantum vortex lines are measured in a turbulent flow of superfluid He, at temperatures corresponding to superfluid fraction of 16%, 47% and 81%. The probe is a micro-fabricated second sound resonator that allows…
The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its ``unreasonable effectiveness'' (which shows up best in the formulation of…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…