Quantum information for a solitonic particle with hyperbolic interaction

In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a hyperbolic barrier potential. The kinetic energy ordering of BenDaniel-Duke guarantees the hermiticity of the Hamiltonian operator. We find the analytical solutions of the Schrödinger equation and their respective quantized energies. In addition, we calculate the Shannon entropy and Fisher information for the solutions in the case of the lowest energy states of the system.

Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †

In this article, sources of information in electronic states are reexamined and a need for the resultant measures of the entropy/information content, combining contributions due to probability and phase/current densities, is emphasized. Probability distribution reflects the wavefunction modulus and generates classical contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their nonclassical supplements, due to probability “convection”. The local-energy concept is used to examine the phase equalization in the equilibrium, phase-transformed states. Continuity relations for the wavefunction modulus and phase components are reexamined, the convectional character of the local source of the resultant gradient information is stressed, and latent probability currents in the equilibrium (stationary) quantum states are related to the horizontal (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the grand-ensemble description, the reactivity criteria are defined by the populational derivatives of the system average electronic energy. Their entropic analogs, given by the associated derivatives of the overall gradient information, are shown to provide an equivalent set of reactivity indices for describing the charge transfer phenomena.

Equalization principles in open subsystems, origins of information descriptors and state-continuity relations

The electronegativity-equalization at several hypothetical stages of chemical reactions is reexamined and phase-equalization in open substrates is explored. The equivalence of the energy and information reactivity criteria is stressed and local energy concept is shown to determine time-evolutions of wavefunction components. Independent sources of information content in electronic states are identifi ed and the need for resultant entropy-information measures in quantum mechanics, combining information contributions due to the classical (probability) and nonclassical (phase/current) distributions, is reemphasized. Limitations for a simultaneous removal of uncertainties in the position and velocity distributions imposed by the Heisenberg indeterminacy principle, are discussed, continuities of the wavefunction modulus and phase components are examined, the convectional character of the local source of resultant gradient information is stressed, and a latent (“horizontal”) probability currents in the stationary quantum states are discussed.

Breakdown of the Einstein’s Equivalence Principle for a quantum body

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite quantum bodies — hydrogen atoms. Our results are as follows. For the most ensembles, the Einstein’s Equivalence Principle is valid. On the other hand, we discuss that for some special quantum ensembles — ensembles of the coherent superpositions of the stationary quantum states in the hydrogen atoms (which we call Gravitational demons) — the Equivalence Principle between passive gravitational mass and energy is broken. We show that, for such superpositions, the expectation values of passive gravitational masses are not related to the expectation values of energies by the famous Einstein’s equation, i.e. [Formula: see text]. Possible experiments at the Earth’s laboratories are briefly discussed, in contrast to the numerous attempts and projects to discover the possible breakdown of the Einstein’s Equivalence Principle during the space missions.