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arXiv:1703.05310 · Entropy

Kinetics of Interactions of Matter, Antimatter and Radiation Consistent with Antisymmetric (CPT-Invariant) Thermodynamics

A. Y. Klimenko

Published May 2, 2017• 8 citations
arXivHTMLPDF

Abstract

This work investigates the influence of directional properties of decoherence on kinetics rate equations. The physical reality is understood as a chain of unitary and decoherence events. The former are quantum-deterministic, while the latter introduce uncertainty and increase entropy. For interactions of matter and antimatter, two approaches are considered: symmetric decoherence, which corresponds to conventional symmetric (CP-invariant) thermodynamics, and antisymmetric decoherence, which corresponds to antisymmetric (CPT-invariant) thermodynamics. Radiation, in its interactions with matter and antimatter, is shown to be decoherence-neutral. The symmetric and antisymmetric assumptions result in different interactions of radiation with matter and antimatter. The theoretical predictions for these differences are testable by comparing absorption (emission) of light by thermodynamic systems made of matter and antimatter. Canonical typicality for quantum mixtures is briefly discussed in Appendix A.

DOI
10.3390/e19050202

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This work investigates the influence of directional properties of decoherence on kinetics rate equations. The physical reality is understood as a chain of unitary and decoherence events. The former are quantum-deterministic, while the latter introduce uncertainty and increase entropy. For interactions of matter and antimatter, two approaches are considered: symmetric decoherence, which corresponds to conventional symmetric (CP-invariant) thermodynamics, and antisymmetric decoherence, which corresponds to antisymmetric (CPT-invariant) thermodynamics. Radiation, in its interactions with matter and antimatter, is shown to be decoherence-neutral. The symmetric and antisymmetric assumptions result in different interactions of radiation with matter and antimatter. The theoretical predictions for these differences are testable by comparing absorption (emission) of light by thermodynamic systems made of matter and antimatter. Canonical typicality for quantum mixtures is briefly discussed in Appendix A.
The influence of quantum interference between different decay channels of three-level atoms on various characteristics of matter and radiation is considered for the case of thermodynamic equilibrium of atoms in a photon gas. It is shown that for rare gases when collisions between atoms are not important, the direct consequence of such an interference is a spontaneously induced atomic coherence between two upper levels. Therefore, for an accurate description of such atoms and radiation in thermodynamic equilibrium with each other it is not sufficient to specify only Boltzmann exponents, which correspond to the diagonal elements of the density matrix. The reason for this is that the conventional Boltzmann description is applied to infinitely sharp eigenstates of the unperturbed Hamiltonian. As we show, it becomes essential to take into account nonzero width of the levels if the levels are relatively close to each other. This produces nonzero nondiagonal elements of the density matrix that modify the emissivity of the equilibrium medium and lead to a zero point at a certain frequency as well as to an enhanced intensity in the red wing at the corresponding temperature. It is shown that the occupation number of the photons is not changed and obeys the equilibrium Planck distribution.
In 1916, A. Einstein developed a model of the absorption and emission of radiation from which he derived M. Planck’s radiation law. He postulated light-induced (stimulated) emission, because within the framework of classical physics an oscillator can, depending on the phase difference, both extract energy from the electromagnetic field and transfer energy to it. In a non-coherent field, α = β should hold, where α denotes the kinetic constant of absorption and β that of stimulated emission. This assumption is indispensable for deriving the radiation law from his model. In this context, it is problematic that a certain degree of field coherence follows necessarily from his model, which implies that α ≠ β. Moreover, the model cannot readily be generalised to fields of arbitrary coherence. An alternative model for the absorption and emission of radiation by matter is therefore developed here. On the one hand, it is based on the assumption that, within a blackbody, quanta of different energies may recombine freely; on the other hand, it employs the “pairwise interference model of quantum theory” (PIMOQ). The alternative model of the interaction between light and matter allows the radiation law to be derived for thermal equilibrium in a non-coherent field, under which conditions, according to the model, no stimulated emissions occur. It also describes the behaviour of systems with a coherent field (interference experiment, laser). Furthermore, considerations are presented regarding the energy distribution within a blackbody and the explanatory scope of A. Einstein’s model in this respect.
If the isolated system of bosons and fermions was initially in a pure maximally entangled quantum state, then, as a result of decoherence caused by the creation and annihilation of particles, this system not only enters a mixed state but also achieves equilibrium. The time of such a transition does not depend on the size of the system but is determined only by the properties of the particles. This phenomenon allows the problem of the horizon (the homogeneity of the universe) to be solved, since the transition time of different parts of the universe (if they were originally entangled with each other) to equilibrium will not depend on their sizes, and the speed of the interaction may be greater than the speed of light. Based on the decay of entangled states, the problem of the predominance of matter over antimatter in the universe can also be solved.
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantization, which relies on the assumption that any admissible quantum state must be either symmetric or antisymmetric under particle permutations. Coherence-induced many-body effects such as superradiance, however, can arise even in systems whose constituents are not fundamentally indistinguishable as long as all relevant dynamical observables are permutation-invariant. Such systems are not confined to symmetric or antisymmetric states and therefore require a different theoretical approach. Focusing on noninteracting systems, here we combine tools from representation theory and thermodynamically consistent master equations to develop such a framework. We characterize the structure and properties of the steady states emerging in permutation-invariant ensembles of arbitrary multilevel systems that are collectively weakly coupled to a thermal environment. As an application of our general theory, we further explore how these states can in principle be used to enhance the performance of quantum thermal machines. Our group-theoretical framework thereby makes it possible to analyze various limiting cases that would not be accessible otherwise. In addition, it allows us to show that the properties of multilevel ensembles differ qualitatively from those of spin ensembles, which have been investigated earlier using the standard Clebsch-Gordan theory. Our results have a large scope for future generalizations and pave the way for systematic investigations of collective effects arising from permutation invariance in quantum thermodynamics.
This subject introduces the key concepts and formalism of quantum mechanics and their relevance to topics in current research and to practical applications. Starting from the foundation of quantum mechanics and its applications in simple discrete systems, it develops the basic principles of interaction of electromagnetic radiation with matter. Topics covered are composite systems and entanglement, open system dynamics and decoherence, quantum theory of radiation, time-dependent perturbation the...