Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

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Validity of Molecular Dynamics by Quantum Mechanics

ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer ◽

10.1115/mnhmt2013-22027 ◽

2013 ◽

Author(s):

Thomas Prevenslik

Keyword(s):

Molecular Dynamics ◽

Heat Capacity ◽

Quantum Mechanics ◽

Statistical Mechanics ◽

Quantum Electrodynamics ◽

Md Simulations ◽

Tensile Tests ◽

Electron Pairs ◽

Linear Motors ◽

The Continuum

MD is commonly used in computational physics to determine the atomic response of nanostructures. MD stands for molecular dynamics. With theoretical basis in statistical mechanics, MD relates the thermal energy of the atom to its momentum by the equipartition theorem. Momenta of atoms in an ensemble are determined by solving Newton’s equations with inter-atomic forces derived from Lennard-Jones potentials. MD therefore assumes the atom always has heat capacity as otherwise the momenta of the atoms cannot be related to their temperature. In bulk materials, the continuum is simulated in MD by imposing PBC on an ensemble of atoms, the atoms always having heat capacity. PBC stands for periodic boundary conditions. MD simulations of the bulk are valid because atoms in the bulk do indeed have heat capacity. Nanostructures differ from the bulk. Unlike the continuum, the atom confined in discrete submicron geometries is precluded by QM from having the heat capacity necessary to conserve absorbed EM energy by an increase in temperature. QM stands for quantum mechanics and EM for electromagnetic. Quantum corrections of MD solutions that would show the heat capacity of nanostructures vanishes are not performed. What this means is the MD simulations of discrete nanostructures in the literature not only have no physical meaning, but are knowingly invalid by QM. In the alternative, conservation of absorbed EM energy is proposed to proceed by the creation of QED induced non-thermal EM radiation at the TIR frequency of the nanostructure. QED stands for quantum electrodynamics and TIR for total internal reflection. The QED radiation creates excitons (holon and electron pairs) that upon recombination produce EM radiation that charges the nanostructure or is emitted to the surroundings — a consequence only possible by QM as charge is not created in statistical mechanics. Invalid discrete MD simulations are illustrated with nanofluids, nanocars, linear motors, and sputtering. Finally, a valid MD simulation by QM is presented for the stiffening of NWs in tensile tests. NW stands for nanowire.

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Exploring Classical Mechanics

10.1093/oso/9780198853787.001.0001 ◽

2020 ◽

Author(s):

G. L. Kotkin ◽

V. G. Serbo

Keyword(s):

Quantum Mechanics ◽

Statistical Mechanics ◽

Classical Mechanics ◽

Theoretical Physics ◽

English Edition ◽

Mechanical Part ◽

Russian Edition ◽

The Given

This book was written by the working physicists for students and teachers of physics faculties of universities. Its contents correspond roughly to the corresponding course in the textbooks Mechanics by L. D. Landau and E. M. Lifshitz (1976) and Classical Mechanics by H. Goldstein, Ch. Poole, and J. Safko (2000). As a rule, the given solution of a problem is not finished with obtaining the required formulae. It is necessary to analyse the results, and this is of great interest and by no means a mechanical part of the solution. The authors consider classical mechanics as the first chapter of theoretical physics; the methods and ideas developed in this chapter are literally important for all other sections of theoretical physics. Thus, the authors have indicated wherever this does not require additional amplification, the analogy or points of contact with the problems in quantum mechanics, electrodynamics, or statistical mechanics. The first English edition of this book was published by Pergamon Press in 1971 with the invaluable help by the translation editor D. ter Haar. This second English publication is based on the fourth Russian edition of 2010 as well as the problems added in the publications in Spanish and French. As a result, this book contains 357 problems instead of the 289 problems that appeared in the first English edition.

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15N NMR Shifts of Eumelanin Building Blocks in Water: A Combined Quantum Mechanics/Statistical Mechanics Approach

Molecules ◽

10.3390/molecules25163616 ◽

2020 ◽

Vol 25 (16) ◽

pp. 3616

Author(s):

Leonardo Bruno Assis Oliveira ◽

Tertius L. Fonseca ◽

Benedito J. C. Cabral

Keyword(s):

Quantum Mechanics ◽

Statistical Mechanics ◽

Gas Phase ◽

Marked Effect ◽

Complex Structure ◽

Building Blocks ◽

15N Nmr ◽

Magnetic Shielding ◽

Atomic Orbitals ◽

Theoretical Results

Theoretical results for the magnetic shielding of protonated and unprotonated nitrogens of eumelanin building blocks including monomers, dimers, and tetramers in gas phase and water are presented. The magnetic property in water was determined by carrying out Monte Carlo statistical mechanics sampling combined with quantum mechanics calculations based on the gauge-including atomic orbitals approach. The results show that the environment polarization can have a marked effect on nitrogen magnetic shieldings, especially for the unprotonated nitrogens. Large contrasts of the oligomerization effect on magnetic shielding show a clear distinction between eumelanin building blocks in solution, which could be detected in nuclear magnetic resonance experiments. Calculations for a π-stacked structure defined by the dimer of a tetrameric building block indicate that unprotonated N atoms are significantly deshielded upon π stacking, whereas protonated N atoms are slightly shielded. The results stress the interest of NMR experiments for a better understanding of the eumelanin complex structure.

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