A Comparison between Classical Theory of Motional Narrowing and Narrowing Due to Quantum Mechanical Tunnelling Motion

The paper shows that the quantum-mechanical approach is applicable to most macro processes occurring in nature include the power industry. The mathematical apparatus of the isomorphic Heisenberg algebra is proposed. A non-commutative ring is constructed within which the commutation relations are given. The transition from quantum to classical theory is shown.

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Quantum-mechanical solution to fundamental problems of classical theory of water vapor nucleation

Physical Review E ◽

10.1103/physreve.79.021604 ◽

2009 ◽

Vol 79 (2) ◽

Cited By ~ 7

Author(s):

Hua Du ◽

Alexey B. Nadykto ◽

Fangqun Yu

Keyword(s):

Water Vapor ◽

Classical Theory ◽

Quantum Mechanical ◽

Quantum Mechanical Solution ◽

Vapor Nucleation

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The interaction of point particles with charged fields

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100025056 ◽

1949 ◽

Vol 45 (3) ◽

pp. 429-440 ◽

Cited By ~ 12

Author(s):

K. J. Le Couteur

Keyword(s):

Classical Theory ◽

Quantum Mechanical ◽

Neutral Meson ◽

Rest Energy ◽

Point Particles ◽

Neutral Mesons ◽

Meson Theory ◽

Quantum Mechanical Effects ◽

Charged Mesons ◽

A Charge

1. The method introduced by Dirac (1) in his classical theory of the interaction of an electron with an electromagnetic field has since been extended to the interaction of point particles with more general wave fields, such as occur in the neutral meson theory. Bhabha (2, 3) considered the scattering of neutral mesons by nucleons and gave arguments to show that typically quantum-mechanical effects should be unimportant if the energy of the incident meson is less than the rest energy of a nucleon, so that a classical theory with damping is appropriate to such problems. Now only the charged mesons are observable, and therefore a discussion of the classical theory of the interaction of a nucleon with a charge-bearing field is desirable. Apart from a paper by Fierz (4) which omits the dipole-like coupling terms, there is little published work on this subject.

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PRESSURE PROFILES FOR BOSONS IN TRAPS

Modern Physics Letters B ◽

10.1142/s0217984908014742 ◽

2008 ◽

Vol 22 (03) ◽

pp. 209-217

Author(s):

SHALINI LUMB ◽

S. K. MUTHU ◽

K. K. SINGH

Keyword(s):

Critical Temperature ◽

Classical Theory ◽

Weak Interactions ◽

Quantum Statistics ◽

Quantum Mechanical ◽

Exact Quantum ◽

Pressure Profiles ◽

Repulsive Interactions ◽

Grand Canonical

Pressure profiles P(R) for non-interacting bosons in an isotropic trap have been calculated exactly by applying the grand canonical method of quantum statistics to particles in a subsphere of the system. The results are compared with those of local Fermi–Thomas (semi-classical) theory both for non-interacting bosons as well as for bosons having weakly repulsive interactions between them. The essential conclusions are (i) that in the non-degenerate regions, both below as well as above the critical temperature, the pressure profiles remain essentially unaffected by weak interactions, and (ii) that near the center of the trap, the exact quantum mechanical profiles are appreciably lower than the semi-classical profiles.

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Quantum Criticality

Zeitschrift für Naturforschung A ◽

10.1515/zna-2001-0120 ◽

2001 ◽

Vol 56 (1-2) ◽

pp. 133-139 ◽

Cited By ~ 1

Author(s):

P. D. Drummond ◽

S. Chaturvedi ◽

K. Dechoum ◽

J. Comey

Keyword(s):

Classical Theory ◽

Quantum Fluctuations ◽

Quantum Criticality ◽

Quantum Mechanical Calculation ◽

Quantum Mechanical ◽

Pacs 03.65 ◽

Schrödinger Cat ◽

Term Objective ◽

Space Equation

Abstract We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrödinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrödinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrödinger cat. -Pacs: 03.65.Bz

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Analysing causal structures in generalised probabilistic theories

Quantum ◽

10.22331/q-2020-02-27-236 ◽

2020 ◽

Vol 4 ◽

pp. 236 ◽

Cited By ~ 1

Author(s):

Mirjam Weilenmann ◽

Roger Colbeck

Keyword(s):

Classical Theory ◽

Convex Cone ◽

Causal Explanation ◽

Causal Structure ◽

Quantum Mechanical ◽

Probabilistic Theory ◽

Special Cases ◽

Classical Quantum ◽

Causal Structures ◽

Probabilistic Theories

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.

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Emergent quantum mechanics as a thermal ensemble

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814500686 ◽

2014 ◽

Vol 11 (08) ◽

pp. 1450068 ◽

Cited By ~ 6

Author(s):

P. Fernández De Córdoba ◽

J. M. Isidro ◽

Milton H. Perea

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Classical Theory ◽

Thermal Fluctuations ◽

Irreversible Processes ◽

Quantum Mechanical ◽

Transformation Theory ◽

Time Irreversibility ◽

Quantum Mechanical Systems ◽

Emergent Quantum Mechanics

It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool toward this goal, we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.

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