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Journal articles on the topic 'Quantum trajectories, Quantum mechanics, statistical mechanics'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Grössing, Gerhard. "Emergence of quantum mechanics from a sub-quantum statistical mechanics." International Journal of Modern Physics B 28, no. 26 (October 20, 2014): 1450179. http://dx.doi.org/10.1142/s0217979214501793.

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A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.

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Aragón-Muñoz, L., G. Chacón-Acosta, and H. Hernandez-Hernandez. "Effective quantum tunneling from a semiclassical momentous approach." International Journal of Modern Physics B 34, no. 29 (October 28, 2020): 2050271. http://dx.doi.org/10.1142/s0217979220502719.

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In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.

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3

FERRY, D. K., R. AKIS, and J. P. BIRD. "EDGE STATES AND TRAJECTORIES IN QUANTUM DOTS: PROBING THE QUANTUM-CLASSICAL TRANSITION." International Journal of Modern Physics B 21, no. 08n09 (April 10, 2007): 1278–87. http://dx.doi.org/10.1142/s0217979207042744.

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Edge states have been a backbone of our understanding of the experimental basis of the quantum Hall effect for quite some time. Interestingly, this comprises a quantum system with well defined currents and particle trajectories. The role of trajectories in quantum mechanics has been a problematic question of interpretation for quite some time, and the open quantum dot is a natural system in which to probe this question. Contrary to early speculation, a set of well defined quantum states survives in the open quantum dot. These states are the pointer states and provide a transition into the classical states that can be found in these structures. These states provide resonances, which are observable as oscillatory behavior in the magnetoconductance of the dots. But, they have well defined current directions within the dots. Consequently, one expects trajectories to be a property of these states as well. As one crosses from the low to the high field regime, quite steady trajectories and consequent wave functions can easily be identified and examined. In this talk, we review the current understanding and the support for the decoherence theory.

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4

Yang, Ciann-Dong, and Shiang-Yi Han. "Extending Quantum Probability from Real Axis to Complex Plane." Entropy 23, no. 2 (February 8, 2021): 210. http://dx.doi.org/10.3390/e23020210.

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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability |Ψ|2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.

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5

ELLIS, JOHN, N. E. MAVROMATOS, and D. V. NANOPOULOS. "VALLEYS IN NONCRITICAL STRING FOAM SUPPRESS QUANTUM COHERENCE." Modern Physics Letters A 10, no. 05 (February 20, 1995): 425–40. http://dx.doi.org/10.1142/s0217732395000466.

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As an example of our noncritical string approach to microscopic black hole dynamics, we exhibit some string contributions to the [Formula: see text] matrix relating in- and out-state density matrices that do not factorize as a product of S and S† matrices. They are associated with valley trajectories between topological defects on the string worldsheet, that appear as quantum fluctuations in the space-time foam. Through their uv renormalization scale dependences these valleys cause non-Hamiltonian time evolution and suppress off-diagonal entries in the density matrix at large times. Our approach is a realization of previous formulations of nonequilibrium quantum statistical mechanics with an arrow of time.

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6

Prigogine, Ilya. "From Poincare's Divergences to Quantum Mechanics with Broken Time Symmetry." Zeitschrift für Naturforschung A 52, no. 1-2 (February 1, 1997): 37–45. http://dx.doi.org/10.1515/zna-1997-1-212.

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AbstractWe discuss the spectral property of unstable dynamical systems in both classical and quantum mechanics. An important class of unstable dynamical systems corresponds to the Large Poincare Systems (LPS). Conventional perturbation technique leads then to divergences. We introduce methods for the elimination of Poincare divergences to obtain a solution of the spectral problem analytic in the coupling constant. To do so, we have to enlarge the class of permissible transformations, to include non-unitary transformations as well as to extend the Hilbert space. A simple example refers to the Friedrichs model, which was studied independently by George Sudarshan and his co-workers. However, our main interest is the irreducible representations in the Liouville space. In these representations the central quantity is the density matrix, and the eigenfunctions of the Liouville operator cannot be expressed in terms of the wave functions. We suggest that this situation corresponds to quantum chaos. Indeed, classical chaos does not mean that Newton's equation becomes "wrong" but that trajectories loose their operational meaning. Similarly, whenever we have an irreducible representation in the Liouville space this means that the wave function description looses its operational meaning. Additional statistical features appear. A simple example corresponds to persistent interactions in the scattering problem which cannot be treated in the frame of usual S-matrix theory.

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7

Horton, George, and Chris Dewdney. "A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories." Journal of Physics A: Mathematical and General 34, no. 46 (November 13, 2001): 9871–78. http://dx.doi.org/10.1088/0305-4470/34/46/310.

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8

Горобей, Н. Н., and А. С. Лукьяненко. "О термодинамических параметрах адиабатически изолированного тела." Физика твердого тела 63, no. 5 (2021): 663. http://dx.doi.org/10.21883/ftt.2021.05.50818.003.

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The definition of the main thermodynamic functions for an adiabatically isolated body with constant internal energy is proposed in the framework of the formalism of the covariant quantum theory with reparametrization invariance of proper time. The modification does not change the dynamic content of the theory at the classical level, but it allows one to define the unitary evolution operator in quantum theory. In this operator, proper time is a measure of the internal movement of the body. The transition to statistical mechanics is carried out by the Wick rotation of proper time in the complex plane. As a result, a representation of the partition function of an isolated body in the form of a Euclidean functional integral on the space of closed trajectories in the configuration space is obtained. For a given internal energy, the average return temperature and free energy are determined, which under lie the thermomechanics of an adiabatically isolated body.

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9

Krok, Kamila A., Artur P. Durajski, and Radosław Szczȩśniak. "The Abraham–Lorentz force and the time evolution of a chaotic system: The case of charged classical and quantum Duffing oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073130. http://dx.doi.org/10.1063/5.0090477.

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This paper proves that the Abraham–Lorentz (AL) force can noticeably modify the trajectories of the charged Duffing oscillators over time. The influence of the reaction force on the oscillator evolution is strongly enhanced if the system is considered at the level of quantum mechanics. For example, the AL force examined within the scope of Newtonian description can change the trajectory of the Duffing oscillator only if it has the mass of an electron. However, we showed that when quantum corrections along with the nondeterministic contributions are taken into account, the reaction force of the electromagnetic field affects noticeably even the oscillator with a mass equal to the mass of the [Formula: see text] ion. The charged Duffing oscillators belong to the class of systems characterized by the chaotic nondeterministic dynamics. In classical terms, the nondeterministic behavior of the discussed systems results from the breaking of the causality principle by the AL force.

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10

Kovalenko, Andriy. "Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials." Pure and Applied Chemistry 85, no. 1 (January 4, 2013): 159–99. http://dx.doi.org/10.1351/pac-con-12-06-03.

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Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.

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11

Griffiths, Robert B. "Consistent interpretation of quantum mechanics using quantum trajectories." Physical Review Letters 70, no. 15 (April 12, 1993): 2201–4. http://dx.doi.org/10.1103/physrevlett.70.2201.

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12

Kyprianidis, A. "Particle trajectories in relativistic quantum mechanics." Physics Letters A 111, no. 3 (September 1985): 111–16. http://dx.doi.org/10.1016/0375-9601(85)90435-9.

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13

Raedt, H. De, A. H. Hams, K. Michielsen, S. Miyashita, and K. Saito. "Quantum Statistical Mechanics on a Quantum Computer." Progress of Theoretical Physics Supplement 138 (2000): 489–94. http://dx.doi.org/10.1143/ptps.138.489.

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14

Ubriaco, Marcelo R. "Quantum group invariant, nonextensive quantum statistical mechanics." Physics Letters A 283, no. 3-4 (May 2001): 157–62. http://dx.doi.org/10.1016/s0375-9601(01)00236-5.

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15

Yan, GU. "Quantum statistical mechanics, quantum probability and quantum characteristic function." SCIENTIA SINICA Physica, Mechanica & Astronomica 50, no. 7 (April 20, 2020): 070002. http://dx.doi.org/10.1360/sspma-2019-0365.

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16

Fink, Helmut, and Hajo Leschke. "Comment on ‘‘Consistent interpretation of quantum mechanics using quantum trajectories’’." Physical Review Letters 72, no. 11 (March 14, 1994): 1770. http://dx.doi.org/10.1103/physrevlett.72.1770.

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17

Brody, Dorje C., and Lane P. Hughston. "Statistical geometry in quantum mechanics." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, no. 1977 (September 8, 1998): 2445–75. http://dx.doi.org/10.1098/rspa.1998.0266.

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18

Kaniadakis, G. "Statistical origin of quantum mechanics." Physica A: Statistical Mechanics and its Applications 307, no. 1-2 (April 2002): 172–84. http://dx.doi.org/10.1016/s0378-4371(01)00626-4.

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19

Maćkowiak, J. "Operator algebras and quantum statistical mechanics II, equilibrium states, models in quantum statistical mechanics." Reports on Mathematical Physics 21, no. 3 (June 1985): 419–20. http://dx.doi.org/10.1016/0034-4877(85)90042-4.

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20

Frieden, B. Roy, and A. Plastino. "Alternative classical trajectories compatible with quantum mechanics." Physics Letters A 287, no. 5-6 (September 2001): 325–30. http://dx.doi.org/10.1016/s0375-9601(01)00481-9.

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21

Eveson, Simon P., Christopher J. Fewster, and Rainer Verch. "Quantum Inequalities in Quantum Mechanics." Annales Henri Poincaré 6, no. 1 (February 2005): 1–30. http://dx.doi.org/10.1007/s00023-005-0197-9.

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22

Khrennikov, Andrei. "Quantum mechanics from statistical mechanics of classical fields." Journal of Physics: Conference Series 70 (May 1, 2007): 012009. http://dx.doi.org/10.1088/1742-6596/70/1/012009.

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23

Chu, Shu-Yuan. "Statistical origin of classical mechanics and quantum mechanics." Physical Review Letters 71, no. 18 (November 1, 1993): 2847–50. http://dx.doi.org/10.1103/physrevlett.71.2847.

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24

Cini, Marcello, and Maurizio Serva. "Measurement in quantum mechanics and classical statistical mechanics." Physics Letters A 167, no. 4 (July 1992): 319–25. http://dx.doi.org/10.1016/0375-9601(92)90265-n.

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25

WIDOM, A., and Y. N. SRIVASTAVA. "QUANTUM FLUID MECHANICS AND QUANTUM ELECTRODYNAMICS." Modern Physics Letters B 04, no. 01 (January 10, 1990): 1–8. http://dx.doi.org/10.1142/s0217984990000027.

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The commutation relations of Landau quantum fluid mechanics are compared with those of quantum electrodynamics. In both cases, the operator representation of the commutators require a macroscopic phase, and a wavefunction periodic in that phase. A physical discussion is given for analogous effects in superfluids and superconductors, with regard to quantum coherence on a macroscopic scale. Other applications are then briefly described.

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26

Ralston, John P. "and quantum mechanics embedded in symplectic quantum mechanics." Journal of Physics A: Mathematical and Theoretical 40, no. 32 (July 24, 2007): 9883–904. http://dx.doi.org/10.1088/1751-8113/40/32/013.

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27

Zhang, Zhidong. "Topological Quantum Statistical Mechanics and Topological Quantum Field Theories." Symmetry 14, no. 2 (February 4, 2022): 323. http://dx.doi.org/10.3390/sym14020323.

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The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z2 symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan–von Neumann–Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan–von Neumann–Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.

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28

Smolin, Lee. "Quantum gravity and the statistical interpretation of quantum mechanics." International Journal of Theoretical Physics 25, no. 3 (March 1986): 215–38. http://dx.doi.org/10.1007/bf00668705.

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29

Carrara, Nicholas. "Quantum Trajectories in Entropic Dynamics." Proceedings 33, no. 1 (December 13, 2019): 25. http://dx.doi.org/10.3390/proceedings2019033025.

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Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

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30

BANNUR, VISHNU M., and K. M. UDAYANANDAN. "STATISTICAL MECHANICS OF CONFINED QUANTUM PARTICLES." Modern Physics Letters A 22, no. 30 (September 28, 2007): 2297–305. http://dx.doi.org/10.1142/s0217732307022499.

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We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose–Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.

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31

Lenzi, E. K., R. S. Mendes, and A. K. Rajagopal. "Quantum statistical mechanics for nonextensive systems." Physical Review E 59, no. 2 (February 1, 1999): 1398–407. http://dx.doi.org/10.1103/physreve.59.1398.

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32

Providencia, J. da, and C. Fiolhais. "Variational principles in quantum statistical mechanics." European Journal of Physics 8, no. 1 (January 1, 1987): 12–17. http://dx.doi.org/10.1088/0143-0807/8/1/004.

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33

NEŠKOVIĆ, P. V., and B. V. UROŠEVIĆ. "QUANTUM OSCILLATORS: APPLICATIONS IN STATISTICAL MECHANICS." International Journal of Modern Physics A 07, no. 14 (June 10, 1992): 3379–88. http://dx.doi.org/10.1142/s0217751x92001496.

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We consider a canonical ensemble of q oscillators. Using classical realization for q oscillator algebra,17 we calculate, for a small real q, the partition function and thermodynamic potentials F, E and S. We show that F reaches the minimum and E and S the maximum (as functions of the deformation parameter q) when q = 1 (for the classical oscillator). We argue about possible far-reaching consequences of this fact. As an application we obtain a first quantum correction to Planck's black body radiation law. We introduce the slightly deformed oscillator (SDO) model, which provides us with a significant amount of information about the system. When q = 1, our results are shown to coincide with classical results.

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34

Nielsen, Steve, Raymond Kapral, and Giovanni Ciccotti. "Statistical mechanics of quantum-classical systems." Journal of Chemical Physics 115, no. 13 (October 2001): 5805–15. http://dx.doi.org/10.1063/1.1400129.

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35

Klein, U. "The Statistical Origins of Quantum Mechanics." Physics Research International 2010 (February 23, 2010): 1–18. http://dx.doi.org/10.1155/2010/808424.

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It is shown that Schrödinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared, and some fundamental differences are identified.

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36

Consani, Caterina, and Matilde Marcolli. "Quantum statistical mechanics over function fields." Journal of Number Theory 123, no. 2 (April 2007): 487–528. http://dx.doi.org/10.1016/j.jnt.2006.12.002.

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37

Cornelissen, Gunther, and Matilde Marcolli. "Graph reconstruction and quantum statistical mechanics." Journal of Geometry and Physics 72 (October 2013): 110–17. http://dx.doi.org/10.1016/j.geomphys.2013.03.021.

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38

Marcolli, Matilde, and Yujie Xu. "Quantum statistical mechanics in arithmetic topology." Journal of Geometry and Physics 114 (April 2017): 153–83. http://dx.doi.org/10.1016/j.geomphys.2016.11.029.

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39

Sen, Diptiman. "Quantum and statistical mechanics of anyons." Nuclear Physics B 360, no. 2-3 (August 1991): 397–408. http://dx.doi.org/10.1016/0550-3213(91)90408-p.

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40

Schmidt, Andreas U. "Zeno dynamics in quantum statistical mechanics." Journal of Physics A: Mathematical and General 36, no. 4 (January 15, 2003): 1135–48. http://dx.doi.org/10.1088/0305-4470/36/4/319.

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41

Schmidt, A. U. "Zeno dynamics in quantum statistical mechanics." Journal of Physics A: Mathematical and General 37, no. 46 (November 4, 2004): 11309–10. http://dx.doi.org/10.1088/0305-4470/37/46/c01.

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42

Zaripov, R. G. "Parastatistics in Quantum Nonextensive Statistical Mechanics." Russian Physics Journal 59, no. 12 (April 2017): 2059–67. http://dx.doi.org/10.1007/s11182-017-1014-x.

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43

Robles-Pérez, Salvador J. "Quantum Cosmology in the Light of Quantum Mechanics." Galaxies 7, no. 2 (April 24, 2019): 50. http://dx.doi.org/10.3390/galaxies7020050.

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There is a formal analogy between the evolution of the universe, when it is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e., evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

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44

Hall, Richard L. "Constructive inversion of energy trajectories in quantum mechanics." Journal of Mathematical Physics 40, no. 2 (February 1999): 699–707. http://dx.doi.org/10.1063/1.532712.

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45

Dewdney, C. "Nonlocally correlated trajectories in two-particle quantum mechanics." Foundations of Physics 18, no. 9 (September 1988): 867–86. http://dx.doi.org/10.1007/bf01855940.

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46

Cufaro-Petroni, Nicola, and Jean-Pierre Vigier. "Single-particle trajectories and interferences in quantum mechanics." Foundations of Physics 22, no. 1 (January 1992): 1–40. http://dx.doi.org/10.1007/bf01883379.

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47

Antoine, J.-P. "Relativistic Quantum Mechanics." Journal of Physics A: Mathematical and General 37, no. 4 (January 9, 2004): 1465. http://dx.doi.org/10.1088/0305-4470/37/4/b01.

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Whitaker, A. "Quantum Mechanics: Fundamentals." Journal of Physics A: Mathematical and General 37, no. 8 (February 11, 2004): 3073–76. http://dx.doi.org/10.1088/0305-4470/37/8/b01.

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Boghosian, Bruce M., and Washington Taylor. "Simulating quantum mechanics on a quantum computer." Physica D: Nonlinear Phenomena 120, no. 1-2 (September 1998): 30–42. http://dx.doi.org/10.1016/s0167-2789(98)00042-6.

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UGULAVA, A., L. CHOTORLISHVILI, T. GVARJALADZE, and S. CHKHAIDZE. "INVESTIGATION OF THE QUANTUM CHAOS OF INTERNAL ROTATIONAL MOTION IN POLYATOMIC MOLECULES." Modern Physics Letters B 21, no. 07 (March 20, 2007): 415–30. http://dx.doi.org/10.1142/s0217984907012840.

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Abstract:

Polyatomic molecules can perform internal rotational motion of two types: torsional oscillation and free rotation of one part of the molecule with respect to the other part. On the phase plane, these two types of motion are separated by the separatrix. Phase trajectories, originated as a result of periodical external force action on the system, have stochastic nature. For quantum consideration, regarding the motion near to the classical separatrix, transition from the pure quantum-mechanical state to the mixed one takes place. Originating at that mixed state, this must be considered as the quantum analog of the classical dynamic stochasticity and is named as the quantum chaos. This work is devoted to the investigation of the quantum chaos manifestation in the polyatomic molecules, which have a property that performs internal rotation. For the molecule of ethane C 2 H 6, the emergence of quantum chaos and possible ways of its experimental observation has been studied. It is shown that radio-frequency field can produce the non-direct transitions between rotational and oscillatory states. These transitions, being the sign of the existence of quantum chaos, are able to change population levels sizeably. Due to this phenomenon, experimental observation of the infrared absorption is possible.

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