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Journal articles on the topic 'Quantum mechanics'

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Published: 4 June 2021

Last updated: 30 July 2024

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1

UBRIACO, MARCELO R. "QUANTUM DEFORMATIONS OF QUANTUM MECHANICS." Modern Physics Letters A 08, no. 01 (January 10, 1993): 89–96. http://dx.doi.org/10.1142/s0217732393000106.

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Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

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2

Liboff, Richard L., P. J. Peebles, and David Finkelstein. "Introductory Quantum Mechanics and Quantum Mechanics." Physics Today 46, no. 4 (April 1993): 60–62. http://dx.doi.org/10.1063/1.2808872.

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3

Mercier de Lépinay, Laure, Caspar F. Ockeloen-Korppi, Matthew J. Woolley, and Mika A. Sillanpää. "Quantum mechanics–free subsystem with mechanical oscillators." Science 372, no. 6542 (May 6, 2021): 625–29. http://dx.doi.org/10.1126/science.abf5389.

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Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics–free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.

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4

YF, Chang. "Restructure of Quantum Mechanics by Duality, the Extensive Quantum Theory and Applications." Physical Science & Biophysics Journal 8, no. 1 (February 2, 2024): 1–9. http://dx.doi.org/10.23880/psbj-16000265.

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Reconstructing quantum mechanics has been an exploratory direction for physicists. Based on logical structure and basic principles of quantum mechanics, we propose a new method on reconstruction quantum mechanics completely by the waveparticle duality. This is divided into two steps: First, from wave form and duality we obtain the extensive quantum theory, which has the same quantum formulations only with different quantum constants H; then microscopic phenomena determine H=h. Further, we derive the corresponding commutation relation, the uncertainty principle and Heisenberg equation, etc. Then we research potential and interactions in special relativity and general relativity. Finally, various applications and developments, and some basic questions are discussed.

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5

Luna, Homero. "The Mercury Orbit and the Quantum Mechanics." International Journal of Science and Research (IJSR) 12, no. 9 (September 5, 2023): 487–88. http://dx.doi.org/10.21275/sr23310042612.

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6

Hammerer, K. "Quantum Mechanics Tackles Mechanics." Science 342, no. 6159 (November 7, 2013): 702–3. http://dx.doi.org/10.1126/science.1245797.

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7

Farina, John, and Franz Schwabl. "Quantum Mechanics." Mathematical Gazette 77, no. 480 (November 1993): 394. http://dx.doi.org/10.2307/3619811.

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8

Sontag, Frederick. "Quantum Mechanics." International Studies in Philosophy 24, no. 1 (1992): 97–98. http://dx.doi.org/10.5840/intstudphil199224121.

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9

Rae, Alastair I. M., and Doug Cohn. "Quantum Mechanics." American Journal of Physics 53, no. 9 (September 1985): 925. http://dx.doi.org/10.1119/1.14383.

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10

McMurry, Sara M., and Donald H. Kobe. "Quantum Mechanics." American Journal of Physics 63, no. 7 (July 1995): 671–72. http://dx.doi.org/10.1119/1.17836.

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11

Ballentine, Leslie E., and David Griffiths. "Quantum Mechanics." American Journal of Physics 59, no. 12 (December 1991): 1153–54. http://dx.doi.org/10.1119/1.16631.

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12

Beeby, J. L. "Quantum mechanics." Endeavour 17, no. 1 (March 1993): 42. http://dx.doi.org/10.1016/0160-9327(93)90017-w.

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13

Charlesby, A. "Quantum mechanics." Radiation Physics and Chemistry 48, no. 4 (October 1996): 530–31. http://dx.doi.org/10.1016/0969-806x(96)82562-x.

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14

Merzbacher, Eugen, and Daniel Greenberger. "Quantum Mechanics." Physics Today 52, no. 5 (May 1999): 64–66. http://dx.doi.org/10.1063/1.882667.

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15

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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16

Fernández de Córdoba, P., J. M. Isidro, Milton H. Perea, and J. Vazquez Molina. "The irreversible quantum." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550013. http://dx.doi.org/10.1142/s0219887815500139.

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We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.

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17

Owczarek, Robert. "Quantum mechanics for quantum computing." Journal of Knot Theory and Its Ramifications 25, no. 03 (March 2016): 1640009. http://dx.doi.org/10.1142/s0218216516400095.

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Quantum computing is a field of great interest, attracting, among others, the attention of many mathematicians. Although not all quantum mechanics is needed to successfully engage in research on quantum computing, the somewhat superficial approach usually applied by non-physicists is, in the opinion of the author of the lectures, not feasible. The following notes from lectures given at the mathematics department of George Washington University are meant to be a partial remedy to the situation, offering a very brief and slightly unorthodox introduction to one-particle quantum mechanics, and even shorter discussion of passage to multi-particle quantum mechanics, as needed for quantum computing.

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18

Niehaus, Arend. "Quantum Interference without Quantum Mechanics." Journal of Modern Physics 10, no. 04 (2019): 423–31. http://dx.doi.org/10.4236/jmp.2019.104027.

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19

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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20

Gavrilik, A. M., I. I. Kachurik, and A. V. Lukash. "New Version of q-Deformed Supersymmetric Quantum Mechanics." Ukrainian Journal of Physics 58, no. 11 (November 2013): 1025–32. http://dx.doi.org/10.15407/ujpe58.11.1025.

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21

Beyer, Michael, and Wolfgang Paul. "On the Stochastic Mechanics Foundation of Quantum Mechanics." Universe 7, no. 6 (May 27, 2021): 166. http://dx.doi.org/10.3390/universe7060166.

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Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the wave-function. This article recaps the development of stochastic mechanics with a focus on variational and extremal principles. Furthermore, based on recent developments of optimal control theory, the derivation of generalized canonical equations of motion for quantum systems within the stochastic picture are discussed. These so-called quantum Hamilton equations add another layer to the different formalisms from classical mechanics that find their counterpart in quantum mechanics.

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22

Nash, C. G., and G. C. Joshi. "Quaternionic quantum mechanics is consistent with complex quantum mechanics." International Journal of Theoretical Physics 31, no. 6 (June 1992): 965–81. http://dx.doi.org/10.1007/bf00675088.

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23

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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24

Schwab, Keith C., and Michael L. Roukes. "Putting Mechanics into Quantum Mechanics." Physics Today 58, no. 7 (July 2005): 36–42. http://dx.doi.org/10.1063/1.2012461.

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25

De-Ming, Ren. "Classical Mechanics and Quantum Mechanics." Communications in Theoretical Physics 41, no. 5 (May 15, 2004): 685–88. http://dx.doi.org/10.1088/0253-6102/41/5/685.

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26

ACOSTA, D., P. FERNÁNDEZ DE CÓRDOBA, J. M. ISIDRO, and J. L. G. SANTANDER. "EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS." International Journal of Geometric Methods in Modern Physics 10, no. 04 (March 6, 2013): 1350007. http://dx.doi.org/10.1142/s0219887813500072.

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We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.

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27

Yamaguchi, Y. "Quantum Mechanics and Quantum Field Theories in the Quantized Space. II: -- Quantum Mechanics --." Progress of Theoretical Physics 113, no. 4 (April 1, 2005): 883–909. http://dx.doi.org/10.1143/ptp.113.883.

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28

Yokoi, Yuho, and Sumiyoshi Abe. "On quantum-mechanical origin of statistical mechanics." Journal of Physics: Conference Series 1113 (November 2018): 012012. http://dx.doi.org/10.1088/1742-6596/1113/1/012012.

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29

Lawrence, Jay, Marcin Markiewicz, and Marek Żukowski. "Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics." Quantum 7 (May 23, 2023): 1015. http://dx.doi.org/10.22331/q-2023-05-23-1015.

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Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory \cite{Rovelli.21}. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system S and an observer A without decoherence, and (ii) such an outcome is a "fact" relative to the observer A, but it is not a fact relative to another observer B who has not interacted with S or A during the foregoing measurement process. For B the system S⊗A remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.

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30

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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31

Walmsley, M., and J. R. Killingbeck. "Microcomputer Quantum Mechanics." Mathematical Gazette 69, no. 448 (June 1985): 153. http://dx.doi.org/10.2307/3616960.

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32

Mudge, Michael R., and R. C. Greenhow. "Introductory Quantum Mechanics." Mathematical Gazette 75, no. 474 (December 1991): 495. http://dx.doi.org/10.2307/3618668.

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33

Farina, John E. G., W. Greiner, and B. Muller. "Quantum Mechanics: Symmetries." Mathematical Gazette 75, no. 472 (June 1991): 262. http://dx.doi.org/10.2307/3620315.

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34

Mills, Randell L. "Classical Quantum Mechanics." Physics Essays 16, no. 4 (December 2003): 433–98. http://dx.doi.org/10.4006/1.3025609.

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35

Vedral, Vlatko. "Untangling quantum mechanics." Nature 420, no. 6913 (November 2002): 271. http://dx.doi.org/10.1038/420271a.

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36

Frappier, Mélanie. "Questioning quantum mechanics." Science 359, no. 6383 (March 29, 2018): 1474.1–1474. http://dx.doi.org/10.1126/science.aas9190.

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37

Tati, T. "Local Quantum Mechanics." Progress of Theoretical Physics 78, no. 5 (November 1, 1987): 996–1008. http://dx.doi.org/10.1143/ptp.78.996.

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38

Laskin, Nick. "Fractional quantum mechanics." Physical Review E 62, no. 3 (September 1, 2000): 3135–45. http://dx.doi.org/10.1103/physreve.62.3135.

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39

Zhang, Qi, and Biao Wu. "Lorentz quantum mechanics." New Journal of Physics 20, no. 1 (January 22, 2018): 013024. http://dx.doi.org/10.1088/1367-2630/aa8496.

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40

FRYDRYSZAK, ANDRZEJ M. "NILPOTENT QUANTUM MECHANICS." International Journal of Modern Physics A 25, no. 05 (February 20, 2010): 951–83. http://dx.doi.org/10.1142/s0217751x10047786.

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We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (η-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of η-wavefunctions, η-Hilbert space and generalized Schrödinger equation we study properties of pure multiqubit systems and also properties of some composed, hybrid models: fermion–qubit, boson–qubit. The fermion–qubit system can be truly supersymmetric, with both SUSY partners having identical spectra. It is a novel feature that SUSY transformations relate here only nilpotent object. The η-eigenfunctions of the Hamiltonian for the qubit–qubit system give the set of Bloch vectors as a natural basis.

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41

Swanson, John. "‘Advance’ quantum mechanics." Physics World 27, no. 05 (May 2014): 56. http://dx.doi.org/10.1088/2058-7058/27/05/48.

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42

Hiller, J. R., I. D. Johnston, D. F. Styer, Dale Syphers, Susan R. McKay, and Wolfgang Christian. "Quantum Mechanics Simulations." Computers in Physics 10, no. 3 (1996): 260. http://dx.doi.org/10.1063/1.4822398.

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43

Counihan, Martin. "Nonrelativistic Quantum Mechanics." Physics Bulletin 37, no. 12 (December 1986): 503. http://dx.doi.org/10.1088/0031-9112/37/12/040.

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44

Odake, Satoru, and Ryu Sasaki. "Discrete quantum mechanics." Journal of Physics A: Mathematical and Theoretical 44, no. 35 (August 10, 2011): 353001. http://dx.doi.org/10.1088/1751-8113/44/35/353001.

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45

Brody, Dorje C. "Biorthogonal quantum mechanics." Journal of Physics A: Mathematical and Theoretical 47, no. 3 (December 24, 2013): 035305. http://dx.doi.org/10.1088/1751-8113/47/3/035305.

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46

Mackintosh, Ray. "Summertime quantum mechanics." Physics World 2, no. 10 (October 1989): 68. http://dx.doi.org/10.1088/2058-7058/2/10/32.

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47

Sakurai, Jun John, San Fu Tuan, and Roger G. Newton. "Modern Quantum Mechanics." Physics Today 39, no. 7 (July 1986): 69–70. http://dx.doi.org/10.1063/1.2815083.

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48

Bender, Carl M., Maarten DeKieviet, and S. P. Klevansky. "PT quantum mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120523. http://dx.doi.org/10.1098/rsta.2012.0523.

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-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.

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49

Weinstein, Steven. "Absolute Quantum Mechanics." British Journal for the Philosophy of Science 52, no. 1 (March 1, 2001): 67–73. http://dx.doi.org/10.1093/bjps/52.1.67.

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50

Sakurai, J. J., and Richard L. Liboff. "Modern Quantum Mechanics." American Journal of Physics 54, no. 7 (July 1986): 668. http://dx.doi.org/10.1119/1.14491.

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