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Journal articles on the topic 'Symmetry (Physics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Wang, Yifeng. "Symmetry and symmetric transformations in mathematical imaging." Theoretical and Natural Science 31, no. 1 (April 2, 2024): 320–23. http://dx.doi.org/10.54254/2753-8818/31/20241037.

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The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.

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2

Iachello, F. "Symmetry in physics." European Physical Journal A 20, no. 1 (April 2003): 1–3. http://dx.doi.org/10.1140/epja/i2003-10193-0.

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3

Osborne, I. S. "PHYSICS: Stimulated Symmetry." Science 317, no. 5846 (September 28, 2007): 1834d—1835d. http://dx.doi.org/10.1126/science.317.5846.1834d.

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4

Barone, M., and A. K. Theophilou. "Symmetry and symmetry breaking in modern physics." Journal of Physics: Conference Series 104 (March 1, 2008): 012037. http://dx.doi.org/10.1088/1742-6596/104/1/012037.

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5

Kosso, Peter. "Symmetry arguments in physics." Studies in History and Philosophy of Science Part A 30, no. 3 (September 1999): 479–92. http://dx.doi.org/10.1016/s0039-3681(99)00012-6.

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6

Green, HS. "A Cyclic Symmetry Principle in Physics." Australian Journal of Physics 47, no. 1 (1994): 25. http://dx.doi.org/10.1071/ph940025.

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Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow 7r-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow 7r-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras.

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7

Boi, Luciano. "Symmetry and Symmetry Breaking in Physics: From Geometry to Topology." Symmetry 13, no. 11 (November 5, 2021): 2100. http://dx.doi.org/10.3390/sym13112100.

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Symmetry (and group theory) is a fundamental principle of theoretical physics. Finite symmetries, continuous symmetries of compact groups, and infinite-dimensional representations of noncompact Lie groups are at the core of solid physics, particle physics, and quantum physics, respectively. The latter groups now play an important role in many branches of mathematics. In more recent years, we have been faced with the impact of topological quantum field theory (TQFT). Topology and symmetry have deep connections, but topology is inherently broader and more complex. While the presence of symmetry in physical phenomena imposes strong constraints, topology seems to be related to low-energy states and is very likely to provide information about the different dynamical trajectories and patterns that particles can follow. For example, regarding the relationship of topology to low-energy states, Hodge’s theory of harmonic forms shows that the zero-energy states (for differential forms) correspond to the cohomology. Regarding the relationship of topology to particle trajectories, a topological knot can be seen as an orbit with complex properties in spacetime. The various deformations or embeddings of the knot, performed in low or high dimensions, allow defining different equivalence classes or topological types, and interestingly, it is possible from these types to study the symmetries associated with the deformations and their changes. More specifically, in the present work, we address two issues: first, that quantum geometry deforms classical geometry, and that this topological deformation may produce physical effects that are specific to the quantum physics scale; and second, that mirror symmetry and the phenomenon of topological change are closely related. This paper was aimed at understanding the conceptual and physical significance of this connection.

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8

HOURI, TSUYOSHI. "KILLING–YANO SYMMETRY IN SUPERGRAVITY THEORIES." International Journal of Modern Physics: Conference Series 21 (January 2013): 132–35. http://dx.doi.org/10.1142/s2010194513009483.

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Killing–Yano symmetry has played an important role in the study of black hole physics. In supergravity theories, Killing–Yano symmetry is deformed by the presence of the fluxes which can be identified with skew-symmetric torsion. Therefore, we attempt to classify spacetimes admitting Killing-Yano symmetry with torsion. In particular, the classification problem of metrics admitting a principal Killing–Yano tensor with torsion is discussed.

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9

Faraoni, Valerio. "Turnaround physics beyond spherical symmetry." Journal of Physics: Conference Series 2156, no. 1 (December 1, 2021): 012017. http://dx.doi.org/10.1088/1742-6596/2156/1/012017.

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Abstract The concept of turnaround radius in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, as needed by astronomy. As a check, previous results for small deviations from spherical symmetry are recovered.

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10

Bahri, C., J. Draayer, and S. Moszkowski. "Pseudospin symmetry in nuclear physics." Physical Review Letters 68, no. 14 (April 1992): 2133–36. http://dx.doi.org/10.1103/physrevlett.68.2133.

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11

Koptsik, V. A. "Generalized symmetry in crystal physics." Computers & Mathematics with Applications 16, no. 5-8 (1988): 407–24. http://dx.doi.org/10.1016/0898-1221(88)90231-3.

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12

Gross, David J. "Symmetry in Physics: Wigner's Legacy." Physics Today 48, no. 12 (December 1995): 46–50. http://dx.doi.org/10.1063/1.881480.

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13

Bagnato, Vanderlei S., Rashid G. Nazmitdinov, and Vyacheslav I. Yukalov. "Symmetry in Many-Body Physics." Symmetry 15, no. 1 (December 27, 2022): 72. http://dx.doi.org/10.3390/sym15010072.

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14

Shuryak, E. V. "Physics of chiral symmetry breaking." Nuclear Physics A 527 (May 1991): 513–18. http://dx.doi.org/10.1016/0375-9474(91)90147-x.

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15

Hu, Zhou, Zhao-Yun Zeng, Jia Tang, and Xiao-Bing Luo. "Quasi-parity-time symmetric dynamics in periodically driven two-level non-Hermitian system." Acta Physica Sinica 71, no. 7 (2022): 074207. http://dx.doi.org/10.7498/aps.70.20220270.

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<sec>In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare.</sec><sec></sec><sec>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.</sec>

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16

Kim, M., Y. Yang, Y. S. Gui, and C. M. Hu. "Visualization of synchronization zone on the Bloch sphere through an anti-PT-symmetric electrical circuit." AIP Advances 12, no. 3 (March 1, 2022): 035217. http://dx.doi.org/10.1063/5.0081693.

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This work reports an analysis of the anti-parity-time (APT) symmetry system produced by pure dissipative coupled passive electric oscillators. Through spectral and time-domain measurements, the complex eigenfrequencies of the APT-symmetric system were measured. Interesting physics, such as exceptional points, APT-symmetry breaking transitions, and frequency synchronization with explicitly defined phase differences, were observed. Most importantly, we found that synchronous signals span the equator of the Bloch sphere. Therefore, our methodology functions as an analogon understructure to explore APT-symmetric systems.

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17

Eltschka, Christopher, and Jens Siewert. "Optimal class-specific witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry." Quantum Information and Computation 13, no. 3&4 (March 2013): 210–20. http://dx.doi.org/10.26421/qic13.3-4-3.

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Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for detecting class-specific entanglement in arbitrary three-qubit states.

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18

Gazeau, Jean-Pierre. "The Language of Spheres in Physics." Universe 10, no. 3 (March 1, 2024): 117. http://dx.doi.org/10.3390/universe10030117.

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Physical laws manifest themselves through the amalgamation of mathematical symbols, numbers, functions, geometries, and relationships. These intricate combinations unfold within a mathematical model devised to capture and represent the “objective reality” of the system under examination. In this symbiotic relationship between physics and mathematics, the language of mathematics becomes a powerful tool for describing and predicting the behavior of the physical world. The language used and the associated concepts are in a perpetual state of evolution, mirroring the ongoing expansion of the phenomena accessible to our scientific understanding. In this contribution, written in honor of Richard Kerner, we delve into fundamental, at times seemingly elementary, elements of the mathematical language inherent to the physical sciences, guided by the overarching principles of symmetry and group theory. Our focus turns to the captivating realm of spheres, those strikingly symmetric entities that manifest prominently within our geometric landscape. By exploring the interplay between mathematical abstraction and the tangible beauty of symmetry, we seek to deepen our understanding of the underlying structures that govern our interpretation of the physical world.

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19

Koch, Volker. "Aspects of Chiral Symmetry." International Journal of Modern Physics E 06, no. 02 (June 1997): 203–49. http://dx.doi.org/10.1142/s0218301397000147.

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This article is an attempt to a pedagogical introduction and review into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.

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20

Ferrando, Albert, and Miguel Ángel García-March. "Symmetry in Electromagnetism." Symmetry 12, no. 5 (April 26, 2020): 685. http://dx.doi.org/10.3390/sym12050685.

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21

Li, Chunbiao, Zhinan Li, Yicheng Jiang, Tengfei Lei, and Xiong Wang. "Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry." Symmetry 15, no. 8 (August 10, 2023): 1564. http://dx.doi.org/10.3390/sym15081564.

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A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.

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22

Petitjean, Michel. "Symmetry, Antisymmetry, and Chirality: Use and Misuse of Terminology." Symmetry 13, no. 4 (April 4, 2021): 603. http://dx.doi.org/10.3390/sym13040603.

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We outline the need for rigorous and consensual definitions in the field of symmetry, in particular about chirality. We provide examples of confusing use of such terminology in the mathematical literature and in the physics literature. In particular, we prove that an antisymmetric function is symmetric for a wide class of metrics. It may be either direct-symmetric or achiral or both direct-symmetric and achiral.

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23

Mannheim, Philip D. "Symmetry and spontaneously broken symmetry in the physics of elementary particles." Computers & Mathematics with Applications 12, no. 1-2 (January 1986): 169–83. http://dx.doi.org/10.1016/0898-1221(86)90149-5.

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24

Kudryashova, Olga B. "Dispersed Systems: Physics, Optics, Invariants, Symmetry." Symmetry 14, no. 8 (August 4, 2022): 1602. http://dx.doi.org/10.3390/sym14081602.

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25

Yavahchova, Mariya S., and Dimitar Tonev. "Example for symmetry in nuclear physics." Symmetry: Culture and Science 32, no. 2 (2021): 294–97. http://dx.doi.org/10.26830/symmetry_2021_2_294.

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26

Gaponov, Y. V., D. M. Vladimirov, and J. Bang. "Spin-isospin symmetry in nuclear physics." Acta Physica Hungarica A) Heavy Ion Physics 3, no. 3-4 (August 1996): 189–228. http://dx.doi.org/10.1007/bf03053666.

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27

Villain, J. "Symmetry and group theory throughout physics." EPJ Web of Conferences 22 (2012): 00002. http://dx.doi.org/10.1051/epjconf/20122200002.

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28

El-Ganainy, Ramy, Konstantinos G. Makris, Mercedeh Khajavikhan, Ziad H. Musslimani, Stefan Rotter, and Demetrios N. Christodoulides. "Non-Hermitian physics and PT symmetry." Nature Physics 14, no. 1 (January 2018): 11–19. http://dx.doi.org/10.1038/nphys4323.

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29

Baker, David John. "Symmetry and the Metaphysics of Physics." Philosophy Compass 5, no. 12 (December 2010): 1157–66. http://dx.doi.org/10.1111/j.1747-9991.2010.00361.x.

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30

Kaneko, Toshiaki, and Hirotaka Sugawara. "Broken S3 symmetry in flavor physics." Physics Letters B 697, no. 4 (March 2011): 329–32. http://dx.doi.org/10.1016/j.physletb.2011.02.017.

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31

Rosen, Joe. "Fundamental manifestations of symmetry in physics." Foundations of Physics 20, no. 3 (March 1990): 283–307. http://dx.doi.org/10.1007/bf00731694.

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32

Shirkov, D. V. "Imagery of symmetry in current physics." Theoretical and Mathematical Physics 170, no. 2 (February 2012): 239–48. http://dx.doi.org/10.1007/s11232-012-0026-5.

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33

Ahmed, Zafar. "PT-symmetry in conventional quantum physics." Journal of Physics A: Mathematical and General 39, no. 32 (July 26, 2006): 9965–74. http://dx.doi.org/10.1088/0305-4470/39/32/s01.

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34

Kreinovich, Vladik, and Luc Longpré. "Unreasonable effectiveness of symmetry in physics." International Journal of Theoretical Physics 35, no. 7 (July 1996): 1549–55. http://dx.doi.org/10.1007/bf02084960.

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35

Tselnik, F. "Platonic solids symmetry in particle physics." Communications in Nonlinear Science and Numerical Simulation 12, no. 8 (December 2007): 1427–39. http://dx.doi.org/10.1016/j.cnsns.2006.03.016.

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36

Iachello, F. "Symmetry and supersymmetry in nuclear physics." La Rivista del Nuovo Cimento 19, no. 7 (July 1996): 1–26. http://dx.doi.org/10.1007/bf02757355.

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37

Chmyr’, S. N., A. S. Kazakov, A. V. Galeeva, D. E. Dolzhenko, A. I. Artamkin, A. V. Ikonnikov, N. N. Mikhailov, et al. "PT-Symmetric Microwave Photoconductivity in Heterostructures Based on the Hg1 − xCdxTe Topological Phase." JETP Letters 118, no. 5 (September 2023): 339–42. http://dx.doi.org/10.1134/s0021364023602385.

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The PT-symmetric photoconductivity has been detected for the first time in microwave-irradiated heterostructures based on thick Hg1 −xCdxTe films with the CdTe content x corresponding to the topological phase although the magnetic field symmetry (T symmetry) and the symmetry in the positions of potential contact pairs (P symmetry) are not conserved separately. The microwave photoconductivity in similar heterostructures based on the trivial Hg1 −xCdxTe phase is both P- and T-symmetric.

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38

Tishchenko, I. Yu, D. Yu Tishchenko, S. A. Zavgorodny, and S. A. Berezhanskaya. "SPONTANEOUS SYMMETRY BREAKING ON THE EXAMPLE OF THE KLEIN —GORDON REAL FIELD." Chronos 7, no. 5(67) (August 13, 2022): 55–58. http://dx.doi.org/10.52013/2658-7556-67-5-18.

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This scientific work examiner symmetry in nature and physics, its mathematical description. The spontaneous breaking of the Klein—Gordon real field is considered. The role of symmetry and spontaneous symmetry breaking in the development of physics is shown.

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39

GEORGI, HOWARD. "UNPARTICLE PHYSICS." International Journal of Modern Physics A 25, no. 02n03 (January 30, 2010): 573–86. http://dx.doi.org/10.1142/s0217751x1004886x.

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40

dell’Isola, Francesco, and Hovik A. Matevossian. "Foundations of Continuum Mechanics and Mathematical Physics—Editorial 2021–2023." Symmetry 15, no. 9 (August 25, 2023): 1643. http://dx.doi.org/10.3390/sym15091643.

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41

Schlatter, Andreas. "On the Role of Unitary-Symmetry for the Foundation of Probability and Time in a Realist Approach to Quantum Physics." Symmetry 10, no. 12 (December 10, 2018): 737. http://dx.doi.org/10.3390/sym10120737.

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We show that probabilities in quantum physics can be derived from permutation-symmetry and the principle of indifference. We then connect unitary-symmetry to the concept of “time” and define a thermal time-flow by symmetry breaking. Finally, we discuss the coexistence of quantum physics and relativity theory by making use of the thermal time-flow.

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42

Watanabe, Hikaru, and Youichi Yanase. "Magnetic parity violation and parity-time-reversal-symmetric magnets." Journal of Physics: Condensed Matter 36, no. 37 (June 19, 2024): 373001. http://dx.doi.org/10.1088/1361-648x/ad52dd.

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Abstract Parity-time-reversal symmetry ( PT symmetry), a symmetry for the combined operations of space inversion ( P ) and time reversal ( T ), is a fundamental concept of physics and characterizes the functionality of materials as well as P and T symmetries. In particular, the PT -symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leaves PT symmetry intact, the simultaneous violation of P and T symmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagnetic P -symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

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Tan, Wanpeng. "Mirror Symmetry for New Physics beyond the Standard Model in 4D Spacetime." Symmetry 15, no. 7 (July 14, 2023): 1415. http://dx.doi.org/10.3390/sym15071415.

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The two discrete generators of the full Lorentz group O(1,3) in 4D spacetime are typically chosen to be parity inversion symmetry P and time reversal symmetry T, which are responsible for the four topologically separate components of O(1,3). Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of P, while CP symmetry resembles T in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi–Yau mirror symmetry in string theory is clarified. Extension beyond the Standard Model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy are discussed.

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KATZIR, SHAUL. "The emergence of the principle of symmetry in physics." Historical Studies in the Physical and Biological Sciences 35, no. 1 (September 1, 2004): 35–65. http://dx.doi.org/10.1525/hsps.2004.35.1.35.

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ABSTRACT: In 1894 Pierre Curie formulated rules for relations between physical phenomena and their symmetry. The symmetry concept originated in the geometrical study of crystals, which it served as a well-defined concept from the 1830s. Its extension as a rule for all physics was a gradual and slow process in which applications, though often partial, preceded the formulation and clear conceptualization of the rules. Two traditions that involved ““interdisciplinary”” study were prominent in applying consideration of symmetry to physics. One is a French tradition of physical crystallography that linked crystalline structure and form to their physical, chemical and even biological qualities, which drew back to Haüüy, and included Delafosse, Pasteur, Senarmont, and Curie. This tradition (until Curie) employed qualitative argument in deducing physical properties. A mathematical approach characterizes the second tradition of Franz Neumann and his students. During the 1880s two members of this tradition, Minnigerode and Voigt, formulated rules of symmetry and implicitly recognized their significance. Yet, until 1894 both traditions studied only crystalline or other asymmetric matter. Then, Curie, who drew on the two traditions, extended the rules of symmetry to any physical system including fields and forces. Although originated in a specific idealistic ontological context, symmetry served also adherents of molecular materialism and was eventually found most effective for a phenomenological approach, which avoided any commitment to a specific view of nature or causal processes. Therefore, the rule of symmetry resembles the principles of thermodynamics. Its emergence suggests parallels to the history of energy conservation.

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45

Bochkarev, N. G., and M. Yu Khlopov. "Observational Physics of Mirror World." Symposium - International Astronomical Union 183 (1999): 309. http://dx.doi.org/10.1017/s0074180900133005.

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Mirror (shadow) particles are required to restore symmetry between left- and right-handed coordinate systems. If mirror world exists, it has been born at the same time as the ordinary world and has the same evolution (in the case of the shadow world - broken mirror symmetry, the evolution and structure of the shadow world does not correspond with the observed world). Mirror world is a kind of dark matter. According to Bahcall (1984) local dark matter has a density approximately equal to the density of observed (ordinary) matter.

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46

LaBorde, Margarite L., Soorya Rethinasamy, and Mark M. Wilde. "Testing symmetry on quantum computers." Quantum 7 (September 25, 2023): 1120. http://dx.doi.org/10.22331/q-2023-09-25-1120.

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Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.

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47

Hammer, Hans-Werner, and Dam Thanh Son. "Unnuclear physics: Conformal symmetry in nuclear reactions." Proceedings of the National Academy of Sciences 118, no. 35 (August 23, 2021): e2108716118. http://dx.doi.org/10.1073/pnas.2108716118.

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Abstract:

We investigate a nonrelativistic version of Georgi’s “unparticle physics.” We define the unnucleus as a field in a nonrelativistic conformal field theory. Such a field is characterized by a mass and a conformal dimension. We then consider the formal problem of scatterings to a final state consisting of a particle and an unnucleus and show that the differential cross-section, as a function of the recoil energy received by the particle, has a power-law singularity near the maximal recoil energy, where the power is determined by the conformal dimension of the unnucleus. We argue that unlike the relativistic unparticle, which remains a hypothetical object, the unnucleus is realized, to a good approximation, in nuclear reactions involving emission of a few neutrons, when the energy of the final-state neutrons in their center-of-mass frame lies in the range between about 0.1 MeV and 5 MeV. Combining this observation with the known universal properties of fermions at unitarity in a harmonic trap, we predict a power-law behavior of an inclusive cross-section in this kinematic regime. We verify our predictions with previous effective field theory and model calculations of the 6He(p,pα)2n, 3H(π−,γ)3n, and 3H(μ−,νμ)3n reactions and discuss opportunities to measure unnuclei at radioactive beam facilities.

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48

Hill, Christopher T., and Leon M. Lederman. "Teaching symmetry in the introductory physics curriculum." Physics Teacher 38, no. 6 (September 2000): 348–53. http://dx.doi.org/10.1119/1.1321816.

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49

Iachello, Francesco. "The role of symmetry in nuclear physics." Journal of Physics: Conference Series 580 (February 9, 2015): 012041. http://dx.doi.org/10.1088/1742-6596/580/1/012041.

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50

Ovchinnikova, E. N., and R. N. Kuz'min. "Symmetry in the nuclear solid state physics." Computers & Mathematics with Applications 16, no. 5-8 (1988): 657–61. http://dx.doi.org/10.1016/0898-1221(88)90253-2.

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