Journal articles: 'Born rule'

1

Shrapnel, Sally, Fabio Costa, and Gerard Milburn. "Updating the Born rule." New Journal of Physics 20, no. 5 (May 4, 2018): 053010. http://dx.doi.org/10.1088/1367-2630/aabe12.

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2

Logiurato, Fabrizio, and Augusto Smerzi. "Born Rule and Noncontextual Probability." Journal of Modern Physics 03, no. 11 (2012): 1802–12. http://dx.doi.org/10.4236/jmp.2012.311225.

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3

Rae, Alastair I. M. "Everett and the Born rule." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40, no. 3 (August 2009): 243–50. http://dx.doi.org/10.1016/j.shpsb.2009.06.001.

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4

Ericksen, J. L. "On the Cauchy—Born Rule." Mathematics and Mechanics of Solids 13, no. 3-4 (May 2008): 199–220. http://dx.doi.org/10.1177/1081286507086898.

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5

Monod, Paul, and Ellis Wasson. "Born to Rule: British Political Elites." Albion: A Quarterly Journal Concerned with British Studies 35, no. 1 (2003): 139. http://dx.doi.org/10.2307/4054549.

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6

Rubinstein, W. D. "Born to Rule: British Political Elites." English Historical Review 117, no. 472 (June 1, 2002): 730. http://dx.doi.org/10.1093/ehr/117.472.730.

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7

De Zela, Francisco. "Gudder’s Theorem and the Born Rule." Entropy 20, no. 3 (March 2, 2018): 158. http://dx.doi.org/10.3390/e20030158.

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8

Page, Don N. "The Born rule fails in cosmology." Journal of Cosmology and Astroparticle Physics 2009, no. 07 (July 3, 2009): 008. http://dx.doi.org/10.1088/1475-7516/2009/07/008.

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9

Weinberg, S. L. "System/apparatus superposition and the Born rule." Physics Essays 21, no. 1 (March 1, 2008): 78–83. http://dx.doi.org/10.4006/1.3001691.

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10

Costins, Pauline. "Refining or defining the Born Alive Rule?" Women and Birth 26 (October 2013): S24. http://dx.doi.org/10.1016/j.wombi.2013.08.168.

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11

Cooperman, Joshua H. "Rescuing the Born rule for quantum cosmology." Journal of Cosmology and Astroparticle Physics 2011, no. 02 (February 9, 2011): 014. http://dx.doi.org/10.1088/1475-7516/2011/02/014.

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12

Arve, Per. "Everett’s Missing Postulate and the Born Rule." Foundations of Physics 50, no. 7 (April 26, 2020): 665–92. http://dx.doi.org/10.1007/s10701-020-00338-4.

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13

Prodanov, Dimiter. "The Burgers equations and the Born rule." Chaos, Solitons & Fractals 144 (March 2021): 110637. http://dx.doi.org/10.1016/j.chaos.2020.110637.

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14

de Gosson, Maurice. "Short-Time Propagators and the Born–Jordan Quantization Rule." Entropy 20, no. 11 (November 10, 2018): 869. http://dx.doi.org/10.3390/e20110869.

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We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born–Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

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15

Cour, Brian R. La, and Morgan C. Williamson. "Emergence of the Born rule in quantum optics." Quantum 4 (October 26, 2020): 350. http://dx.doi.org/10.22331/q-2020-10-26-350.

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The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of reproducing several observed phenomena thought to be uniquely quantum in nature, thus providing greater elucidation of the quantum-classical boundary.

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16

Oeckl, Robert. "Born rule and Schroedinger equation from first principles." Journal of Physics: Conference Series 1275 (September 2019): 012049. http://dx.doi.org/10.1088/1742-6596/1275/1/012049.

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17

Saunders, Simon. "Derivation of the Born rule from operational assumptions." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460, no. 2046 (June 8, 2004): 1771–88. http://dx.doi.org/10.1098/rspa.2003.1230.

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18

Schlosshauer, Maximilian, and Arthur Fine. "On Zurek?s Derivation of the Born Rule." Foundations of Physics 35, no. 2 (February 2005): 197–213. http://dx.doi.org/10.1007/s10701-004-1941-6.

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19

Pozrikidis, C. "On the applicability of the Cauchy-Born rule." Computational Materials Science 46, no. 2 (August 2009): 438–42. http://dx.doi.org/10.1016/j.commatsci.2009.03.031.

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20

Ojima, Izumi, Kazuya Okamura, and Hayato Saigo. "Derivation of Born Rule from Algebraic and Statistical Axioms." Open Systems & Information Dynamics 21, no. 03 (August 7, 2014): 1450005. http://dx.doi.org/10.1142/s123016121450005x.

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In this paper we propose a new system of algebraic and statistical axioms as working hypotheses, from which Born rule can be seen to emerge. In this process the concept of sectors defined as quasi-equivalence classes of factor states plays a crucial role.

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21

Oliva-Leyva, Maurice, and Chumin Wang. "Theory for Strained Graphene Beyond the Cauchy-Born Rule." physica status solidi (RRL) - Rapid Research Letters 12, no. 9 (July 4, 2018): 1800237. http://dx.doi.org/10.1002/pssr.201800237.

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22

Towler, M. D., N. J. Russell, and Antony Valentini. "Time scales for dynamical relaxation to the Born rule." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (November 30, 2011): 990–1013. http://dx.doi.org/10.1098/rspa.2011.0598.

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We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born rule ones and stay there; in analogy with the classical case this represents a decay to ‘quantum equilibrium’. The proximity to equilibrium is characterized by the coarse-grained subquantum H -function which is found to decrease roughly exponentially towards zero over the course of time. The time scale τ for this relaxation is calculated for various values of M and the coarse-graining length ε . Its dependence on M is found to disagree with an earlier theoretical prediction. A power law, τ ∝ M −1 , is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of τ on ε is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of time scales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early Universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.

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23

Patterson, J. D., and S. L. Lehoczky. "The second Born approximation and the Friedel sum rule." Physics Letters A 137, no. 3 (May 1989): 137–38. http://dx.doi.org/10.1016/0375-9601(89)90099-6.

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24

Hsu, Stephen D. H. "Discrete Hilbert space, the Born Rule, and quantum gravity." Modern Physics Letters A 36, no. 03 (January 28, 2021): 2150013. http://dx.doi.org/10.1142/s0217732321500139.

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Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

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25

LANDSMAN, N. P. "MACROSCOPIC OBSERVABLES AND THE BORN RULE, I: LONG RUN FREQUENCIES." Reviews in Mathematical Physics 20, no. 10 (November 2008): 1173–90. http://dx.doi.org/10.1142/s0129055x08003511.

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We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein [17] and Hartle [21], intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program — notably the one due to Farhi, Goldstone, and Gutmann [15] as completed by Van Wesep [50] — in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. Furthermore, instead of relying on the controversial eigenstate-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables.

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26

Chandraseker, Karthick, and Subrata Mukherjee. "Coupling of Extension and Twist in Single-Walled Carbon Nanotubes." Journal of Applied Mechanics 73, no. 2 (August 22, 2005): 315–26. http://dx.doi.org/10.1115/1.2125987.

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This paper presents a study of the deformation behavior of single-walled carbon nanotubes (SWNTs) subjected to extension and twist. The interatomic force description is provided by the Tersoff-Brenner potential for carbon. The rolling of a flat graphene sheet into a SWNT is first simulated by minimizing the energy per atom, the end result being the configuration of an undeformed SWNT. The Cauchy-Born rule is then used to connect the atomistic and continuum descriptions of the deformation of SWNTs, and leads to a multilength scale mechanics framework for simulating deformation of SWNTs under applied loads. Coupled extension and twist of SWNTs is considered next. As an alternative to the Cauchy-Born rule for coupled extension-twist problems, a direct map is formulated. Analytic expressions are derived for the deformed bond lengths using the Cauchy-Born rule and the direct map for this class of deformations. Numerical results are presented for kinematic coupling, for imposed extension and imposed twist problems, using the Cauchy-Born rule as well as the direct map, for representative chiral, armchair and zig-zag SWNTs. Results from both these approaches are carefully compared.

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27

LU, S., C. D. CHO, and L. SONG. "ENERGY OF ARMCHAIR NANOTUBE USING THE MODIFIED CAUCHY-BORN RULE." International Journal of Modern Physics B 22, no. 31n32 (December 30, 2008): 5881–86. http://dx.doi.org/10.1142/s0217979208051315.

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Due to the difference of nanotube diameters, the single-walled carbon nanotubes (SWCNTs) show the different energy and mechanical properties. In order to take the effect of the curvature of nanotubes into account in the modeling of those structures, the present paper proposes an atomistic based continuum model with using a type of modified Cauchy-Born to link the continuum strain energy to the interatomic potential. This modified Cauchy-Born is developed by incorporating the concept of differential mean value theorem into the standard Cauchy-Born rule. The present model not only can bridge the microscopic and macroscopic length scales, but also can investigate the curvature effect of a single layer film on the continuum level. Application of the current model to armchair carbon nanotubes and graphite shows an excellent prediction of the size dependent strain energy which are compared in a good agreement with the existing experimental and theoretical results.

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28

Fauser, Bertfried, Guillaume Raynaud, and Steven Vickers. "The Born rule as structure of spectral bundles (extended abstract)." Electronic Proceedings in Theoretical Computer Science 95 (October 1, 2012): 81–90. http://dx.doi.org/10.4204/eptcs.95.8.

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29

Bacci, Marco, and Paolo Maria Mariano. "Protein dynamics: An approach based on the Cauchy–Born rule." Physica E: Low-dimensional Systems and Nanostructures 61 (July 2014): 69–82. http://dx.doi.org/10.1016/j.physe.2014.03.009.

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30

Brezhnev, Yurii V. "The Born rule as a statistics of quantum micro-events." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2244 (December 2020): 20200282. http://dx.doi.org/10.1098/rspa.2020.0282.

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We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a linear, not Hilbert’, vector space—and empirical notion of the Statistical Length of a state. Its statistical nature comes from the lab micro-events (detector-clicks) being formalized into the C -coefficients of quantum superpositions. We also comment that not only has the use not been made of quantum axioms (scalar-product, operators, interpretations , etc.), but that the involving thereof would be, in a sense, inconsistent when deriving the rule. In point of fact, the quadratic character of the statistical length, and even not (the ‘physics’ of) Born’s formula, represents a first step in constructing the mathematical structure we name the Hilbert space of quantum states.

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31

Harris, Jérémie, Frédéric Bouchard, Enrico Santamato, Wojciech H. Zurek, Robert W. Boyd, and Ebrahim Karimi. "Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule." New Journal of Physics 18, no. 5 (May 11, 2016): 053013. http://dx.doi.org/10.1088/1367-2630/18/5/053013.

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32

Kollander, Patricia. "Born to Rule: Five Reigning Consorts, Granddaughters of Queen Victoria." History: Reviews of New Books 34, no. 1 (January 2005): 22. http://dx.doi.org/10.1080/03612759.2005.10526743.

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33

Donoghue, Victoria A., and David H. Nachman. "Foreign-born scientists and the two-year home residency rule." JOM 62, no. 4 (April 2010): 80. http://dx.doi.org/10.1007/s11837-010-0065-z.

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34

Bonness, Dania Jovanna. "The Northern Subject Rule in the Irish diaspora." English World-Wide 38, no. 2 (September 19, 2017): 125–52. http://dx.doi.org/10.1075/eww.38.2.01bon.

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Abstract This article examines the Northern Subject Rule in the Irish diaspora, studying letters from two generations of an Ulster emigrant family in 19th-century New Zealand. The study shows that the concord pattern frequently used by the parent generation almost completely disappeared in the language of their New Zealand-born children. The results suggest that the children skipped the stage of “extreme variability” that is claimed to be characteristic of the language of the first colony-born immigrants in the new-dialect formation framework (Trudgill 2004). This study aims to contribute to work on early New Zealand English grammar (e.g. Hundt 2012, 2015a, 2015b; Hundt and Szmrecsanyi 2012) and it adds new insights into the formation of New Zealand English. It, furthermore, contributes to research on dialect contact between Irish English and other colonial varieties of English as well as new-dialect formation.

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35

ENDO, RIKA, RIE KURIKI, AKIO SUGAMOTO, and SHIN'ICHI NOJIRI. "A RULE OF THUMB DERIVATION OF BORN–INFELD ACTION FOR D-BRANES." Modern Physics Letters A 13, no. 16 (May 30, 1998): 1309–17. http://dx.doi.org/10.1142/s0217732398001364.

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A rule of thumb derivation of the Dirac–Born–Infeld action for D-branes is studied à la Fradkin and Tseytlin, by simply integrating out of the superstring coordinates in a narrow strip attached to the D-branes. In case of superstrings, the coupling of Ramond–Ramond fields as well as the Dirac–Born–Infeld type coupling of the Neveu Schwarz–Neveu Schwarz fields come out in this way.

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36

Hanson, Robin D. "Drift–diffusion in mangled worlds quantum mechanics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (February 21, 2006): 1619–27. http://dx.doi.org/10.1098/rspa.2005.1640.

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In Everett's many-worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world measure. I solve a growth–drift–diffusion–absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus, inexact decoherence may allow the Born rule to be derived in a many-worlds approach via world counting, using a finite number of worlds and no new fundamental physics.

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37

Schumann, Thomas G. "Three arguments for the quantum dream analogy plus Born Rule derivation." Physics Essays 24, no. 4 (December 2011): 564–69. http://dx.doi.org/10.4006/1.3655848.

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38

Powell, James M. "Calixtus II (1119-1124): A Pope Born to Rule. Mary Stroll." Speculum 81, no. 3 (July 2006): 925–27. http://dx.doi.org/10.1017/s0038713400016511.

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39

Shan, Wenzhe, and Udo Nackenhorst. "Applying Cauchy-Born rule for converting atomistic model to continuum model." PAMM 10, no. 1 (November 16, 2010): 425–26. http://dx.doi.org/10.1002/pamm.201010205.

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40

Richards, Bernadette, Bill Madden, and Tina Cockburn. "Considering the “Born-Alive” Rule and Possession of Sperm Following Death." Journal of Bioethical Inquiry 8, no. 4 (September 13, 2011): 323–27. http://dx.doi.org/10.1007/s11673-011-9324-0.

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41

Lu, Sheng, and Chongdu Cho. "A New Extension of Cauchy–Born Rule for Monolayer Crystal Films." Nanoscale Research Letters 5, no. 5 (March 23, 2010): 863–67. http://dx.doi.org/10.1007/s11671-010-9576-3.

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42

E, Weinan, and Pingbing Ming. "Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems." Archive for Rational Mechanics and Analysis 183, no. 2 (September 13, 2006): 241–97. http://dx.doi.org/10.1007/s00205-006-0031-7.

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43

Xiao, Shaoping, and Weixuan Yang. "Temperature-related Cauchy–Born rule for multiscale modeling of crystalline solids." Computational Materials Science 37, no. 3 (September 2006): 374–79. http://dx.doi.org/10.1016/j.commatsci.2005.09.007.

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44

Wei-nan*, E., and Ming Ping-bing**. "Cauchy-Born Rule and the Stability of Crystalline Solids: Dynamic Problems." Acta Mathematicae Applicatae Sinica, English Series 23, no. 4 (October 2007): 529–50. http://dx.doi.org/10.1007/s10255-007-0393.

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45

Luo, Tao, Yang Xiang, Jerry Zhijian Yang, and Cheng Yuan. "Cauchy–Born rule and stability of crystalline solids at finite temperature." Communications in Mathematical Sciences 19, no. 6 (2021): 1461–90. http://dx.doi.org/10.4310/cms.2021.v19.n6.a1.

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46

Hsu, Stephen D. H. "The measure problem in no-collapse (many worlds) quantum mechanics." International Journal of Modern Physics D 26, no. 03 (February 3, 2017): 1730008. http://dx.doi.org/10.1142/s0218271817300087.

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We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

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47

Baán, Izsák. "Nyugati életszabály, keleti ihletettség a 6. század eleji latin szerzetesség világából." Belvedere Meridionale 32, no. 1 (2020): 17–32. http://dx.doi.org/10.14232/belv.2020.1.3.

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Amongst the early Latin, pre-benedictine monastic legislative texts there is a rule called “Regula Orientalis” conserved in the Codex Regularum of Saint Benedict of Aniane. Although it says nothing about its author and the community it was written to, it is easy to discover that its text quotes a lot from the Latin version of Saint Pachomius’ Rule translated by Saint Jerome and from an other source very close to the early rules of Lerins, particularly to the so called Second rule of the Fathers. The Regula Orientalis is a detailed presentation of the most important monastic charges beginning with to abbot and the prior arriving to the doorkeeper and the kitchen service. According to the theory of A. de Vogüé, one of the greatest scholars of the early western monasticism, the Regula Orientalis was born in the first decades of the 6th century in Gaul, maybe in a monastery in the Jura mountains, and it is a fusion between the lost rule of Lerins written by abbot Marinus and the pachomian institutions. The article presents the first Hungarian translation of the rule followed by a study of its major features and of its possible dating.

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48

García-Calderón, Gastón, and Lorea Chaos-Cador. "Underlying non-Hermitian character of the Born rule in open quantum systems." Fortschritte der Physik 65, no. 6-8 (September 21, 2016): 1600037. http://dx.doi.org/10.1002/prop.201600037.

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49

Zanzotto, Giovanni. "On the material symmetry group of elastic crystals and the Born Rule." Archive for Rational Mechanics and Analysis 121, no. 1 (1992): 1–36. http://dx.doi.org/10.1007/bf00375438.

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50

Ilyin, Aleksey V. "The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion." Foundations of Physics 46, no. 7 (April 1, 2016): 845–51. http://dx.doi.org/10.1007/s10701-016-0006-y.

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Journal articles on the topic 'Born rule'

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