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Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Quantum-classical correspondence principle.'
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Journal articles on the topic "Quantum-classical correspondence principle":
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WÓJCIK, ANTONI, and RAVINDRA W. CHHAJLANY. "QUANTUM-CLASSICAL CORRESPONDENCE IN THE ORACLE MODEL OF COMPUTATION." International Journal of Quantum Information 04, no. 04 (August 2006): 633–40. http://dx.doi.org/10.1142/s0219749906002109.
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used as a platform for comparison of oracle complexity. Here, we question the grounds on which this correspondence is based. Obviously, results on quantum speed-up depend on the chosen correspondence. So, we introduce the notion of genuine quantum speed-up which can serve as a tool for reliable comparison of quantum versus classical complexity, independent of the chosen correspondence principle.
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KAZAKOV, KIRILL A. "CLASSICAL SCALE OF QUANTUM GRAVITY." International Journal of Modern Physics D 12, no. 09 (October 2003): 1715–19. http://dx.doi.org/10.1142/s0218271803004110.
Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius r g . The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at r g leads to the question of correspondence between classical and quantum theories, which in turn can be unambiguously resolved by considering the issue of general covariance. The O(ℏ0) loop contributions turn out to violate the principle of general covariance, thus revealing their essentially quantum nature. The violation is O(1/N), where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence principle.
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Chen, Jin-Fu, Tian Qiu, and Hai-Tao Quan. "Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion." Entropy 23, no. 12 (November 29, 2021): 1602. http://dx.doi.org/10.3390/e23121602.
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.
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Liu, Q. H., and B. Hu. "The hydrogen atom's quantum-to-classical correspondence in Heisenberg's correspondence principle." Journal of Physics A: Mathematical and General 34, no. 28 (July 6, 2001): 5713–19. http://dx.doi.org/10.1088/0305-4470/34/28/307.
Lu, Jun, and Xue Mei Wang. "Quantum Spectra and Classical Orbits in Nano-Microstructure." Advanced Materials Research 160-162 (November 2010): 625–29. http://dx.doi.org/10.4028/www.scientific.net/amr.160-162.625.
A kind of new classical-quantum correspondence principle is proposed using the idea of closed-orbit theory. The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of one-dimensional nano-microstructure. The Fourier transformation of the quantum spectrum function is found corresponding with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some two-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science, for example, molecular reaction dynamics and quantum information.
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TZENOV, STEPHAN I. "IRROTATIONAL MOMENTUM FLUCTUATIONS CONDITIONING THE QUANTUM NATURE OF PHYSICAL PROCESSES." International Journal of Modern Physics A 21, no. 26 (October 20, 2006): 5299–316. http://dx.doi.org/10.1142/s0217751x06033866.
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt, so that the quantum mechanical framework resembles to a large extent that of the classical statistical mechanics and hydrodynamics. The main assumption used here is the existence of a random irrotational component in the classical momentum. Various basic elements of the quantum formalism (calculation of expectation values, the Heisenberg uncertainty principle, the correspondence principle) are recovered by applying traditional techniques, borrowed from classical statistical mechanics.
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Mauro, M. Di, A. Drago, and A. Naddeo. "Understanding the relation between classical and quantum mechanics: prospects for undergraduate teaching." Journal of Physics: Conference Series 2727, no. 1 (March 1, 2024): 012013. http://dx.doi.org/10.1088/1742-6596/2727/1/012013.
Abstract Classical and quantum mechanics are two very different theories, each describing the world within its own range of validity. It is often stated that classical mechanics emerges from quantum mechanics in a certain limit. This is known as the correspondence principle. According to Planck’s version of the correspondence principle, classical mechanics is recovered when the limit in which a dimensionless parameter containing Planck’s constant h goes to zero is taken, while Bohr’s version entails taking the limit of large quantum numbers. However, despite what is usually stated in textbooks, the relation between the two theories is much more complex to state and understand. Here we deal with this issue by analysing some key examples, in some of which also the analogously subtle relation between wave and geometric optics is considered. Implications for quantum mechanics teaching at undergraduate level are carefully discussed.
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Bonnar, James D., and Jeffrey R. Schmidt. "Classical orbits from the wave function in the large-quantum-number limit." Canadian Journal of Physics 81, no. 7 (July 1, 2003): 929–39. http://dx.doi.org/10.1139/p03-065.
Classical trajectories for the Coulomb potential are obtained from the large principle quantum-number limit of solutions to the nonrelativistic Schrödinger equation, by use of integral equations satisfied by the radial probability density function. These trajectories are found to be in excellent agreement with those computed directly from classical mechanics, in accordance with a statement of the Bohr Correspondence principle, except in a region very close to the center of force. PACS No.: 05.45.Mt
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Manjavidze, J., and A. Sissakian. "Symmetries, variational principles, and quantum dynamics." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 205–12. http://dx.doi.org/10.1155/s1026022604310022.
We describe the role of symmetries in formation of quantum dynamics. A quantum version of d'Alembert's principle is proposed to take into account the symmetry constrains more exact. It is argued that the time reversibility of quantum process, as the quantum analogy of d'Alembert's principle, makes the measure of the corresponding path integralδ-like. The argument of thisδ-function is the sum of all classical forces of the problem under consideration plus the random force of quantum excitations. Such measure establishes the one-to-one correspondence with classical mechanics and, for this reason, allows a free choice of the useful dynamical variables. The analysis shows that choosing the action-angle variables, one may get to the free-from-divergences quantum field theory. Moreover, one can try to get an independence from necessity to extract the degrees of freedom constrained by the symmetry. These properties of new quantization scheme are vitally essential for such theories as the non-Abelian Yang-Mills gauge theory and quantum gravity.
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Astapenko, Valery, and Timur Bergaliyev. "Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction." Foundations 3, no. 3 (September 4, 2023): 549–59. http://dx.doi.org/10.3390/foundations3030031.
A brief review of the classical and quantum description of the interaction of electromagnetic radiation with matter based on the model of a harmonic oscillator is presented. This review includes the generalized Bohr correspondence principle, the excitation of a quantum oscillator by electromagnetic pulses including saturation effect, the harmonic limit of the Bloch equations, and a phenomenological account of the damping of the quantum oscillator. In all cases, at the mathematical level, the relationship between the classical and quantum descriptions of the electromagnetic interaction is established and the conditions for such compliance are identified.
Dissertations / Theses on the topic "Quantum-classical correspondence principle":
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Rosaler, Joshua S. "Inter-theory relations in physics : case studies from quantum mechanics and quantum field theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1fc6c67d-8c8e-4e92-a9ee-41eeae80e145.
I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
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Prouff, Antoine. "Correspondance classique-quantique et application au contrôle d'équations d'ondes et de Schrödinger dans l'espace euclidien." Electronic Thesis or Diss., université Paris-Saclay, 2024. https://theses.hal.science/tel-04634673.
Les équations des ondes et de Schrödinger modélisent une grande variété de phénomènes ondulatoires, tels que la propagation de la lumière, les vibrations d'un objet ou l'évolution temporelle d'une particule quantique. Dans ces modèles, l'asymptotique des hautes énergies peut être décrite par des équations de la mécanique classique, comme l'optique géométrique. Dans cette thèse, nous étudions plusieurs applications de la correspondance classique-quantique à des problèmes de contrôle des équations des ondes et de Schrödinger dans l'espace euclidien, en utilisant des méthodes d'analyse microlocale.Dans les deux premières parties, nous étudions l'équation des ondes amorties et l'équation de Schrödinger avec un potentiel confinant dans l'espace euclidien. Nous donnons des conditions nécessaires et suffisantes de stabilité uniforme pour la première, et d'observabilité pour la seconde. Ces conditions font intervenir la dynamique classique sous-jacente qui consiste en une optique géométrique tordue par la présence du potentiel.Nous analysons ensuite dans une troisième partie la correspondance classique-quantique dans un cadre général qui contient les deux problèmes mentionnés ci-dessus. Nous démontrons une version du théorème d'Egorov dans le formalisme des métriques sur l'espace des phases et du calcul de Weyl--Hörmander. On présente différents cadres d'application de ce théorème pour des équations de Schrödinger, de demi-ondes et de transport Wave and Schrödinger equations model a variety of phenomena, such as propagation of light, vibrating structures or the time evolution of a quantum particle. In these models, the high-energy asymptotics can be approximated by classical mechanics, as geometric optics. In this thesis, we study several applications of this principle to control problems for wave and Schrödinger equations in the Euclidean space, using microlocal analysis.In the first two chapters, we study the damped wave equation and the Schrödinger equation with a confining potential in the euclidean space. We provide necessary and sufficient conditions for uniform stability in the first case, or observability in the second one. These conditions involve the underlying classical dynamics which consists in a distorted version of geometric optics, due to the presence of the potential.Then in the third part, we analyze the quantum-classical correspondence principle in a general setting that encompasses the two aforementioned problems. We prove a version of Egorov's theorem in the Weyl--Hörmander framework of metrics on the phase space. We provide with various examples of application of this theorem for Schrödinger, half-wave and transport equations
Books on the topic "Quantum-classical correspondence principle":
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Drexel Symposium on Quantum Nonintegrability (4th 1994 Philadelphia, Pa.). Quantum classical correspondence: Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, Drexel University, Philadelphia, USA, September 8-11, 1994. Cambridge, MA: International Press, 1997.
Book chapters on the topic "Quantum-classical correspondence principle":
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Duncan, Anthony, and Michel Janssen. "Guiding Principles." In Constructing Quantum Mechanics, 205–58. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198845478.003.0005.
The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.
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Baggott, Jim, and John L. Heilbron. "Mutual Admiration." In Quantum Drama, 13–28. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780192846105.003.0002.
Abstract The nature of the Bohr–Einstein debate was framed long before our protagonists became engaged in it. Both were reformers, ready to embrace controversy and even absurdity in their theories. But where Einstein held fast to classical principles he considered sacrosanct, Bohr would cheerfully embrace their violent reworking or replacement. Einstein’s 1921 Nobel prize was awarded in 1922. He had entertained the absurd notion that light consists of ‘quanta’, endowing particle-like properties governed by a characteristic wave frequency. Bohr’s 1922 Nobel prize involved entertaining the absurd notion of quantum ‘jumps’ between atomic orbits driven entirely by chance. He defended the inconsistencies with vague wordplay, declaring the quantities defining the orbits as ‘symbolic’, and introduced a fuzzy demand called the ‘correspondence principle’. At appropriate limits, the value of a quantity should be the same whether calculated using classical or quantum rules. Few quantum physicists could make it work.
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Lavoura, Luís, and João Paulo Silva. "The Discrete Symmetries in Quantum Physics." In CP Violation, 15–26. Oxford University PressOxford, 1999. http://dx.doi.org/10.1093/oso/9780198503996.003.0002.
Abstract In quantum theory the transformations P, T, and C are represented by operators P, T, and C, respectively. In this chapter we introduce the main properties of those operators. We shall not construct them explicitly in formal quantum field theory; for this reason, some of the properties will remain undemonstrated. The symmetry T requires a mathematical formalism distinct from the one used for P and C symmetries. We shall treat C and P jointly, leaving T to a separate section, which may be skipped without loss of continuity. In classical physics, the parity transformation does not affect the time coordinate. In particular, it commutes with a time translation. Following the principle of correspondence for passing from classical mechanics to quantum mechanics (Dirac 1958), we require the quantum-mechanical representations of parity through the operator.
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Heilbron, J. L. "3. Magic wand." In Niels Bohr: A Very Short Introduction, 40–63. Oxford University Press, 2020. http://dx.doi.org/10.1093/actrade/9780198819264.003.0003.
‘Magic wand’ refers to the ‘correspondence principle’ that Bohr devised and deployed to investigate the interface between quantum and ordinary (‘classical’) physics. The chapter covers various lines of work, some inspired by his approach and some independent of it, all of which confirmed its fertility. The mobilization of the international brotherhood of physicists for the Great War gave Bohr breathing space to develop the correspondence principle with the help of Hendrik Kramers, who had come to neutral Denmark to study with him, and in friendly competition with Arnold Sommerfeld, who made important formal extensions of the theory.
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Dyall, Kenneth G., and Knut Faegri. "The Dirac Equation." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0009.
The purpose of this chapter is to introduce the Dirac equation, which will provide us with a basis for developing the relativistic quantum mechanics of electronic systems. Thus far we have reviewed some basic features of the classical relativistic theory, which is the foundation of relativistic quantum theory. As in the nonrelativistic case, quantum mechanical equations may be obtained from the classical relativistic particle equations by use of the correspondence principle, where we replace classical variables by operators. Of particular interest are the substitutions In terms of the momentum four-vector introduced earlier, this yields In going from a classical relativistic description to relativistic quantum mechanics, we require that the equations obtained are invariant under Lorentz transformations. Other basic requirements, such as gauge invariance, must also apply to the equations of relativistic quantum mechanics. We start this chapter by reexamining the quantization of the nonrelativistic Hamiltonian and draw out some features that will be useful in the quantization of the relativistic Hamiltonian. We then turn to the Dirac equation and sketch its derivation. We discuss some properties of the equation and its solutions, and show how going to the nonrelativistic limit reduces it to a Schrödinger-type equation containing spin.
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Duncan, Anthony, and Michel Janssen. "Dispersion Theory in the Old Quantum Theory." In Constructing Quantum Mechanics Volume Two, 135–208. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780198883906.003.0003.
Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.
Conference papers on the topic "Quantum-classical correspondence principle":
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Babushkin, Ihar, Surajit Bose, Philip Rübeling, Oliver Melchert, Ayhan Demircan, Michael Kurtsiefer, and Uwe Morgner. "Modeling of Weak Ultrashort Photonic Wavepackets Using Quantum-Classical Correspondence Principle." In 2023 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC). IEEE, 2023. http://dx.doi.org/10.1109/cleo/europe-eqec57999.2023.10232763.
Sheinfux, A. Hanan, Tal Kachman, Yaakov Lumer, Yonatan Plotnik, and Mordechai Segev. "Breakdown of quantum-classical Correspondence Principle when light interacts with fluctuating disorder." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2013. http://dx.doi.org/10.1364/cleo_qels.2013.qw3a.6.
Babushkin, Ihar, Surajit Bose, Philip Rübeling, Oliver Melchert, Ayhan Demircan, Michael Kues, and Uwe Morgner. "Simple description of ultrafast single-photon wavepackets interacting with moving fronts." In CLEO: Fundamental Science. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cleo_fs.2023.fth3a.8.
We consider photons experiencing reflection, tunneling or trapping by refractive index fronts moving at the speed of light. We show that evolution equations in such situations are determined uniquely via the quantum-classical correspondence principle.
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Bose, Surajit, Ihar Babushkin, Stefanus Wijaya, Alì M. Angulo M., Oliver Melchert, Philip Rübeling, Raktim Haldar, et al. "All-optical control of single-photon wavepackets via Kerr nonlinearity induced refractive index fronts." In CLEO: Fundamental Science. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cleo_fs.2023.ftu3b.2.
We experimentally demonstrate the efficient, broadband (4.7 THz), and controllable all-optical manipulation of single photons in a nonlinear photonic crystal fiber, in agreement with performed simulations of nonlinear pulse propagation, based on the quantum-classical correspondence principle.
