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Journal articles on the topic 'Ehrenfest'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Sergi, Alessandro, Daniele Lamberto, Agostino Migliore, and Antonino Messina. "Quantum–Classical Hybrid Systems and Ehrenfest’s Theorem." Entropy 25, no. 4 (2023): 602. http://dx.doi.org/10.3390/e25040602.

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The conceptual analysis of quantum mechanics brings to light that a theory inherently consistent with observations should be able to describe both quantum and classical systems, i.e., quantum–classical hybrids. For example, the orthodox interpretation of measurements requires the transient creation of quantum–classical hybrids. Despite its limitations in defining the classical limit, Ehrenfest’s theorem makes the simplest contact between quantum and classical mechanics. Here, we generalized the Ehrenfest theorem to bipartite quantum systems. To study quantum–classical hybrids, we employed a fo

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2

DI GENNARO, LUCA, and UBALDO GARIBALDI. "ECONOMIC GROWTH AND THE EHRENFEST FLEAS: THE CONVERGENCE AMONG COUNTRIES." International Journal of Modern Physics C 19, no. 01 (2008): 33–47. http://dx.doi.org/10.1142/s0129183108011929.

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The aim of this work is to predict the economic convergence among countries by using a generalization of Ehrenfest's urn. In particular this work shows that the Ehrenfest model captures the convergence among countries. A empirical analysis is presented on the European Union countries, the G7 countries and the emerging countries.

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3

Chen, Yung-Pin. "A central limit property under a modified Ehrenfest urn design." Journal of Applied Probability 43, no. 2 (2006): 409–20. http://dx.doi.org/10.1239/jap/1152413731.

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We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary distribution under the Ehrenfest urn model, the corresponding process under this modified Ehrenfest urn design satisfies the central limit property. We prove this asymptotic normality property using a c

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4

Chen, Yung-Pin. "A central limit property under a modified Ehrenfest urn design." Journal of Applied Probability 43, no. 02 (2006): 409–20. http://dx.doi.org/10.1017/s0021900200001728.

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We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary distribution under the Ehrenfest urn model, the corresponding process under this modified Ehrenfest urn design satisfies the central limit property. We prove this asymptotic normality property using a c

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5

Elishakoff, Isaac. "Who developed the so-called Timoshenko beam theory?" Mathematics and Mechanics of Solids 25, no. 1 (2019): 97–116. http://dx.doi.org/10.1177/1081286519856931.

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The use of the Google Scholar produces about 78,000 hits on the term “Timoshenko beam.” The question of priority is of great importance for this celebrated theory. For the first time in the world literature, this study is devoted to the question of priority. It is that Stephen Prokofievich Timoshenko had a co-author, Paul Ehrenfest. It so happened that the scientific work of Timoshenko dealing with the effect of rotary inertia and shear deformation does not carry the name of Ehrenfest as the co-author. In his 2002 book, Grigolyuk concluded that the theory belonged to both Timoshenko and Ehrenf

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6

Feder, Toni. "Ehrenfest letters surface." Physics Today 61, no. 6 (2008): 26–27. http://dx.doi.org/10.1063/1.2947641.

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7

Liberalquino, Rafael, and Fernando Parisio. "Semiclassical Ehrenfest paths." Physics Letters A 377, no. 19-20 (2013): 1333–36. http://dx.doi.org/10.1016/j.physleta.2013.04.009.

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8

Bolivar, A. O. "Teorema de Ehrenfest e o limite clássico da mecânica quântica." Revista Brasileira de Ensino de Física 23, no. 2 (2001): 190–95. http://dx.doi.org/10.1590/s1806-11172001000200009.

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Apresentamos argumentos sustentando que o teorema de Ehrenfest não é formal e conceitualmente adequado para conectar a mecânica quântica à mecãnica clássica. Além disso, a fim de ressaltarmos a importância pedagógica de jamais deixarmos de ler os textos originais, traduzimos o artigo de Paul Ehrenfest publicado em 1927 na revista Zeitschrift für Physik.

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9

Shepelyansky, Dima. "Ehrenfest time and chaos." Scholarpedia 15, no. 9 (2020): 55031. http://dx.doi.org/10.4249/scholarpedia.55031.

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10

Krafft, Olaf, and Martin Schaefer. "Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model." Journal of Applied Probability 30, no. 4 (1993): 964–70. http://dx.doi.org/10.2307/3214525.

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A two-parameter Ehrenfest urn model is derived according to the approach taken by Karlin and McGregor [7] where Krawtchouk polynomials are used. Furthermore, formulas for the mean passage times of finite homogeneous Markov chains with general tridiagonal transition matrices are given. In the special case of the Ehrenfest model they have quite a different structure as compared with those of Blom [2] or Kemperman [9].

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11

Elishakoff, Isaac, Yuchen Li, Noël Challamel, and J. N. Reddy. "Simplified Timoshenko–Ehrenfest beam equation to analyze metamaterials." Journal of Applied Physics 131, no. 10 (2022): 104902. http://dx.doi.org/10.1063/5.0077001.

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This paper is devoted to the incorporation of rotary inertia and shear deformation in the study of acoustic metamaterials. An overwhelming majority of investigators resort to either Bernoulli–Euler or to the Timoshenko–Ehrenfest beam theories. Here, we demonstrate that the full version of the Timoshenko–Ehrenfest beam theory is not needed, and the truncated version is sufficient. An extensive numerical investigation is conducted to this end.

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12

Krafft, Olaf, and Martin Schaefer. "Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model." Journal of Applied Probability 30, no. 04 (1993): 964–70. http://dx.doi.org/10.1017/s0021900200044697.

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A two-parameter Ehrenfest urn model is derived according to the approach taken by Karlin and McGregor [7] where Krawtchouk polynomials are used. Furthermore, formulas for the mean passage times of finite homogeneous Markov chains with general tridiagonal transition matrices are given. In the special case of the Ehrenfest model they have quite a different structure as compared with those of Blom [2] or Kemperman [9].

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13

TANG, CHI-SHUNG, and PI-GANG LUAN. "TIME-DEPENDENT EVOLUTION OF A WAVE PACKET IN QUANTUM SYSTEMS." International Journal of Modern Physics B 22, no. 24 (2008): 4225–41. http://dx.doi.org/10.1142/s0217979208048887.

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We consider wave packet propagation in mesoscopic quantum systems. A number of approaches are compared to look at the general solution of a time-dependent Schrödinger equation and the validity of the Ehrenfest theorem. Detailed calculations are presented to illustrate the results of a charged particle motion in the time-dependent systems, and show that the Ehrenfest theorem is not directly applicable in topologically nontrivial systems.

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14

FAN, HONGYI. "BOSE OPERATOR HAMILTONIAN MODEL FOR ROTATING ELECTRIC DIPOLE AND GENERALIZED EHRENFEST'S THEOREM." International Journal of Modern Physics A 17, no. 01 (2002): 45–50. http://dx.doi.org/10.1142/s0217751x02006055.

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We present a Bose operator Hamiltonian model for totally quantum mechanically describing energy and eigenfunctions of a rotating dipole in the presence of electric field. The corresponding Heisenberg equations of motion are derived which leads us to the generalized Ehrenfest theorem for rotating system. Remarkably, a zero-point angular momentum ℏ/2 appears in the generalized Ehrenfest theorem corresponding to the classical equation Iω=L.

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15

Godwe, Emile, Justin Mibaile, Betchewe Gambo, and Serge Y. Doka. "Semiquantum Chaos in Two GaAs Quantum Dots Coupled Linearly and Quadratically by Two Harmonic Potentials in Two Dimensions." Advances in Mathematical Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/6450687.

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We analyze the phenomenon of semiquantum chaos in two GaAs quantum dots coupled linearly and quadratically by two harmonic potentials. We show how semiquantum dynamics should be derived via the Ehrenfest theorem. The extended Ehrenfest theorem in two dimensions is used to study the system. The numerical simulations reveal that, by varying the interdot distance and coupling parameters, the system can exhibit either periodic or quasi-periodic behavior and chaotic behavior.

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16

ten Brink, M., S. Gräber, M. Hopjan, et al. "Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods." Journal of Chemical Physics 156, no. 23 (2022): 234109. http://dx.doi.org/10.1063/5.0092063.

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We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born–Huang formalism, covering different initial states, which either start on a single Born–Oppenheime

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17

Bonet-Luz, Esther, and Cesare Tronci. "Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (2016): 20150777. http://dx.doi.org/10.1098/rspa.2015.0777.

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The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group . The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical

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18

Cremaschini, Claudio, Jiří Kovář, Zdeněk Stuchlík, and Massimo Tessarotto. "Kinetic formulation of Tolman–Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times." Physics of Fluids 34, no. 9 (2022): 091701. http://dx.doi.org/10.1063/5.0111200.

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A review of the original thermodynamic formulation of the Tolman–Ehrenfest effect prescribing the temperature profile of uncharged fluid at thermal equilibrium forming stationary configurations in curved space-time is proposed. A statistical description based on the relativistic kinetic theory is implemented. In this context, the Tolman–Ehrenfest relation arises in the Schwarzschild space-time for collisionless uncharged particles at Maxwellian kinetic equilibrium. However, the result changes considerably when non-ideal fluids, i.e., non-Maxwellian distributions, are treated, whose statistical

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19

Einstein, Albert, and Bertram Schwarzschild. "Albert Einstein to Paul Ehrenfest." Physics Today 58, no. 4 (2005): 88. http://dx.doi.org/10.1063/1.1955505.

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20

Zhao, Luning, Andrew Wildman, Zhen Tao, Patrick Schneider, Sharon Hammes-Schiffer, and Xiaosong Li. "Nuclear–electronic orbital Ehrenfest dynamics." Journal of Chemical Physics 153, no. 22 (2020): 224111. http://dx.doi.org/10.1063/5.0031019.

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21

Pavelka, Michal, Václav Klika, and Miroslav Grmela. "Ehrenfest regularization of Hamiltonian systems." Physica D: Nonlinear Phenomena 399 (December 2019): 193–210. http://dx.doi.org/10.1016/j.physd.2019.06.006.

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22

Balaji, Srinivasan, Hosam M. Mahmoud, and Osamu Watanabe. "Distributions in the Ehrenfest process." Statistics & Probability Letters 76, no. 7 (2006): 666–74. http://dx.doi.org/10.1016/j.spl.2005.09.013.

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23

Kumar, Jitendra. "Ehrenfest paradox: A careful examination." American Journal of Physics 92, no. 2 (2024): 140–45. http://dx.doi.org/10.1119/5.0153190.

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The Ehrenfest paradox for a rotating ring is examined and a kinematic resolution, within the framework of the special theory of relativity, is presented. Two different ways by which a ring can be brought from rest to rotational motion, whether by keeping the rest lengths of the blocks constituting the ring constant or by keeping their lengths in the inertial frame constant, are explored and their effect on the length of the material ring in the inertial as well as the co-rotating frame is checked. It is found that the ring tears at a point in the former case and remains intact in the latter ca

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24

Domínguez-Castro, Adrian, and Thomas Frauenheim. "Impact of vibronic coupling effects on light-driven charge transfer in pyrene-functionalized middle and large-sized metalloid gold nanoclusters from Ehrenfest dynamics." Physical Chemistry Chemical Physics 23, no. 32 (2021): 17129–33. http://dx.doi.org/10.1039/d1cp02890a.

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25

Friesecke, Gero, and Bernd Schmidt. "A sharp version of Ehrenfest’s theorem for general self-adjoint operators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (2010): 2137–43. http://dx.doi.org/10.1098/rspa.2009.0351.

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26

Dette, Holger. "On a generalization of the ehrenfest urn model." Journal of Applied Probability 31, no. 04 (1994): 930–39. http://dx.doi.org/10.1017/s0021900200099460.

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Krafft and Schaefer [14] considered a two-parameter Ehrenfest urn model and found then-step transition probabilities using representations by Krawtchouk polynomials. For a special case of the model Palacios [17] calculated some of the expected first-passage times. This note investigates a generalization of the two-parameter Ehrenfest urn model where the transition probabilitiespi,i+1andpi,i+1are allowed to be quadratic functions of the current statei. The approach used in this paper is based on the integral representations of Karlin and McGregor [9] and can also be used for Markov chains with

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27

Van Beek, K. W. H., and A. J. Stam. "A variant of the Ehrenfest model." Advances in Applied Probability 19, no. 4 (1987): 995–96. http://dx.doi.org/10.2307/1427112.

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28

Van Beek, K. W. H., and A. J. Stam. "A variant of the Ehrenfest model." Advances in Applied Probability 19, no. 04 (1987): 995–96. http://dx.doi.org/10.1017/s0001867800017535.

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29

Palacios, José Luis. "Another Look at the Ehrenfest Urn Via Electric Networks." Advances in Applied Probability 26, no. 3 (1994): 820–24. http://dx.doi.org/10.2307/1427822.

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30

Palacios, José Luis. "Another Look at the Ehrenfest Urn Via Electric Networks." Advances in Applied Probability 26, no. 03 (1994): 820–24. http://dx.doi.org/10.1017/s0001867800026562.

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31

Dette, Holger. "On a generalization of the ehrenfest urn model." Journal of Applied Probability 31, no. 4 (1994): 930–39. http://dx.doi.org/10.2307/3215318.

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Krafft and Schaefer [14] considered a two-parameter Ehrenfest urn model and found the n-step transition probabilities using representations by Krawtchouk polynomials. For a special case of the model Palacios [17] calculated some of the expected first-passage times. This note investigates a generalization of the two-parameter Ehrenfest urn model where the transition probabilities pi,i+1 and pi,i+1 are allowed to be quadratic functions of the current state i. The approach used in this paper is based on the integral representations of Karlin and McGregor [9] and can also be used for Markov chains

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32

Freixas, Victor M., Sebastian Fernandez-Alberti, Dmitry V. Makhov, Sergei Tretiak, and Dmitrii Shalashilin. "An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules." Physical Chemistry Chemical Physics 20, no. 26 (2018): 17762–72. http://dx.doi.org/10.1039/c8cp02321b.

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33

Schlatter, Andreas E. "On the quantum Tolman-Ehrenfest effect." Physics Essays 28, no. 3 (2015): 296–99. http://dx.doi.org/10.4006/0836-1398-28.3.296.

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34

Bingham, N. H. "Fluctuation Theory for the Ehrenfest urn." Advances in Applied Probability 23, no. 3 (1991): 598–611. http://dx.doi.org/10.2307/1427624.

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The Ehrenfest urn model with d balls, or alternatively random walk on the unit cube in d dimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model—behaviour on unusual states—and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.

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35

Fischer, Sean A., Craig T. Chapman, and Xiaosong Li. "Surface hopping with Ehrenfest excited potential." Journal of Chemical Physics 135, no. 14 (2011): 144102. http://dx.doi.org/10.1063/1.3646920.

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36

Chen, Guan-Yu, Yang-Jen Fang, and Yuan-Chung Sheu. "The cutoff phenomenon for Ehrenfest chains." Stochastic Processes and their Applications 122, no. 8 (2012): 2830–53. http://dx.doi.org/10.1016/j.spa.2012.05.003.

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37

Bingham, N. H. "Fluctuation Theory for the Ehrenfest urn." Advances in Applied Probability 23, no. 03 (1991): 598–611. http://dx.doi.org/10.1017/s0001867800023752.

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The Ehrenfest urn model withdballs, or alternatively random walk on the unit cube inddimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model—behaviour on unusual states—and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.

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38

Holba, Pavel. "Ehrenfest equations for calorimetry and dilatometry." Journal of Thermal Analysis and Calorimetry 120, no. 1 (2015): 175–81. http://dx.doi.org/10.1007/s10973-015-4406-6.

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39

de la Peña, L., A. M. Cetto, and A. Valdés-Hernández. "Extended Ehrenfest theorem with radiative corrections." Physica Scripta T165 (October 1, 2015): 014004. http://dx.doi.org/10.1088/0031-8949/2015/t165/014004.

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40

MacCluer, C. R. "Nonconvergence of the Ehrenfest thought experiment." American Journal of Physics 77, no. 8 (2009): 695–96. http://dx.doi.org/10.1119/1.3130022.

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41

Ding, Feizhi, Joshua J. Goings, Hongbin Liu, David B. Lingerfelt, and Xiaosong Li. "Ab initio two-component Ehrenfest dynamics." Journal of Chemical Physics 143, no. 11 (2015): 114105. http://dx.doi.org/10.1063/1.4930985.

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42

Doyen, G. "Tunnel current and generalized Ehrenfest theorem." Journal of Physics: Condensed Matter 5, no. 20 (1993): 3305–12. http://dx.doi.org/10.1088/0953-8984/5/20/003.

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43

Tully, John C. "Ehrenfest dynamics with quantum mechanical nuclei." Chemical Physics Letters 816 (April 2023): 140396. http://dx.doi.org/10.1016/j.cplett.2023.140396.

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44

Ismayasari, D., I. W. Sudarsana, and I. N. Suwastika. "ALGORITMA VAN AARDENNE-EHRENFEST DAN DE BRUIJN DALAM MENCARI SIRKUIT EULER PADA GRAF BERARAH UNTUK MEREKONSTRUKSI RANTAI RNA DARI G-FRAGMENTS DAN (U,C)-FRAGMENTS." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 14, no. 2 (2017): 173–92. http://dx.doi.org/10.22487/2540766x.2017.v14.i2.9020.

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45

Feuillet, Mathieu, and Philippe Robert. "On the Transient Behavior of Ehrenfest and Engset Processes." Advances in Applied Probability 44, no. 2 (2012): 562–82. http://dx.doi.org/10.1239/aap/1339878724.

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Two classical stochastic processes are considered, the Ehrenfest process, introduced in 1907 in the kinetic theory of gases to describe the heat exchange between two bodies, and the Engset process, one of the early (1918) stochastic models of communication networks. In this paper we investigate the asymptotic behavior of the distributions of hitting times of these two processes when the number of particles/sources goes to infinity. Results concerning the hitting times of boundaries in particular are obtained. We rely on martingale methods; a key ingredient is an important family of simple nonn

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46

Feuillet, Mathieu, and Philippe Robert. "On the Transient Behavior of Ehrenfest and Engset Processes." Advances in Applied Probability 44, no. 02 (2012): 562–82. http://dx.doi.org/10.1017/s0001867800005723.

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Two classical stochastic processes are considered, the Ehrenfest process, introduced in 1907 in the kinetic theory of gases to describe the heat exchange between two bodies, and the Engset process, one of the early (1918) stochastic models of communication networks. In this paper we investigate the asymptotic behavior of the distributions of hitting times of these two processes when the number of particles/sources goes to infinity. Results concerning the hitting times of boundaries in particular are obtained. We rely on martingale methods; a key ingredient is an important family of simple nonn

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47

van der Heijden, Margriet. "More is known about him than about her: Tatiana Ehrenfest-Afanassjewa." Physics Today 77, no. 1 (2024): 40–47. http://dx.doi.org/10.1063/pt.3.5381.

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48

SZEPESSY, ANDERS. "LANGEVIN MOLECULAR DYNAMICS DERIVED FROM EHRENFEST DYNAMICS." Mathematical Models and Methods in Applied Sciences 21, no. 11 (2011): 2289–334. http://dx.doi.org/10.1142/s0218202511005751.

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Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac–Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio M of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy o(M-1/2) on bounded time intervals and by o(1) on unbounded time intervals, which makes the small [Formula: see text] friction and o(M-1/2) diffusion terms visible. The initial electron p

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49

Blom, Gunnar. "Mean transition times for the Ehrenfest urn model." Advances in Applied Probability 21, no. 2 (1989): 479–80. http://dx.doi.org/10.2307/1427173.

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50

Blom, Gunnar. "Mean transition times for the Ehrenfest urn model." Advances in Applied Probability 21, no. 02 (1989): 479–80. http://dx.doi.org/10.1017/s000186780001867x.

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