Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Analogues in Classical Physics

Елена Стоянова, Elena Stoyanova

Published Nov 2, 2021• 0 citations
OpenAlex

Abstract

This thesis examine the problem of analogies between quantum and classical physics. Analogies put together different things, giving them similar properties or similar behavior, helping us better understand and further develop our knowledge about them. The most impressing thing here is that classical and quantum physics have both different formalism and fundamental concepts. The role of mathematics is stunning, because the analogy principle exist in the fact that totally different systems can be modeled by similar mathematical equations. The interest in quantum-classical analogies increased after the development of new schemes for quantum control for population transfer,such as excitation with rapid adiabatic passage, stimulated Raman adiabatic passage and composite pulses.

Related papers

Quantum Optical Analogues

Andon A. Rangelov

Analogy is a fundamental tool for understanding Mother Nature, since it associates various phenomena related by common properties or comparable behavior. In particular, the analogies between classical physics and quantum world show the fact that similar scientiffic formalisms apply to phenomena that are completely different. The role of mathematics is essential, because the analogy principle exist in the fact that totally different systems can be modeled by similar mathematical equations. Speciffically, analogies between quantum mechanics and wave optics have been emphasized since the beginning of quantum mechanics: wave effects like interference and diffraction were taken from optics and applied to exhibit the wavy idea of quantum particles, as electrons, neutrons and atoms. After the complete development of quantum theory the exchange of ideas in the opposite way started to happen. In the recent decade quantum-classical analogies have seen a great revival thanks to quantum control schemes for transfer of populations, such as excitation with rapid adiabatic passage, stimulated Raman adiabatic passage and composite pulses. Now in this dissertation we will use the concepts of composite pulses and adiabatic evolution, from the realm of coherent quantum control, to demonstrate: (a) novel robust polarization manipulation devices; (b) efficient broadband and scalable frequency conversion schemes as well as optical parametric ampliffication schemes;(c) several new optical ...

•May 11, 2021•0 citations

A Mathematical Foundation of the Quantum-Classical Correspondence

Nina Culver

In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities in classical mechanics.

Journal of international women's studies•Jan 1, 2015•0 citations

Unifying Quantum and Classical Dynamics

Abdul Rahaman Shaikh, Tabish Qureshi

Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting conditions. Nevertheless, this remains a challenging objective. In this work, we explore the potential for unifying the dynamics of classical and quantum physics. This discussion does not suggest that classical behavior emerges from quantum mechanics; rather, it demonstrates the exact equivalence between the dynamics of quantum observables and their classical counterparts. It is shown that the Heisenberg equations of motion can be cast in a form that is structurally equivalent to Newton's equations of motion, with $\hbar$ dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.

quant-pharXiv:2601.10423•Jan 16, 2026•0 citations

Experimental demonstration of composite stimulated Raman adiabatic passage

Alexander Bruns, Genko T. Genov, Marcel Hain +2 more

We experimentally demonstrate composite stimulated Raman adiabatic passage (CSTIRAP), which combines the concepts of composite pulse sequences and adiabatic passage. The technique is applied for population transfer in a rare-earth doped solid. We compare the performance of CSTIRAP with conventional single and repeated STIRAP, either in the resonant or the highly detuned regime. In the latter case, CSTIRAP improves the peak transfer efficiency and robustness, boosting the transfer efficiency substantially compared to repeated STIRAP. We also propose and demonstrate a universal version of CSTIRAP, which shows improved performance compared to the originally proposed composite version. Our findings pave the way towards new STIRAP applications, which require repeated excitation cycles, e.g., for momentum transfer in atom optics, or dynamical decoupling to invert arbitrary superposition states in quantum memories.

arXiv:1811.05719•Physical Review A•Nov 13, 2018•37 citations

On the Equivalence Principle of Quantum Mechanics

J. M. Isidro

A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation of a given classical mechanics. Instead, our approach to quantum mechanics is modelled on a statement that is close in spirit to the equivalence principle of general relativity, thus bearing a strong resemblance with the equivalence principle of quantum mechanics formulated by Faraggi-Matone.

arXiv:quant-ph/0105012•May 3, 2001•1 citation

Topology of adiabatic passage

Леонід Петрович Яценко, S. Guérin, Hans Rudolf Jauslin

We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage. Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level that will be populated in STIRAP process in $\ensuremath{\Lambda}$ or V systems by the choice of the peak amplitudes or the pulse sequence.

arXiv:quant-ph/0107065•Physical Review A•Apr 2, 2002•59 citations
This thesis examine the problem of analogies between quantum and classical physics. Analogies put together different things, giving them similar properties or similar behavior, helping us better understand and further develop our knowledge about them. The most impressing thing here is that classical and quantum physics have both different formalism and fundamental concepts. The role of mathematics is stunning, because the analogy principle exist in the fact that totally different systems can be modeled by similar mathematical equations. The interest in quantum-classical analogies increased after the development of new schemes for quantum control for population transfer,such as excitation with rapid adiabatic passage, stimulated Raman adiabatic passage and composite pulses.
Analogy is a fundamental tool for understanding Mother Nature, since it associates various phenomena related by common properties or comparable behavior. In particular, the analogies between classical physics and quantum world show the fact that similar scientiffic formalisms apply to phenomena that are completely different. The role of mathematics is essential, because the analogy principle exist in the fact that totally different systems can be modeled by similar mathematical equations. Speciffically, analogies between quantum mechanics and wave optics have been emphasized since the beginning of quantum mechanics: wave effects like interference and diffraction were taken from optics and applied to exhibit the wavy idea of quantum particles, as electrons, neutrons and atoms. After the complete development of quantum theory the exchange of ideas in the opposite way started to happen. In the recent decade quantum-classical analogies have seen a great revival thanks to quantum control schemes for transfer of populations, such as excitation with rapid adiabatic passage, stimulated Raman adiabatic passage and composite pulses. Now in this dissertation we will use the concepts of composite pulses and adiabatic evolution, from the realm of coherent quantum control, to demonstrate: (a) novel robust polarization manipulation devices; (b) efficient broadband and scalable frequency conversion schemes as well as optical parametric ampliffication schemes;(c) several new optical ...
In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities in classical mechanics.
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting conditions. Nevertheless, this remains a challenging objective. In this work, we explore the potential for unifying the dynamics of classical and quantum physics. This discussion does not suggest that classical behavior emerges from quantum mechanics; rather, it demonstrates the exact equivalence between the dynamics of quantum observables and their classical counterparts. It is shown that the Heisenberg equations of motion can be cast in a form that is structurally equivalent to Newton's equations of motion, with ℏ\hbarℏ dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.
We experimentally demonstrate composite stimulated Raman adiabatic passage (CSTIRAP), which combines the concepts of composite pulse sequences and adiabatic passage. The technique is applied for population transfer in a rare-earth doped solid. We compare the performance of CSTIRAP with conventional single and repeated STIRAP, either in the resonant or the highly detuned regime. In the latter case, CSTIRAP improves the peak transfer efficiency and robustness, boosting the transfer efficiency substantially compared to repeated STIRAP. We also propose and demonstrate a universal version of CSTIRAP, which shows improved performance compared to the originally proposed composite version. Our findings pave the way towards new STIRAP applications, which require repeated excitation cycles, e.g., for momentum transfer in atom optics, or dynamical decoupling to invert arbitrary superposition states in quantum memories.
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation of a given classical mechanics. Instead, our approach to quantum mechanics is modelled on a statement that is close in spirit to the equivalence principle of general relativity, thus bearing a strong resemblance with the equivalence principle of quantum mechanics formulated by Faraggi-Matone.
We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage. Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level that will be populated in STIRAP process in $\ensuremath{\Lambda}$ or V systems by the choice of the peak amplitudes or the pulse sequence.