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

Physics Letters A

Comparison between quantum and classical diffusion functions for channeled particles

H. Nitta, Shu Namiki, Y. H. Ohtsuki

Published Apr 1, 1988• 4 citations
Publisher
DOI
10.1016/0375-9601(88)90884-5

Related papers

Quantum theory of local diffusion coefficient and stopping power for channeled particles

英雄 新田

•Jan 1, 1987•0 citations

Implementing Quantum Random Walks in Two-Dimensions with Application to Diffusion-Limited Aggregation

Colin Frederick Sanberg

This study simulates random movement and aggregation of particles in two-dimensional space based upon both quantum and classical mechanics. Using an original computer program to perform the calculations, the objective is to compare how quantum effects influence the random movement of a particle in comparison to the classical random movement. These effects are further studied by analyzing how the amassing of particles around a "seed" is affected by the differences in the random movement. Using the classical models that were generated as the basis of comparison, the initial results show that the quantum model aggregate grows at a slower ratc than the classical case. Also, the quantum model grows in a more amorphous manner than the clear branching of the classical example. In an effort to more accurately simulate the behavior of the probability function as it encounters other particles, both the quantum and classical models were adjusted. This yielded a quantum aggregation that developed more similarly than the classical model. The primary difference in the quantum model was a noticeable lack of symmetry as the particles amassed around the seeded particles. It is possible that this iteration of the quantum model develops more rapidly then the classical model, though more simulations are needed to further test this. The effect other particles have on the development of the probability function also needs to be further examined lo ensure that it is being modeled as accurately as possible.

•Jan 1, 2007•1 citation

Wigner function's numerical propagator for open system dynamics

Renán Cabrera, Denys I. Bondar, HERSCHEL A. RABITZ

We employ a recently developed formalism for describing open quantum systems, to device efficient ab initio numerical techniques for the time propagation of the Wigner function. The propagator's complexity is $O(N\log N)$, where N is the length of the array containing the Wigner function. We illustrate the developed method by propagating single particle systems undergoing decoherence and draw a faithful comparison with the classical evolution governed by both the Fokker-Planck and the Koopman-von Neumann equations. These simulations allow us to witness the emergence of the classical world by observing how the Wigner function converges to the solution of the Fokker-Planck equation with sufficient classical diffusion. As a second example we simulate for first time a numerically challenging quantum system made of two coupled particles and observe the loss of decoherence on one of the particles as a result of continuous measurements performed on the other one, therefore obtaining quantitative predictions for the loss of coherence of both particles as a function of time.

•Dec 14, 2012•1 citation

Multichannel Quantum-Classical Diffusion Equations

Michael V. Basilevsky, A. I. Voronin

Springer eBooks•Jan 1, 2003•0 citations

Time evolution law of Wigner operator in diffusion channel

Ke Zhang, Lanlan Li, Gang Ren +2 more

As is well known, the evolution of quantum state can be replaced by its Wigner function’s time evolution. The Wigner function of a quantum state is the same as the density matrix of a quantum state, because they both contain many messages, such as the probability distribution and phases. Thus, the important information about the quantum state in the evolution process can be obtained more quickly and effectively by studying the Wigner function of a quantum state. In this paper, based on the classical diffusion equation, the diffusion equation of the quantum state density operator is derived by using the P representation of the density operator. Furthermore, by introducing the Weyl ordering symbol of the quantum operator, the corresponding Weyl quantization scheme is given. In addition, the evolution equation of Wigner operator in diffusion channel is established by using another phase space representation of density operator—Wigner function, and the solution form of Wigner operator is given. In this paper, we derive the evolution law of Wigner operator in quantum diffusion channel for the first time, that is, the form of Wigner operator at any time in the evolution process. Based on this conclusion, the evolution of coherent states through quantum diffusion channels is discussed.

Acta Physica Sinica•Jan 1, 2020•1 citation

Quantum Brownian motion and classical diffusion

Roumen Tsekov, Georgi N. Vayssilov

Chemical Physics Letters•Jul 1, 1992•8 citations
This study simulates random movement and aggregation of particles in two-dimensional space based upon both quantum and classical mechanics. Using an original computer program to perform the calculations, the objective is to compare how quantum effects influence the random movement of a particle in comparison to the classical random movement. These effects are further studied by analyzing how the amassing of particles around a "seed" is affected by the differences in the random movement. Using the classical models that were generated as the basis of comparison, the initial results show that the quantum model aggregate grows at a slower ratc than the classical case. Also, the quantum model grows in a more amorphous manner than the clear branching of the classical example. In an effort to more accurately simulate the behavior of the probability function as it encounters other particles, both the quantum and classical models were adjusted. This yielded a quantum aggregation that developed more similarly than the classical model. The primary difference in the quantum model was a noticeable lack of symmetry as the particles amassed around the seeded particles. It is possible that this iteration of the quantum model develops more rapidly then the classical model, though more simulations are needed to further test this. The effect other particles have on the development of the probability function also needs to be further examined lo ensure that it is being modeled as accurately as possible.
We employ a recently developed formalism for describing open quantum systems, to device efficient ab initio numerical techniques for the time propagation of the Wigner function. The propagator's complexity is O(Nlog⁡N)O(N\log N)O(NlogN), where N is the length of the array containing the Wigner function. We illustrate the developed method by propagating single particle systems undergoing decoherence and draw a faithful comparison with the classical evolution governed by both the Fokker-Planck and the Koopman-von Neumann equations. These simulations allow us to witness the emergence of the classical world by observing how the Wigner function converges to the solution of the Fokker-Planck equation with sufficient classical diffusion. As a second example we simulate for first time a numerically challenging quantum system made of two coupled particles and observe the loss of decoherence on one of the particles as a result of continuous measurements performed on the other one, therefore obtaining quantitative predictions for the loss of coherence of both particles as a function of time.
As is well known, the evolution of quantum state can be replaced by its Wigner function’s time evolution. The Wigner function of a quantum state is the same as the density matrix of a quantum state, because they both contain many messages, such as the probability distribution and phases. Thus, the important information about the quantum state in the evolution process can be obtained more quickly and effectively by studying the Wigner function of a quantum state. In this paper, based on the classical diffusion equation, the diffusion equation of the quantum state density operator is derived by using the P representation of the density operator. Furthermore, by introducing the Weyl ordering symbol of the quantum operator, the corresponding Weyl quantization scheme is given. In addition, the evolution equation of Wigner operator in diffusion channel is established by using another phase space representation of density operator—Wigner function, and the solution form of Wigner operator is given. In this paper, we derive the evolution law of Wigner operator in quantum diffusion channel for the first time, that is, the form of Wigner operator at any time in the evolution process. Based on this conclusion, the evolution of coherent states through quantum diffusion channels is discussed.