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dynamical quantization and classical limit

CANADIAN JOURNAL OF PHYSICS 2003年第4期81卷 663-673页

作者： Bolivar, AO Inst Cultural Eudoro Sousa Grp Mario Schonberg Estudos Fis Matemat Filosofia BR-72221970 Ceilandia DF Brazil

We have worked out a quantization method directly from classical dynamics without using Hamiltonian and Lagrangian functions;we call it dynamical quantization. The present article compares such a method with the Dirac and Feynman quantization procedures and also verifies the logical consistence of the dynamical quantization calculating the classical limit of a Brownian particle, for example.

关键词： .Brownian CLASSICAL LIMIT quantum physics quantize Lagrangians Liouville equation classical mechanics quantization method dynamical quantization Dirac and Feynman quantization schemes

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ON A dynamical quantization

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CZECHOSLOVAK JOURNAL OF PHYSICS 1982年第6期32卷 680-687页

作者： PALEV, T Institute of Nuclear Research and Nuclear Energy Bulg. Acad. Sci. Boulevard Lenin 72 1113 Sofia Bulgaria

A concept of a noncanonical quantization, called dynamical quantization, is defined in an axiomatic way. A dynamical quantization of a system of two nonrelativistic point particles interacting via a harmonic potential is considered in more details. The quantized system exhibits some new features. In particular, it has finite space dimensions. The distance between the particles is preserved in time and can have at most four different values. The position of any one of them cannot be localized, since the operators of the coordinates do not commute. The particles are smeared with a certain probability within a finite volume, which moves together with their centre of mass. The orbital momentum of the composite system is either one or zero.

关键词： Finite Volume Space Dimension Composite System dynamical quantization Point Particle

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The dynamical-quantization approach to open quantum systems

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ANNALS OF PHYSICS 2012年第3期327卷 705-732页

作者： Bolivar, A. O. Univ Fed Minas Gerais Dept Fis BR-30123970 Belo Horizonte MG Brazil

The dynamical-quantization approach to open quantum systems does consist in quantizing the Brownian motion starting directly from its stochastic dynamics under the framework of both Langevin and Fokker-Planck equations, without alluding to any model Hamiltonian. On the ground of this non-Hamiltonian quantization method, we can derive a non-Markovian Caldeira-Leggett quantum master equation as well as a non-Markovian quantum Smoluchowski equation. The former is solved for the case of a quantum Brownian particle in a gravitational field whilst the latter for a harmonic oscillator. In both physical situations, we come up with the existence of a non-equilibrium thermal quantum force and investigate its classical limit at high temperatures as well as its quantum limit at zero temperature. Further, as a physical application of our quantum Smoluchowski equation, we take up the tunneling phenomenon of a non-inertial quantum Brownian particle over a potential barrier. Lastly, we wish to point out, corroborating conclusions reached in our previous paper [A. O. Bolivar, Ann. Phys. 326 (2011) 1354], that the theoretical predictions in the present article uphold the view that our non-Hamiltonian quantum mechanics is able to capture novel features inherent in quantum Brownian motion, thereby overcoming shortcomings underlying the Caldeira-Leggett Hamiltonian model. (C) 2011 Elsevier Inc. All rights reserved.

关键词： dynamical quantization Quantum Brownian motion Non-Markovian effect Caldeira-Leggett quantum master equation Quantum Smoluchowski equation Quantum tunneling

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Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation

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ANNALS OF PHYSICS 2011年第5期326卷 1354-1367页

作者： Bolivar, A. O. Univ Fed Minas Gerais Dept Fis BR-30123970 Belo Horizonte MG Brazil

We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Quantum Brownian motion dynamical quantization Non-Markovian Caldeira-Leggett equation Non-equilibrium effects

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Multiple Description Coding with Delta-Sigma Modulation 10th

Multiple Description Coding with Delta-Sigma Modulation

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10th IEEE International Conference on Industrial Informatics (INDIN)

作者： Shiomi, Ryuta Abe, Daiki Yakoh, Takahiro Keio Univ Dept Syst Design Engn Yokohama Kanagawa 223 Japan

ISBN: (纸本)9781467303118

Multiple description coding (MDC) can be applied for multipath communication to reduce the negative affect of packet loss, and it is composed of three processes: encoding, quantizing, and decoding. Encoding and decoding are well researched in MDC, but there are few researches that focus on the quantization process. Therefore, this paper focuses on the quantization process of MDC. The aim of this paper is to improve the quality of the received data, and to reduce the bit width by employing static quantization (uniform quantization) with dynamic quantizer (Delta Sigma modulation). Performance evaluation was done using a block diagram input module XCos which is attached to the formula processing software Scilab. As a result of using the Delta Sigma modulation, the distortion improved by 95.2% when both of the descriptions were received, and 45.3% when only one of the description was received. Also, the experimental result showed that the quantization bit width can be reduced from 8 bit to 6 bit when the Delta Sigma modulation was used.

关键词： Multiple description coding MDC dynamical quantization delta-sigma modulation

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Multiple Description Coding with Delta-Sigma Modulation

Multiple Description Coding with Delta-Sigma Modulation

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IEEE 10th International Conference on Industrial Informatics(第十届IEEE工业信息学国际学术会议 INDIN2012)

作者： Ryuta Shiomi Daiki Abe Takahiro Yakoh Department ofSystem Design EngineeringKeio University Yokohama Japan Department of System Design Engineering Keio University Yokohama Japan

ISBN: (纸本)9781467303125

Multiple description coding (MDC) can be applied for multipath communication to reduce the negative affect of packet loss, and it is composed of three processes: encoding, quantizing, and decoding. Encoding and decoding are well researched in MDC, but there are few researches that focus on the quantization process. Therefore, this paper focuses on the quantization process of MDC. The aim of this paper is to improve the quality of the received data, and to reduce the bit width by employing static quantization (uniform quantization) with dynamic quantizer (△∑ modulation). Performance evaluation was done using a block diagram input module XCos which is attached to the formula processing software Scilab. As a result of using the △∑ modulation, the distortion improved by 95.2％ when both of the descriptions were received, and 45.3％ when only one of the description was received. Also, the experimental result showed that the quantization bit width can be reduced from 8 bit to 6 bit when the △∑ modulation was used.

关键词： Multiple description coding MDC dynamical quantization delta-sigma modulation

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