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Relevant bibliographies by topics / Phase Space Formulation

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Academic literature on the topic 'Phase Space Formulation'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Phase Space Formulation"

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CIRELLI, RENZO, ALESSANDRO MANIÀ, and LIVIO PIZZOCCHERO. "QUANTUM PHASE SPACE FORMULATION OF SCHRÖDINGER MECHANICS." International Journal of Modern Physics A 06, no. 12 (1991): 2133–46. http://dx.doi.org/10.1142/s0217751x91001064.

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We develop a geometrical approach to Schrödinger quantum mechanics, alternative to the usual one, which is based on linear and algebraic structures such as Hilbert spaces, operator algebras, etc. The starting point of this approach is the Kähler structure possessed by the set of the pure states of a quantum system. The Kähler manifold of the pure states is regarded as a “quantum phase space”, conceptually analogous to the phase space of a classical hamiltonian system, and all the constituents of the conventional formulation, in particular the algebraic structure of the observables, are reprodu

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Chruściński, Dariusz. "Phase-Space Approach to Berry Phases." Open Systems & Information Dynamics 13, no. 01 (2006): 67–74. http://dx.doi.org/10.1007/s11080-006-7268-3.

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We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

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ZACHOS, COSMAS. "DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE." International Journal of Modern Physics A 17, no. 03 (2002): 297–316. http://dx.doi.org/10.1142/s0217751x02006079.

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Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or

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Wu, Xizeng, and Hong Liu. "Phase-space formulation for phase-contrast x-ray imaging." Applied Optics 44, no. 28 (2005): 5847. http://dx.doi.org/10.1364/ao.44.005847.

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Tosiek, J., and P. Brzykcy. "States in the Hilbert space formulation and in the phase space formulation of quantum mechanics." Annals of Physics 332 (May 2012): 1–15. http://dx.doi.org/10.1016/j.aop.2013.01.010.

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Kalmykov, Yuri P., and William T. Coffey. "Transition state theory for spins: phase-space formulation." Journal of Physics A: Mathematical and Theoretical 41, no. 18 (2008): 185003. http://dx.doi.org/10.1088/1751-8113/41/18/185003.

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Batalin, I. A., K. Bering, and P. H. Damgaard. "Superfield formulation of the phase space path integral." Physics Letters B 446, no. 2 (1999): 175–78. http://dx.doi.org/10.1016/s0370-2693(98)01537-8.

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Rosato, J. "A quantum phase space formulation of radiative transfer." Physics Letters A 378, no. 34 (2014): 2586–89. http://dx.doi.org/10.1016/j.physleta.2014.07.003.

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SOBOUTI, Y., and S. NASIRI. "A PHASE SPACE FORMULATION OF QUANTUM STATE FUNCTIONS." International Journal of Modern Physics B 07, no. 18 (1993): 3255–72. http://dx.doi.org/10.1142/s0217979293003218.

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Allowing for virtual paths in phase space permits an extension of Hamilton’s principle of least action, of lagrangians and of hamiltonians to phase space. A subsequent canonical quantization, then, provides a framework for quantum statistical mechanics. The classical statistical mechanics and the conventional quantum mechanics emerge as special case of this formalism. Von Neumann’s density matrix may be inferred from it. Wigner’s functions and their evolution equation may also be obtained by a unitary transformation.

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Torre, C. G. "Covariant phase space formulation of parametrized field theories." Journal of Mathematical Physics 33, no. 11 (1992): 3802–12. http://dx.doi.org/10.1063/1.529878.

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Dissertations / Theses on the topic "Phase Space Formulation"

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Meusburger, Catherine. "Phase space and quantisation of (2+1)-dimensional gravity in the Chern-Simons formulation." Thesis, Heriot-Watt University, 2004. http://hdl.handle.net/10399/320.

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Strandberg, Per Erik. "Mathematical models of bacteria population growth in bioreactors: formulation, phase space pictures, optimisation and control." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2337.

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<p>There are many types of bioreactors used for producing bacteria populations in commercial, medical and research applications. </p><p>This report presents a systematic discussion of some of the most important models corresponding to the well known reproduction kinetics such as the Michaelis-Menten kinetics, competitive substrate inhibition and competitive product inhibition. We propose a modification of a known model, analyze it in the same manner as known models and discuss the most popular types of bioreactors and ways of controlling them. </p><p>This work summarises much of the known resu

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Lee, Ming-Tsung, and 李明聰. "Implications of Quantum Mechanics based on a Random Medium Model and a Stochastic Micro-Phase-Space Formulation." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/20811272010135150210.

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博士<br>國立臺灣大學<br>物理學研究所<br>90<br>Based on the framework of stochastic interpretation for quantum mechanics, two approaches are proposed to present several implications of quantum mechanics. One is the microscopic transport conservation approach for the random medium model. In this model, the quantum fluctuation of the microscopic object is assumed to arise from the collision between the microscopic object and the medion. Some assumptions for the object-medion collision are proposed to guarantee that the statistical ensemble manifestation of Schrodinger wave mechanics can be reproduced. Accordin

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GIOVANNINI, ELISA. "A Wigner Equation with Decoherence." Doctoral thesis, 2020. http://hdl.handle.net/2158/1238624.

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Dopo un’introduzione sui fondamenti matematici della Meccanica Quantistica e la sua formulazione wigneriana, si ricava un’equazione 1-dimensionale di Wigner con termine di decoerenza partendo dalla descrizione dettagliata di R. Adami, M. Hauray, C. Negulescu per la decoerenza di una particella pesante che interagisce con una particella leggera. Si mostra che il modello ottenuto ne contiene, quali casi particolari, altri già utilizzati per descrivere il fenomeno della decoerenza quantistica, come ad esempio l’equazione di Wigner–Fokker–Planck o le funzioni di Wigner con lunghezza di coerenza fi

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Books on the topic "Phase Space Formulation"

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Mann, Peter. Noether’s Theorem for Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0028.

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This is a unique chapter that discusses classical path integrals in both configuration space and phase space. It examines both Lagrangian and Hamiltonian formulations before qualitatively discussing some interesting features of gauge fixing. This formulation is then linked to superspace and Grassmann variables for a fermionic field theory. The chapter then shows that the corresponding operatorial formulation is none other than the Koopman–von Neumann theory. In parallel to quantum theory, the classical propagator or the transition amplitude between two classical states is given exactly by the

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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and dis

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Deruelle, Nathalie, and Jean-Philippe Uzan. Hamiltonian mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0009.

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This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension o

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Mann, Peter. Newton’s Three Laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0001.

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This chapter introduces Newton’s laws, the Newtonian formulation of mechanics and key concepts such as configuration space and phase space for later development. In 1687, the natural philosopher Sir Isaac Newton published the Principia Mathematica and, with it, sparked the revolutionary ideas key to all branches of classical physics. In this chapter, the system is the object of interest and is considered to be either a single or a collection of generic particles that are not governed by quantum mechanics, for quantum systems do not follow these laws explicitly. Results for systems of particles

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Mann, Peter. Hamilton’s Equations & Routhian Reduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0016.

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In this chapter, the Poisson bracket and angular momentum are investigated and first integrals are used to develop conservation laws as a canonical Noether’s theorem. The Poisson bracket was developed by the French mathematician Poisson in the late nineteenth century and it is a reformulation, or at least a tidying up, of Hamilton’s equations into one neat package. The Poisson bracket of a quantity with the Hamiltonian describes the time evolution of that quantity as one moves along a curve in phase space. The Lie algebra structure of symmetries in mechanics is highlighted using this formulati

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Mercati, Flavio. Shape Dynamics and the Linking Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0012.

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This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational d

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Mann, Peter. Lagrangian Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0025.

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In this chapter, Hamiltonian field theory is derived classically via a Hamiltonian density, using the zeroth component of a 4-momentum density. In field theory, space and time are considered to be on equal footing but, in the canonical formalism, time is treated as being special and therefore, by definition, it is not covariant. Consequently, most field theoretic models are built on Lagrangian formulations. A covariant canonical formalism is the subject of the de Donder–Weyl formalism, which is briefly discussed as a covariant Hamiltonian field theory. In addition, the chapter examines the cas

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Kondrakiewicz, Dariusz. Prognozowanie i symulacje międzynarodowe. Instytut Europy Środkowej, 2021. http://dx.doi.org/10.36874/m21580.

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International forecasting and simulation is a study that summarizes research, in a shortened and integrated version. The thematic scope concerns the basic terminology and methodological issues of forecasts and the forecasting process itself, forecasting institutions and the final product, i.e. international forecasts. The main goal is to present and systematize basic knowledge in the field of forecasting in international relations. The book is generally aimed at all those interested in international affairs. However, the author hopes that the publication will also be helpful for researchers an

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Book chapters on the topic "Phase Space Formulation"

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Nair, V. Parameswaran. "Symplectic Form and Poisson Brackets." In SpringerBriefs in Physics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65801-3_2.

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Ashtekar, Abhay, Luca Bombelli, and Rabinder Koul. "Phase space formulation of general relativity without a 3+1 splitting." In The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17894-5_378.

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Schroeck, Franklin E. "Consequences of Formulating Quantum Mechanics on Phase Space." In Quantum Mechanics on Phase Space. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2830-0_4.

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Kenkre, V. M. "Thermal Effects: Phase-Space and Langevin Formulations." In Interplay of Quantum Mechanics and Nonlinearity. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94811-5_8.

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Trigg, Dylan. ""The Horror of Darkness"." In Speculations IV. punctum books, 2013. https://doi.org/10.21983/p3.0032.1.18.

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“Life,” so Gaston Bachelard writes in The Poetics of Space on a note of steadfast optimism, “begins well, it begins enclosed, protected, all warm in the bosom of the house.”1 To the critic, Bachelard’s remarks might be seen as emblematic of a kind of failure in phenomenology to think outside an anthropomor-phised cosmos, in which the endless void of dark space is nothing less than the warm enclosure of the primal breast. To this end, the critic would have a point. After all, it is hard not to agree that much of phenomenology has indeed failed to move beyond the human realm and instead has emph

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Biagini, Carlo, Alberto Aglietti, LUCA MARZI, and Andrea Bongini. "A BIM-Based Framework for Facility Management Data Integration in Heritage Assets." In CONVR 2023 - Proceedings of the 23rd International Conference on Construction Applications of Virtual Reality. Firenze University Press, 2023. http://dx.doi.org/10.36253/979-12-215-0289-3.115.

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The operational phase of a real estate asset accounts for approximately 80% of the overall investment and management costs throughout the entire life cycle of the building, and the activities of space management and monitoring of building components and systems play a crucial role in ensuring the well-being and health of users. The AECO (Architecture, Engineering, Construction, and Operation) industry is transitioning towards a new framework governed by data-driven processes. In this context, Building Information Modeling (BIM) can support the utilization of big data generated throughout diffe

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Biagini, Carlo, Alberto Aglietti, LUCA MARZI, and Andrea Bongini. "A BIM-Based Framework for Facility Management Data Integration in Heritage Assets." In CONVR 2023 - Proceedings of the 23rd International Conference on Construction Applications of Virtual Reality. Firenze University Press, 2023. http://dx.doi.org/10.36253/10.36253/979-12-215-0289-3.115.

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The operational phase of a real estate asset accounts for approximately 80% of the overall investment and management costs throughout the entire life cycle of the building, and the activities of space management and monitoring of building components and systems play a crucial role in ensuring the well-being and health of users. The AECO (Architecture, Engineering, Construction, and Operation) industry is transitioning towards a new framework governed by data-driven processes. In this context, Building Information Modeling (BIM) can support the utilization of big data generated throughout diffe

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Attard, Phil. "Wave packet formulation." In Quantum Statistical Mechanics in Classical Phase Space. IOP Publishing, 2021. http://dx.doi.org/10.1088/978-0-7503-4055-7ch2.

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"The Phase Space Formulation of Quantum Mechanics." In Advanced Topics in Quantum Mechanics. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108863384.004.

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Bracken, Paul. "Classical and Quantum Integrability: A Formulation That Admits Quantum Chaos." In Chaotic Systems [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94491.

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The concept of integrability of a quantum system is developed and studied. By formulating the concepts of quantum degree of freedom and quantum phase space, a realization of the dynamics is achieved. For a quantum system with a dynamical group G in one of its unitary irreducible representative carrier spaces, the quantum phase space is a finite topological space. It is isomorphic to a coset space G/R by means of the unitary exponential mapping, where R is the maximal stability subgroup of a fixed state in the carrier space. This approach has the distinct advantage of exhibiting consistency bet

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Conference papers on the topic "Phase Space Formulation"

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Curran, Joseph John, Jerry Curran, and Louis MacDowell. "Galvanic Liquid Applied Coating Development for Protection of Steel in Concrete." In CORROSION 2004. NACE International, 2004. https://doi.org/10.5006/c2004-04335.

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Abstract Corrosion of reinforcing steel in concrete is a major problem affecting NASA facilities at Kennedy Space Center (KSC), other government agencies, and the general public. Problems include damage to KSC launch support structures, transportation and marine infrastructures, as well as building structures. A galvanic liquid applied coating was developed at KSC in order to address this problem. The coating is a non-epoxy metal rich ethyl silicate liquid coating. The coating is applied as a liquid from initial stage to final stage. Preliminary data shows that this coating system exceeds the

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Obeyesekere, Nihal, Jonathan Wylde, and Thusitha Wickramarachchi. "Formulation of Corrosion Inhibitors Using Design of Experiment (DOE) Methods and Discovering Highly Performing Inhibitors by High Throughput Experimentation (HTE) Methods Using Critical Micelle Concentration." In CORROSION 2021. AMPP, 2021. https://doi.org/10.5006/c2021-16994.

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ABSTRACT Critical micelle concentration (CMC) is a known indicator for surfactants such as corrosion inhibitors ability to partition from two phase systems such as oil and water. Most corrosion inhibitors are surface active and at critical micelle concentration, the chemical is partitioned to water, physadsorb on metallic surfaces and form a physical barrier between steel and water. This protective barrier thus prevents corrosion from taking place on the metal surface When the applied chemical concentration is equal or higher than the CMC, the chemical is available in aqueous phase, thus preve

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Signorelli, Joel, Duane L. Bindschadler, Kathryn A. Schimmels, and Shin M. Huh. "Operability Engineering for Europa Clipper: Formulation Phase Results and Lessons." In 15th International Conference on Space Operations. American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-2629.

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Ivanco, Marie L., and Christopher A. Jones. "Assessing the Science Benefit of Space Mission Concepts in the Formulation Phase." In 2020 IEEE Aerospace Conference. IEEE, 2020. http://dx.doi.org/10.1109/aero47225.2020.9172755.

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Casey, Thomas M., Nerses V. Armani, Wes L. Alexander, et al. "The wide field infrared survey telescope (WFIRST) observatory: design formulation (phase-A) overview (Conference Presentation)." In Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave, edited by Howard A. MacEwen, Makenzie Lystrup, Giovanni G. Fazio, Natalie Batalha, Edward C. Tong, and Nicholas Siegler. SPIE, 2018. http://dx.doi.org/10.1117/12.2313748.

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SHESTAKOVA, T. P. "THE FORMULATION OF GENERAL RELATIVITY IN EXTENDED PHASE SPACE AS A WAY TO ITS QUANTIZATION." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0247.

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Vladimirov, Igor G. "A phase-space formulation of the Belavkin-Kushner-Stratonovich filtering equation for nonlinear quantum stochastic systems*." In 2016 IEEE Conference on Norbert Wiener in the 21st Century (21CW). IEEE, 2016. http://dx.doi.org/10.1109/norbert.2016.7547465.

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Melamed, Shlomo T., and Ehud Heyman. "Phase-space beam summation for time-harmonic and time-dependent radiation from extended apertures: 3-D formulation." In OE/LASE '92, edited by Howard E. Brandt. SPIE, 1992. http://dx.doi.org/10.1117/12.137134.

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Boledi, Leonardo, Benjamin Terschanski, Stefanie Elgeti, and Julia Kowalski. "A Space-Time FE Level-set method for convection coupled phase-change processes." In VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12329.

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Phase transition processes have great relevance for both engineering and scientific applications. In production engineering, for instance, metal welding and alloy solidification are topics of ongoing research.In this contribution we focus on the convection coupled solid-liquid phase change of a single species, e.g. water. The material is assumed to be incompressible within the two phases, but we account for density changes across the phase interface. To describe the process, we need to solve the incompressible Navier-Stokes equations and the heat equation for both phases over time. The positio

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Obeyesekere, Nihal U., Jonathan J. Wylde, Thusitha Wickramarachchi, and Lucious Kemp. "Formulation of High-Performance Corrosion Inhibitors in the 21St Century: Robotic High Throughput Experimentation and Design of Experiments." In SPE International Conference on Oilfield Chemistry. SPE, 2021. http://dx.doi.org/10.2118/204353-ms.

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Abstract Critical micelle concentration (CMC) is a known indicator for surfactants such as corrosion inhibitors’ ability to partition to water from two phase systems such as oil and water. Most corrosion inhibitors are surface active. At critical micelle concentration, the chemical is partitioned to water from the interface, physisorption on metallic surfaces and forms a physical barrier between steel and corrosive water. This protective barrier thus prevents corrosion initiating on the metal surface. When the applied chemical concentration is equal or higher than the CMC, the surfactant is pa

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