Guglielmo Cinque and Luigi Rizzi
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195393675
- eISBN:
- 9780199796847
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195393675.001.0001
- Subject:
- Linguistics, Syntax and Morphology
The present volume intends to contribute to our understanding of the grammar of spatial prepositional phrases by focusing on one particular aspect of their syntax that has remained relatively ...
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The present volume intends to contribute to our understanding of the grammar of spatial prepositional phrases by focusing on one particular aspect of their syntax that has remained relatively neglected: the fine-grained articulation of their internal structure. The analyses presented in the book, in spite of their being based on rather different data and considerations, reach strikingly convergent conclusions on the existence of a rich internal structure for spatial PPs. These, in addition to being introduced by (overt or covert) directional and stative prepositions comprise degree phrases, deictic, viewpoint and orientation particles, and an often nonpronounced N ‘place.’Less
The present volume intends to contribute to our understanding of the grammar of spatial prepositional phrases by focusing on one particular aspect of their syntax that has remained relatively neglected: the fine-grained articulation of their internal structure. The analyses presented in the book, in spite of their being based on rather different data and considerations, reach strikingly convergent conclusions on the existence of a rich internal structure for spatial PPs. These, in addition to being introduced by (overt or covert) directional and stative prepositions comprise degree phrases, deictic, viewpoint and orientation particles, and an often nonpronounced N ‘place.’
Peter Hagström and Gunnar Hedlund
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198296041
- eISBN:
- 9780191596070
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198296045.003.0008
- Subject:
- Economics and Finance, Microeconomics
Looks at the limits of hierarchy in the internal structure of a firm and suggests an explanation as to why the concept of a simple hierarchy has been so readily accepted and is so seemingly ...
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Looks at the limits of hierarchy in the internal structure of a firm and suggests an explanation as to why the concept of a simple hierarchy has been so readily accepted and is so seemingly successful. The authors argue that the historically successful hierarchy has actually hidden a different underlying structure that is only now being revealed. Hierarchy ensures relative efficiency in a known, stable situation, but these are hardly the salient characteristics of the modern competitive environment, and firms are found to experiment with ways to deal with these new pressures in changes that range from ad hoc measures to radical structural transformations. The fundamental trade‐off here is one of (flexible) efficiency today and of positioning for tomorrow; one‐dimensional hierarchy could achieve that yesterday. The authors conclude that, in effect, there are, and always have been, three structural dimensions at play, namely position, action, and knowledge; these dimensions have coincided (or misalignments have not been apparent) in the past, but that is seen to be less and less the case nowadays, and nowhere is this more apparent than in the modern multinational corporation; this theoretically and historically derived three‐structural‐dimensions model is tried out on an illustrative firm case (Oticon A/S in Denmark).Less
Looks at the limits of hierarchy in the internal structure of a firm and suggests an explanation as to why the concept of a simple hierarchy has been so readily accepted and is so seemingly successful. The authors argue that the historically successful hierarchy has actually hidden a different underlying structure that is only now being revealed. Hierarchy ensures relative efficiency in a known, stable situation, but these are hardly the salient characteristics of the modern competitive environment, and firms are found to experiment with ways to deal with these new pressures in changes that range from ad hoc measures to radical structural transformations. The fundamental trade‐off here is one of (flexible) efficiency today and of positioning for tomorrow; one‐dimensional hierarchy could achieve that yesterday. The authors conclude that, in effect, there are, and always have been, three structural dimensions at play, namely position, action, and knowledge; these dimensions have coincided (or misalignments have not been apparent) in the past, but that is seen to be less and less the case nowadays, and nowhere is this more apparent than in the modern multinational corporation; this theoretically and historically derived three‐structural‐dimensions model is tried out on an illustrative firm case (Oticon A/S in Denmark).
Michio Morishima
- Published in print:
- 1969
- Published Online:
- November 2003
- ISBN:
- 9780198281641
- eISBN:
- 9780191596667
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0012
- Subject:
- Economics and Finance, Development, Growth, and Environmental
Various dynamic utility functions are proposed for optimum economic growth. The different sections of the chapter discuss: maximization of satisfaction over time; whether dynamic utility should be ...
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Various dynamic utility functions are proposed for optimum economic growth. The different sections of the chapter discuss: maximization of satisfaction over time; whether dynamic utility should be cardinal; the postulated properties of dynamic preferences—separability, consistence, and stationariness; and the invariability of the internal structure of the dynamic utility function with respect to monotonic transformation of the index. All this discussion is based on the assumption that the marginal rate of substitution between any two contemporary goods is independent of consumption in any other period. Finally, an alternative proposal is made based on the fact that the marginal rate of substitution between any two contemporary goods is not independent of consumption in any other period.Less
Various dynamic utility functions are proposed for optimum economic growth. The different sections of the chapter discuss: maximization of satisfaction over time; whether dynamic utility should be cardinal; the postulated properties of dynamic preferences—separability, consistence, and stationariness; and the invariability of the internal structure of the dynamic utility function with respect to monotonic transformation of the index. All this discussion is based on the assumption that the marginal rate of substitution between any two contemporary goods is independent of consumption in any other period. Finally, an alternative proposal is made based on the fact that the marginal rate of substitution between any two contemporary goods is not independent of consumption in any other period.
I.S. GLASS
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199550258
- eISBN:
- 9780191718700
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199550258.003.0007
- Subject:
- Physics, History of Physics
This chapter begins by investigating Arthur Eddington's early life and his biography. It discusses that one of his first research programmes concerned the ‘star drifts’ discovered by Jacobus Kapteyn. ...
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This chapter begins by investigating Arthur Eddington's early life and his biography. It discusses that one of his first research programmes concerned the ‘star drifts’ discovered by Jacobus Kapteyn. It narrates his devotion to the study of stellar dynamics as well as the anomalies that he encountered. The chapter also evaluates his investigations regarding the solar eclipse, the internal structure of the stars, and Sirius B. It then examines some of Eddington's wilder speculations.Less
This chapter begins by investigating Arthur Eddington's early life and his biography. It discusses that one of his first research programmes concerned the ‘star drifts’ discovered by Jacobus Kapteyn. It narrates his devotion to the study of stellar dynamics as well as the anomalies that he encountered. The chapter also evaluates his investigations regarding the solar eclipse, the internal structure of the stars, and Sirius B. It then examines some of Eddington's wilder speculations.
Kathleen Gallagher Cunningham
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199364909
- eISBN:
- 9780199364930
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199364909.003.0005
- Subject:
- Political Science, International Relations and Politics
This chapter examines when self-determination (SD) groups and states cannot achieve successful bargains over the status of the group and engage in civil war. Conflict prevention entails compromise ...
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This chapter examines when self-determination (SD) groups and states cannot achieve successful bargains over the status of the group and engage in civil war. Conflict prevention entails compromise that satisfies both the state and most, if not all, of the SD group factions. Barriers to credible commitments and uncertainty about what deal might actually “resolve” the dispute with all parties play a large role in determining when war will break out. As the theory developed in the book suggests, moderately divided states are better able to avoid war, but highly divided SD groups are prone to conflict with the state. Both the large-n statistical analysis and the comparative case studies of northeast Indian SD groups show that the internal structure of states and SD groups have substantial effects on the occurrence of civil war.Less
This chapter examines when self-determination (SD) groups and states cannot achieve successful bargains over the status of the group and engage in civil war. Conflict prevention entails compromise that satisfies both the state and most, if not all, of the SD group factions. Barriers to credible commitments and uncertainty about what deal might actually “resolve” the dispute with all parties play a large role in determining when war will break out. As the theory developed in the book suggests, moderately divided states are better able to avoid war, but highly divided SD groups are prone to conflict with the state. Both the large-n statistical analysis and the comparative case studies of northeast Indian SD groups show that the internal structure of states and SD groups have substantial effects on the occurrence of civil war.
John Sloboda
- Published in print:
- 2004
- Published Online:
- March 2012
- ISBN:
- 9780198530121
- eISBN:
- 9780191689741
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530121.003.0009
- Subject:
- Psychology, Music Psychology
This chapter offers some observations on music as a language. Some of the most important things about music seem to arise from the ways it is different from a language. Like music, the primary medium ...
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This chapter offers some observations on music as a language. Some of the most important things about music seem to arise from the ways it is different from a language. Like music, the primary medium of language is sound. In themselves, however, these sounds are just sounds, with various physical characteristics such as pitch, amplitude, and timbre. They are not language. What makes them language is what human brains do with them. It seems that what human brains do is to attempt to map these sounds onto internal structures. When some kind of match has been made with these structures, then language can be said to have come into existence. These internal structures seem to be divided into these levels of in language: phonology, syntax, and semantics. Generally, some contact has to be made at each level for speech to be understood or created.Less
This chapter offers some observations on music as a language. Some of the most important things about music seem to arise from the ways it is different from a language. Like music, the primary medium of language is sound. In themselves, however, these sounds are just sounds, with various physical characteristics such as pitch, amplitude, and timbre. They are not language. What makes them language is what human brains do with them. It seems that what human brains do is to attempt to map these sounds onto internal structures. When some kind of match has been made with these structures, then language can be said to have come into existence. These internal structures seem to be divided into these levels of in language: phonology, syntax, and semantics. Generally, some contact has to be made at each level for speech to be understood or created.
Rauna Kuokkanen
- Published in print:
- 2019
- Published Online:
- March 2019
- ISBN:
- 9780190913281
- eISBN:
- 9780190913311
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190913281.003.0005
- Subject:
- Political Science, Comparative Politics, Political Theory
Chapter 4 examines the gender power dynamics of existing Indigenous self-government institutions, cultures, and discourses in Canada, Greenland, and Scandinavia. Employing feminist institutional ...
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Chapter 4 examines the gender power dynamics of existing Indigenous self-government institutions, cultures, and discourses in Canada, Greenland, and Scandinavia. Employing feminist institutional analysis, the author investigates how Indigenous political institutions are gendered. Gendering refers to a multiplicity of interacting processes shaped by the distinction between male and female, masculine and feminine, which create and conceptualize social structures and privilege certain groups over others. Gendering occurs through the construction of various divisions along gender lines and through interpersonal interactions that enact gendered hierarchies. Institutions and organizations are also gendered through the construction of symbols, images, and ideologies that legitimize institutions generally conceived as gender-neutral. Using interview data, the chapter analyzes the gender regimes of Indigenous political institutions and women’s participation in the existing self-government institutions. Also considered are alternative forms of advancing Indigenous self-determination by examining Indigenous women’s grassroots leadership and the growing movement of reclaiming Indigenous women’s authority.Less
Chapter 4 examines the gender power dynamics of existing Indigenous self-government institutions, cultures, and discourses in Canada, Greenland, and Scandinavia. Employing feminist institutional analysis, the author investigates how Indigenous political institutions are gendered. Gendering refers to a multiplicity of interacting processes shaped by the distinction between male and female, masculine and feminine, which create and conceptualize social structures and privilege certain groups over others. Gendering occurs through the construction of various divisions along gender lines and through interpersonal interactions that enact gendered hierarchies. Institutions and organizations are also gendered through the construction of symbols, images, and ideologies that legitimize institutions generally conceived as gender-neutral. Using interview data, the chapter analyzes the gender regimes of Indigenous political institutions and women’s participation in the existing self-government institutions. Also considered are alternative forms of advancing Indigenous self-determination by examining Indigenous women’s grassroots leadership and the growing movement of reclaiming Indigenous women’s authority.
Nige West and Oleg Tsarev
- Published in print:
- 2009
- Published Online:
- October 2013
- ISBN:
- 9780300123470
- eISBN:
- 9780300156416
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300123470.003.0031
- Subject:
- History, British and Irish Modern History
This chapter focuses on the information received from STANLEY dated 8 March 1946 regarding SIS's internal structure, according to which, Major General Sinclair was appointed Deputy Director (VCSS); ...
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This chapter focuses on the information received from STANLEY dated 8 March 1946 regarding SIS's internal structure, according to which, Major General Sinclair was appointed Deputy Director (VCSS); he was formerly Director of Military Intelligence at the War Office. He deputized and assisted in all aspects of SIS's work—namely, the procurement of intelligence, its evaluation and distribution, administration, finance, communications, and so on. In theory, CSS determined policy, and VCSS inspected its implementation. The information revealed that Sinclair was proving very active, and also played a significant role in directing SIS's work. VCSS had five directorates reporting to him, headed respectively by the Director of Intelligence, the Director of Information, the Director of Finance and Administration, and the Director of Training and Development. These directorates covered almost all of SIS's activities.Less
This chapter focuses on the information received from STANLEY dated 8 March 1946 regarding SIS's internal structure, according to which, Major General Sinclair was appointed Deputy Director (VCSS); he was formerly Director of Military Intelligence at the War Office. He deputized and assisted in all aspects of SIS's work—namely, the procurement of intelligence, its evaluation and distribution, administration, finance, communications, and so on. In theory, CSS determined policy, and VCSS inspected its implementation. The information revealed that Sinclair was proving very active, and also played a significant role in directing SIS's work. VCSS had five directorates reporting to him, headed respectively by the Director of Intelligence, the Director of Information, the Director of Finance and Administration, and the Director of Training and Development. These directorates covered almost all of SIS's activities.
Ada Bronowski
- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198842880
- eISBN:
- 9780191878794
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198842880.003.0009
- Subject:
- Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy
This chapter focuses on the internal structure of the lekton. It traces the critical development of the notion of a sentence from Plato’s ‘shortest logos’ in the Sophist with minimal parts, a ...
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This chapter focuses on the internal structure of the lekton. It traces the critical development of the notion of a sentence from Plato’s ‘shortest logos’ in the Sophist with minimal parts, a mainstay in the Platonic and Peripatetic tradition, to the Stoic perspective focused on the notion of completeness: complete is all that is necessary to get one lekton said, however many words or parts of speech may be required to do so. This debate was appropriated, and its different strands merged by the ancient Grammarians. The Stoic influence in the establishment of the discipline is brought out in the discussion. Completeness leads to considerations of incompleteness. The different kinds of complete lekta (questions, commands, exclamations) are tested against a standard of completeness by stripping away different elements to discover that there is a constant axiōmatic core within each kind. A final discussion of the relation of the katēgorēma to the case-ptōsis unfolds into an analysis of the ptōsis as nothing other than forever dependent on a katēgorēma, with no status in itself, but ensconced in a web of relations between concepts in our mind, the hybrid case-bearer (tunchanon), and the external object. Problem cases such as the conundrum of the perishing lekton and the parakatēgorēma are examined in the light of previous claims.Less
This chapter focuses on the internal structure of the lekton. It traces the critical development of the notion of a sentence from Plato’s ‘shortest logos’ in the Sophist with minimal parts, a mainstay in the Platonic and Peripatetic tradition, to the Stoic perspective focused on the notion of completeness: complete is all that is necessary to get one lekton said, however many words or parts of speech may be required to do so. This debate was appropriated, and its different strands merged by the ancient Grammarians. The Stoic influence in the establishment of the discipline is brought out in the discussion. Completeness leads to considerations of incompleteness. The different kinds of complete lekta (questions, commands, exclamations) are tested against a standard of completeness by stripping away different elements to discover that there is a constant axiōmatic core within each kind. A final discussion of the relation of the katēgorēma to the case-ptōsis unfolds into an analysis of the ptōsis as nothing other than forever dependent on a katēgorēma, with no status in itself, but ensconced in a web of relations between concepts in our mind, the hybrid case-bearer (tunchanon), and the external object. Problem cases such as the conundrum of the perishing lekton and the parakatēgorēma are examined in the light of previous claims.
Bethany Lochbihler
- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198778264
- eISBN:
- 9780191823770
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198778264.003.0004
- Subject:
- Linguistics, Syntax and Morphology, Theoretical Linguistics
This chapter proposes a distinction between syntactic phases headed by C and D as final, in contrast to other non-final phases. Final phases act as stronger boundaries for head movement and provide ...
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This chapter proposes a distinction between syntactic phases headed by C and D as final, in contrast to other non-final phases. Final phases act as stronger boundaries for head movement and provide final landing sites for A′-movement, but non-final phases, while still constituting spell-out domains, impose weaker boundaries. This chapter particularly investigates the phonological effects of final and non-final phases in Ojibwe, and the different processes that can apply at the spell-out of each type of domain. An analysis is provided for an ordering paradox between palatalization and apocope, which is claimed to be accounted for by reference to the syntactic structure and the timing of application of these processes at the spell-out of final or non-final phases.Less
This chapter proposes a distinction between syntactic phases headed by C and D as final, in contrast to other non-final phases. Final phases act as stronger boundaries for head movement and provide final landing sites for A′-movement, but non-final phases, while still constituting spell-out domains, impose weaker boundaries. This chapter particularly investigates the phonological effects of final and non-final phases in Ojibwe, and the different processes that can apply at the spell-out of each type of domain. An analysis is provided for an ordering paradox between palatalization and apocope, which is claimed to be accounted for by reference to the syntactic structure and the timing of application of these processes at the spell-out of final or non-final phases.
Jean-Luc Bouchez and Adolphe Nicolas
- Published in print:
- 2021
- Published Online:
- October 2021
- ISBN:
- 9780192843876
- eISBN:
- 9780191926501
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192843876.003.0003
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
The discontinuous nature of brittle behavior contrasts with the apparent continuous nature of ductile deformation. Continuity is obviously scale dependent. Faults and fractures are common features of ...
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The discontinuous nature of brittle behavior contrasts with the apparent continuous nature of ductile deformation. Continuity is obviously scale dependent. Faults and fractures are common features of discontinuous deformation. They are particularly abundant in near-surface geological formations, that is, settings at low confining pressures. If ductile behaviour happens to be present in the upper crust, for example in clay and gypsum formations, brittle behaviour is not lacking in the deep crust. This is illustrated by dyke emplacement, feldspar crystals affected by fractures in granite magmas, and brittle behaviour of the mantle at Moho level. Discontinuous structures implying no or limited displacement – namely joints, fissures and tensile cracks – are briefly considered first, and faults, on which large displacements may take place are examined in detail. Faults, ductile faults and shear zones are representative strain localization structures. In this chapter, the relationships between brittle structures and the state of stress responsible for their orientation and evolution are discussed. According to its viscosity (‘viscosity’ is often preferred over ‘competence’), the behaviour of a rock is purely brittle, brittle–ductile or purely ductile. These two latter behaviours will be examined in the following chapter. Fractures are preferred fluid-collection sites, hence potential location for mineralization and formation of ore-veins. They are critically important during the formation stage of plutons and volcanos (see Chapter 7) due to silicate melt circulation into fractures.Less
The discontinuous nature of brittle behavior contrasts with the apparent continuous nature of ductile deformation. Continuity is obviously scale dependent. Faults and fractures are common features of discontinuous deformation. They are particularly abundant in near-surface geological formations, that is, settings at low confining pressures. If ductile behaviour happens to be present in the upper crust, for example in clay and gypsum formations, brittle behaviour is not lacking in the deep crust. This is illustrated by dyke emplacement, feldspar crystals affected by fractures in granite magmas, and brittle behaviour of the mantle at Moho level. Discontinuous structures implying no or limited displacement – namely joints, fissures and tensile cracks – are briefly considered first, and faults, on which large displacements may take place are examined in detail. Faults, ductile faults and shear zones are representative strain localization structures. In this chapter, the relationships between brittle structures and the state of stress responsible for their orientation and evolution are discussed. According to its viscosity (‘viscosity’ is often preferred over ‘competence’), the behaviour of a rock is purely brittle, brittle–ductile or purely ductile. These two latter behaviours will be examined in the following chapter. Fractures are preferred fluid-collection sites, hence potential location for mineralization and formation of ore-veins. They are critically important during the formation stage of plutons and volcanos (see Chapter 7) due to silicate melt circulation into fractures.
Nathalie Deruelle and Jean-Philippe Uzan
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter studies various gravitational effects arising from the non-sphericity of celestial bodies. It first considers the quadrupole expansion of the potential, as well as the causes of the ...
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This chapter studies various gravitational effects arising from the non-sphericity of celestial bodies. It first considers the quadrupole expansion of the potential, as well as the causes of the non-sphericity of the bodies. Finally, it turns to the figure of the Earth. To calculate the proper potential of the Earth, it attempts to determine its deformation due to a perturbing potential. Doing this accurately requires knowledge of the internal structure of the Earth and use of the techniques of the mechanics of continuous media. In this approach, the internal stress–strain relationships of a body are described by various phenomenological parameters and it becomes possible to study the response of the body (deformation, oscillations, etc.) to the field of an external force.Less
This chapter studies various gravitational effects arising from the non-sphericity of celestial bodies. It first considers the quadrupole expansion of the potential, as well as the causes of the non-sphericity of the bodies. Finally, it turns to the figure of the Earth. To calculate the proper potential of the Earth, it attempts to determine its deformation due to a perturbing potential. Doing this accurately requires knowledge of the internal structure of the Earth and use of the techniques of the mechanics of continuous media. In this approach, the internal stress–strain relationships of a body are described by various phenomenological parameters and it becomes possible to study the response of the body (deformation, oscillations, etc.) to the field of an external force.
Bryan J. Dalton, John Jeffers, and Stephen M. Barnett
- Published in print:
- 2014
- Published Online:
- April 2015
- ISBN:
- 9780199562749
- eISBN:
- 9780191747311
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562749.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics
This chapter deals with deriving functional Fokker–Planck equations (FFPEs) that govern the behaviour of phase space distribution functionals (normalised and unnormalised) for boson and fermion ...
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This chapter deals with deriving functional Fokker–Planck equations (FFPEs) that govern the behaviour of phase space distribution functionals (normalised and unnormalised) for boson and fermion systems due to dynamical or thermal evolution. The approach used is to derive correspondence rules, which map changes in the density operator when multiplied from left or right by field annihilation or creation operators (as in evolution equations) onto corresponding changes in distribution functionals, these being functional differentiations and/or multiplications by field functions (left or right for fermions). Derivations are carried out by applying mode expansions to previously established results for distribution functions. Specific forms are obtained for FFPEs relating drift vector and diffusion matrix elements in the FFPE to corresponding quantities in equivalent Fokker–Planck equations and to sums over mode functions. Symmetry (bosons) and antisymmetry (fermions) properties of the diffusion matrix are established. Results are generalised to treat cases with several sets of field operators.Less
This chapter deals with deriving functional Fokker–Planck equations (FFPEs) that govern the behaviour of phase space distribution functionals (normalised and unnormalised) for boson and fermion systems due to dynamical or thermal evolution. The approach used is to derive correspondence rules, which map changes in the density operator when multiplied from left or right by field annihilation or creation operators (as in evolution equations) onto corresponding changes in distribution functionals, these being functional differentiations and/or multiplications by field functions (left or right for fermions). Derivations are carried out by applying mode expansions to previously established results for distribution functions. Specific forms are obtained for FFPEs relating drift vector and diffusion matrix elements in the FFPE to corresponding quantities in equivalent Fokker–Planck equations and to sums over mode functions. Symmetry (bosons) and antisymmetry (fermions) properties of the diffusion matrix are established. Results are generalised to treat cases with several sets of field operators.