18,149 research outputs found
Quantum Mechanics Lecture Notes. Selected Chapters
These are extended lecture notes of the quantum mechanics course which I am
teaching in the Weizmann Institute of Science graduate physics program. They
cover the topics listed below. The first four chapter are posted here. Their
content is detailed on the next page. The other chapters are planned to be
added in the coming months.
1. Motion in External Electromagnetic Field. Gauge Fields in Quantum
Mechanics.
2. Quantum Mechanics of Electromagnetic Field
3. Photon-Matter Interactions
4. Quantization of the Schr\"odinger Field (The Second Quantization)
5. Open Systems. Density Matrix
6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation
7. Mean Field Approaches for Many Body Systems -- Fermions and Boson
Tauberian identities and the connection to Wile E. Coyote physics
The application of the motion of a vertically suspended mass-spring system
released under tension is studied focusing upon the delay timescale for the
bottom mass as a function of the spring constants and masses. This
``hang-time", reminiscent of the Coyote and Road Runner cartoons, is quantified
using the far-field asymptotic expansion of the bottom mass' Laplace transform.
These asymptotics are connected to the short time mass dynamics through
Tauberian identities and explicit residue calculations. It is shown, perhaps
paradoxically, that this delay timescale is maximized in the large mass limit
of the top ``boulder". Experiments are presented and compared with the
theoretical predictions. This system is an exciting example for the teaching of
mass-spring dynamics in classes on Ordinary Differential Equations, and does
not require any normal mode calculations for these predictions
Identifying and responding to people with mild learning disabilities in the probation service
It has long been recognised that, like many other individuals, people with learningdisabilities find their way into the criminal justice system. This fact is not disputed. Whathas been disputed, however, is the extent to which those with learning disabilities arerepresented within the various agencies of the criminal justice system and the ways inwhich the criminal justice system (and society) should address this. Recently, social andlegislative confusion over the best way to deal with offenders with learning disabilities andmental health problems has meant that the waters have become even more muddied.Despite current government uncertainty concerning the best way to support offenders withlearning disabilities, the probation service is likely to continue to play a key role in thesupervision of such offenders. The three studies contained herein aim to clarify the extentto which those with learning disabilities are represented in the probation service, toexamine the effectiveness of probation for them and to explore some of the ways in whichprobation could be adapted to fit their needs.Study 1 and study 2 showed that around 10% of offenders on probation in Kent appearedto have an IQ below 75, putting them in the bottom 5% of the general population. Study 3was designed to assess some of the support needs of those with learning disabilities in theprobation service, finding that many of the materials used by the probation service arelikely to be too complex for those with learning disabilities to use effectively. To addressthis, a model for service provision is tentatively suggested. This is based on the findings ofthe three studies and a pragmatic assessment of what the probation service is likely to becapable of achieving in the near future
Security of Scottish electricity supply: gauging the perceptions of industry stakeholders
Efforts to reduce greenhouse gas (GHG) emissions together with the increase in electricity generated from renewable energy are dramatically changing the electricity supply landscape. This document reports and reviews the opinions of industry experts and stakeholders regarding security of electricity supply in Scotland, collected in May 2021 via an online survey and subsequent discussions in a roundtable event in July 2021.https://www.climatexchange.org.uk/media/5118/cxc-security-of-scottish-electricity-supply-gauging-the-perceptions-of-industry-stakeholders-september-2021.pd
Applications of higher-form symmetries at strong and weak coupling
In this thesis we consider two distinct applications of higher-form symmetries in quantum field theory. First we explore the spontaneous breaking of higher-form symmetry in a holographic quantum field theory containing matter fields in the fundamental representation of the gauge group U(N). At strong coupling, we numerically solve the bulk equations of motion to compute the current-current Green’s function and demonstrate the existence of a goldstone mode. We then compare to direct analytic perturbative results obtained at weak coupling. In the second half of the thesis we work with a hydrodynamic effective field theory which possesses a higher-form symmetry. In particular, we consider a natural higher-derivative correction to force-free electrodynamics and compute a hydrodynamic transport coefficient from microscopics. Concretely, this is a perturbative QED calculation in a background magnetic field. Finally we compare our findings to astrophysical observations
‘Mental fight’ and ‘seeing & writing’ in Virginia Woolf and William Blake
This thesis is the first full-length study to assess the writer and publisher Virginia Woolf’s (1882-1941) responses to the radical Romantic poet-painter, and engraver, William Blake (1757-1827). I trace Woolf’s public and private, overt and subtle references to Blake in fiction, essays, notebooks, diaries, letters and drawings. I have examined volumes in Leonard and Virginia Woolf’s library that are pertinent, directly and indirectly, to Woolf’s understanding of Blake. I focus on Woolf’s key phrases about Blake: ‘Mental fight’, and ‘seeing & writing.’
I consider the other phrases Woolf uses to think about Blake in the context of these two categories. Woolf and Blake are both interested in combining visual and verbal aesthetics (‘seeing & writing’). They are both critical of their respective cultures (‘Mental fight’). Woolf mentions ‘seeing & writing’ in connection to Blake in a 1940 notebook. She engages with Blake’s ‘Mental fight’ in ‘Thoughts on Peace in an Air Raid’ (1940).
I map late nineteenth and early twentieth-century opinion on Blake and explore Woolf’s engagement with Blake in these wider contexts. I make use of the circumstantial detail of Woolf’s friendship with the great Blake collector and scholar, Geoffrey Keynes (1887-1982), brother of Bloomsbury economist John Maynard Keynes. Woolf was party to the Blake centenary celebrations courtesy of Geoffrey Keynes’s organisation of the centenary exhibition in London in 1927.
Chapter One introduces Woolf’s explicit references to Blake and examines the record of Woolf scholarship that unites Woolf and Blake. To see how her predecessors had responded, Chapter Two examines the nineteenth-century interest in Blake and Woolf’s engagement with key nineteenth-century Blakeans. Chapter Three looks at the modernist, early twentieth-century engagement with Blake, to contextualise Woolf’s position on Blake. Chapter Four assesses how Woolf and Blake use ‘Mental fight’ to oppose warmongering and fascist politics. Chapter Five is about what Woolf and Blake write and think about the country and the city. Chapter Six discusses Woolf’s reading of John Milton (1608-1674) in relation to her interest in Blake, drawing on the evidence of Blake’s intense reading of Milton. Chapter Seven examines further miscellaneous continuities between Woolf and Blake. Chapter Eight proposes, in conclusion, that we can only form an impression of Woolf’s Blake.
The thesis also has three appendices. First, a chronology of key publications which chart Blake’s reputation as well as Woolf’s allusions to Blake. Second a list all of Blake’s poetry represented in Woolf’s library including contents page. The third lists all the other volumes in Woolf’s library that proved relevant. Although Woolf’s writing is the subject of this thesis, my project necessitates an attempt to recover how Blake was understood and misunderstood by numerous writers in the early twentieth century. The thesis argues Blake is a model radical Romantic who combines the visual and the verbal and that Woolf sees him as a kindred artist
How to Be a God
When it comes to questions concerning the nature of Reality, Philosophers and Theologians have the answers.
Philosophers have the answers that can’t be proven right. Theologians have the answers that can’t be proven wrong.
Today’s designers of Massively-Multiplayer Online Role-Playing Games create realities for a living. They can’t spend centuries mulling over the issues: they have to face them head-on. Their practical experiences can indicate which theoretical proposals actually work in practice.
That’s today’s designers. Tomorrow’s will have a whole new set of questions to answer.
The designers of virtual worlds are the literal gods of those realities. Suppose Artificial Intelligence comes through and allows us to create non-player characters as smart as us. What are our responsibilities as gods? How should we, as gods, conduct ourselves?
How should we be gods
BECOMEBECOME - A TRANSDISCIPLINARY METHODOLOGY BASED ON INFORMATION ABOUT THE OBSERVER
ABSTRACT
Andrea T. R. Traldi
BECOMEBECOME
A Transdisciplinary Methodology Based on Information about the Observer
The present research dissertation has been developed with the intention to provide practical strategies and discover new intellectual operations which can be used to generate Transdisciplinary insight. For this reason, this thesis creates access to new knowledge at different scales.
Firstly, as it pertains to the scale of new knowledge generated by those who attend Becomebecome events. The open-source nature of the Becomebecome methodology makes it possible for participants in Becomebecome workshops, training programmes and residencies to generate new insight about the specific project they are working on, which then reinforce and expand the foundational principles of the theoretical background.
Secondly, as it pertains to the scale of the Becomebecome framework, which remains independent of location and moment in time. The method proposed to access Transdisciplinary knowledge constitutes new knowledge in itself because the sequence of activities, described as physical and mental procedures and listed as essential criteria, have never been found organised
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in such a specific order before. It is indeed the order in time, i.e. the sequence of the ideas and activities proposed, which allows one to transform Disciplinary knowledge via a new Transdisciplinary frame of reference.
Lastly, new knowledge about Transdisciplinarity as a field of study is created as a consequence of the heretofore listed two processes.
The first part of the thesis is designated ‘Becomebecome Theory’ and focuses on the theoretical background and the intellectual operations necessary to support the creation of new Transdisciplinary knowledge. The second part of the thesis is designated ‘Becomebecome Practice’ and provides practical examples of the application of such operations. Crucially, the theoretical model described as the foundation for the Becomebecome methodology (Becomebecome Theory) is process-based and constantly checked against the insight generated through Becomebecome Practice.
To this effect, ‘information about the observer’ is proposed as a key notion which binds together Transdisciplinary resources from several studies in the hard sciences and humanities. It is a concept that enables understanding about why and how information that is generated through Becomebecome Practice is considered of paramount importance for establishing the reference parameters necessary to access Transdisciplinary insight which is meaningful to a specific project, a specific person, or a specific moment in time
Methods for the analysis of oscillatory integrals and Bochner-Riesz operators
For a smooth surface Γ of arbitrary codimension, one can consider the Lp mapping properties of the Bochner-Riesz multiplier
m(ζ) = dist(ζ,Γ)^α φ(ζ),
where α > 0 and φ is an appropriate smooth cutoff function. Even for the sphere, the exact Lp boundedness range remains a central open problem in Euclidean harmonic analysis. We consider the Lp integrability of the Bochner-Riesz convolution kernel for a particular class of surfaces (of any codimension). For a subclass of these surfaces the range of Lp integrability of the kernels differs substantially from the Lp boundedness range of the corresponding Bochner-Riesz multiplier operator. Extending work of Mockenhoupt, we then establish a range of operator bounds, which are sharp in the α exponent, under the assumption of an appropriate L2 restriction estimate. Hickman and Wright established sharp oscillatory integral estimates, associated with a particular class of surfaces, and derived restriction estimates. We extend this work to certain curves of standard type and corresponding surfaces of revolution. These surfaces are discussed as an explicit class for which we have Lp → Lp boundedness of the corresponding Bochner-Riesz operators.
Understanding the structure of the roots of real polynomials is important in obtaining stable bounds for oscillatory integrals with polynomial phases. For real polynomials with exponents in some fixed set,
Ψ(t)=x+y1 t^{k1} +...+yL t^{kL},
we analyse the different possible root structures that can occur as the coefficients vary. We first establish a stratification of roots into tiers containing roots of comparable sizes. We then show that at most L non-zero roots can cluster about a point. Supposing additional restrictions on the coefficients, we derive structural refinements. These structural results extend work of Kowalski and Wright and provide a characteristic picture of root structure at coarse scales. As an application, these results are used to recover the sharp oscillatory integral estimates of Hickman and Wright, using bounds for oscillatory integrals of Phong and Stein
The labour supply and retirement of older workers: an empirical analysis
This thesis examines the labour supply of older workers, their movement into retirement, and any movement out of retirement and back into work. In particular the labour force participation, labour supply and wage elasticity and other income elasticity of work hours are estimated for older workers and compared to younger workers. The thesis goes on to look at the movement into retirement for older workers as a whole by examining cohorts by gender, wave and age. The thesis also presents a descriptive and quantitative • examination of the changes in income and happiness that occur as an individual retires. Finally the thesis examines the reasons why an individual may return to work from v . retirement. The results of the findings suggest: that younger workers are significantly more responsive to wage and household income changes than older worker
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