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Coherent State Methods in Spectral Asymptotics PhD The number of negative eigenvalues of a Schrödinger operator in the asymptotic regime of large coupling is given by the celebrated Weyl law. A textbook proof of the leading order term in Weyl’s law uses coherent states – states that are as well-localized in phase-space as permitted by the Heisenberg uncertainty principle. This project aims to use coherent state methods (closely related to the so-called FBI transform) to go beyond leading order. Although these results can be obtained by highly sophisticated techniques such as Fourier Integral Operator calculus, coherent states offer a very flexible and robust alternative and are physically well-motivated.
Programme overview
Main Subject
Mathematics
Degree
PhD
Study Level
PHD
Study Mode
On Campus
Coherent State Methods in Spectral Asymptotics PhD The number of negative eigenvalues of a Schrödinger operator in the asymptotic regime of large coupling is given by the celebrated Weyl law. A textbook proof of the leading order term in Weyl’s law uses coherent states – states that are as well-localized in phase-space as permitted by the Heisenberg uncertainty principle. This project aims to use coherent state methods (closely related to the so-called FBI transform) to go beyond leading order. Although these results can be obtained by highly sophisticated techniques such as Fourier Integral Operator calculus, coherent states offer a very flexible and robust alternative and are physically well-motivated.
Admission Requirements
01 Jul 2025
3 Years
Oct
International
22,360
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Coherent State Methods in Spectral Asymptotics PhD
Loughborough University, Loughborough, United Kingdom
# 201-250QS Subject Rankings
36 monthsProgramme duration
22,360 Tuition Fee/year
01 Jul, 2025Application Deadline
Programme overview
Main Subject
Mathematics
Degree
PhD
Study Level
PHD
Study Mode
On Campus
The number of negative eigenvalues of a Schrödinger operator in the asymptotic regime of large coupling is given by the celebrated Weyl law. A textbook proof of the leading order term in Weyl’s law uses coherent states – states that are as well-localized in phase-space as permitted by the Heisenberg uncertainty principle. This project aims to use coherent state methods (closely related to the so-called FBI transform) to go beyond leading order. Although these results can be obtained by highly sophisticated techniques such as Fourier Integral Operator calculus, coherent states offer a very flexible and robust alternative and are physically well-motivated.
Programme overview
Main Subject
Mathematics
Degree
PhD
Study Level
PHD
Study Mode
On Campus
The number of negative eigenvalues of a Schrödinger operator in the asymptotic regime of large coupling is given by the celebrated Weyl law. A textbook proof of the leading order term in Weyl’s law uses coherent states – states that are as well-localized in phase-space as permitted by the Heisenberg uncertainty principle. This project aims to use coherent state methods (closely related to the so-called FBI transform) to go beyond leading order. Although these results can be obtained by highly sophisticated techniques such as Fourier Integral Operator calculus, coherent states offer a very flexible and robust alternative and are physically well-motivated.
Admission Requirements
International
Scholarships
Selecting the right scholarship can be a daunting process. With countless options available, students often find themselves overwhelmed and confused. The decision can be especially stressful for those facing financial constraints or pursuing specific academic or career goals.
To help students navigate this challenging process, we recommend the following articles:
How to get a full scholarship
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Computational Modelling of Sustainable Alloys PhD
Designing Classroom Tasks To Improve Students’ Learning Of Mathematics PhD
Developing Novel Antibiofilm Coatings for Sustainable Biofilm-Free Surfaces PhD
Development of Hybrid Microcomb Sources with Topologically Protected Dark Resonances for Simultaneous Classical and Quantum PhD
Development of Novel Bicyclopentanes (BCP) Bioisosteres From Bench Stable [1.1.1]-Propellane Precursors PhD
Digital Twins for Biofilm Management PhD
Dispersionless Integrable Systems In 2+1 Dimensions PhD
Social Sciences and Management (6)
An Evaluation of Erasmus+ Sport Projects and Their Impact on EU Sport Policy Development PhD
An Evaluation of Erasmus+ Sport Projects and Their Impact on EU Sport Policy Development PhD
Climate Change, Work Design and Worker Wellbeing Phd
Climate Change, Work Design and Worker Wellbeing Phd
Communication and Social Change (CSC) Hub Studentship PhD
Communication and Social Change (CSC) Hub Studentship PhD
Enhancing Motivation in Sport and Exercise Contexts PhD
Enhancing Motivation in Sport and Exercise Contexts PhD
Out of School Youth Provision: An Analysis of Funding and Operational Resilience within the Sector PhD
Out of School Youth Provision: An Analysis of Funding and Operational Resilience within the Sector PhD