Loughborough,
United Kingdom
Type
Public
Degrees offered
Bachelor's Degree
PhD Coherent State Methods in Spectral Asymptotics in Loughborough United Kingdom | Loughborough University
Loughborough University
|
Loughborough United Kingdom
Visit institution website
for more information
Qualification
Doctor of Philosophy
Languages
English
Delivery Mode
On-Campus
Tuition (2025)
GBP
20,250
(c. USD27,019.58)
Attendance
Full-time
Full-time Duration
36 months
The count of negative eigenvalues for a Schrödinger operator in the
asymptotic limit of strong coupling follows the renowned Weyl law. A standard demonstration of the dominant term in Weyl's law employs coherent states—quantum states maximally localized in phase space within the constraints of the Heisenberg uncertainty principle.
This research seeks to extend beyond the leading term using coherent state techniques (closely connected to the FBI transform). While advanced methods like Fourier Integral Operator calculus can derive these results, coherent states provide a versatile, reliable, and physically intuitive approach.
Destination of Study
Subjects of Study
Language Requirements
English
IELTS 6.5
Qualification Requirements
Applicants should have, or expect to achieve, at least a 2:1 Honours degree or equivalent, in a relevant field.
Skills required - A solid grasp of real and functional analysis and some basic knowledge of PDE and / or quantum mechanics.
Links to find out more:
IELTS - 6.5 overall with 6.0 in each individual element (reading, writing, listening and speaking).
TOEFL - iBT - Overall score of 92, with not less than 22 in each test.
Skills required - A solid grasp of real and functional analysis and some basic knowledge of PDE and / or quantum mechanics.
Links to find out more:
IELTS - 6.5 overall with 6.0 in each individual element (reading, writing, listening and speaking).
TOEFL - iBT - Overall score of 92, with not less than 22 in each test.
Tuition
GBP
20,250