Research Webpage for
Quantum Fluctuations in 1309

Last updated on .

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• Meeting information: [829 6770 5989, ihbar, link]
• Team: Venkat Abhignan, Mathias Bostrom, Iver Brevik, Aida Gholamhosseinian, Aryan Illiat, Thushari Jayasekera, Oleksandr Malyi, John Joseph Marchetta, Subhojit Pal, Prachi Parashar, K. V. Shajesh, Niranjan Warnakulasooriya,
• These meetings are organized by Prachi Parashar (JALC, Carterville, Illinois, U.S.A.,) K. V. Shajesh (SIUC, Carbondale, Illinois, U.S.A.,) and Oleksandr Malyi and Mathias Bostrom in the Inverse Materials Design group under the project titled Applied Casimir Theory: from Mesons to Environmental Effects.

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Meeting Content: [recordings]

• 20240210: Kramers-Kronig relation [vnotes, video]
  • Contents of first ten equations in emthin.
  • Examples, like Drude model, plasma model, and Drude-Lorentz model, were not discussed in detail.
  
  Discussion
  • In axion electrodynamics the electric (magnetic) polarization gets a response from the magnetic (electric) field. The implications of the causal nature of this reponse should be investigated. Look up literature.
  
  
• 20240217: Correlation function [vnotes, lnotes, video]
  • Schwinger's quantum action principle
  • Correlations are described by Green's function
  • Zero-dimension example: Harmonic oscillator forced by a noise (not satisfactorily completed)
  
  Discussion
  • The divergences in the single-body Casimir energy of a dielectric ball is known to cancel out for mediums εμ=1. Could this feature be derive as a generic statement at the formalism level for an arbitrary single body.
  • Use our ideas in arXiv:1709.06284 and arXiv:2105.05507 to evaluate conclusions similar to those by Barrow in arXiv:2004.09444. For example, can we derive the horizon radius of a blackhole constructed out of self-similar concentric spheres.
  
  
• 20240224: Maxwell equations [vnotes, lnotes, video]
  • Maxwell equations
  • Lagrangian for macroscopic electrodynamics
  • dielectric function is Hermitian
  
  Discussion
  • What is the physical interpretation of the external Polarization source?
  • Are fluctuations in polarization sources or the fluctuations in the fields the origins of zero point energy?
  • How is the dielectric function being Hermitian compatible with Kramers-Kronig relation? The hermitianity requires the principal dielectric components to be real. Thus, it does not allow dissipation. However, we will assume a small amount of dissipation to accommodate causality. This will then lead to a fluctuation dissipation theorem.
  
  
• 20240302: Quantum vacuum energy [vnotes, lnotes, video]
  • variation in dynamical fields, source function, and background potential.
  • Green's dyadic
  • Quantum vacuum energy
  
  Discussion
  • Derive the expression for quantum vacuum energy presuming magnetic monopoles are allowed in the theory, and magnetic source function is switched on.
  • Does the action formulation in terms of frequency allow one to attend problems that are out of equilibrium? Is Schwinger-Keldysh method about this.
  • The variation in the action due to variation in the background potential is a functional. For a given one body can we use the idea of calculus of variation to find the surface that minimizes the Casimir energy.
  
  
• 20250308: Concentric water, ice, vapor geometry [video]
  • By Yang Li
  
  Discussion
  • Derive the interaction energy between two concentric interfaces using the idea of Proximate Force Approximation and Derivative Expansion by Argentinian group.
  • Find a leading order approximation of the Elbaum-Shick thickness using analytic methods.
  
  
• 20250320: Theory of interfaces and surface forces [video]
  • By Drew Parsons
  
  Discussion
  • Dependence of free energy on frequency bands.
  • Incorporate the plasma or ion contribution to the Hamaker constant calculations.
  
  
• 20250328: Overview of Lifshitz force [video]
  • Force on a capacitor plate using stress tensor method
  • Overview of Lifshtiz calculation
  
  Discussion
  • Go through Mathias calculation.
  • Refer arXiv:1808.02205
  
  
• 20250523: Derivation of Lifshitz energy (isotropic planar case) [vnotes, video]
  • Derived Lifshitz energy.
  • Derivation of dyadic structure [vnotes, video]
  • Filling in details will be useful.
  
  Discussion
  • Based on Section IV in emthin.
  
  
• 20250530: Derivation of Lifshitz energy (isotropic concentric spheres) [lnotes, vnotes, video]
  • Derived Lifshitz energy for isotropic concentric spheres.
  • Based on Axially symmetric configurations.
  
  Discussion
  • Derivation of dyadic structure [vnotes, video]
  
  

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Projected contents:

Green's dyadic
Quantum vacuum energy
Stress tensor method
Separation of electric and magnetic modes
Green's function, Green's dyadic
Multiple scattering formalism, Stress tensor method
Lifshitz energy
Elbaum-Schick systems

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Resources:

1. Prachi's Ph.D. Thesis [thesis, emthin (unpublished precursor to δ-plate)]
2. A formalism developed for axially symmetric configurations.

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Last updated on by K. V. Shajesh (kvshajesh@gmail.com).