Many-body contributions to Green’s functions and Casimir energies

Shajesh, K. V.; Schaden, Martin

doi:10.1103/physrevd.83.125032

Cited by 17 publications

(34 citation statements)

References 41 publications

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“…in terms of modified spherical Bessel functions of Eqs. (16) and generalized derivatives of of modified spherical Bessel functions in Eqs. (17) with…”

Section: Appendix: Lifshitz Interaction Energy For Concentric Spheresmentioning

confidence: 99%

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Role of zero point energy in promoting ice formation in a spherical drop of water

Parashar

Shajesh

Milton

et al. 2019

Phys. Rev. Research

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We demonstrate that the Lifshitz interaction energy (excluding the self-energies of the inner and outer spherical regions) for three concentric spherical dielectric media can be evaluated easily using the immense computation power in recent processors relative to those of a few decades ago. As a prototype, we compute the Lifshitz interaction energy for a spherical shell of water immersed in water vapor of infinite extent while enclosing a spherical ball of ice inside the shell, such that two concentric spherical interfaces are formed: one between solid ice and liquid water and the other between liquid water and gaseous vapor. We evaluate the Lifshitz interaction energy for the above configuration at the triple point of water when the solid, liquid, and gaseous states of water coexist, and, thus, extend the analysis of Elbaum and Schick in Phys. Rev. Lett. 66 (1991) 1713 to spherical configurations. We find that, when the Lifshitz energy contributes dominantly to the total energy of this system, which is often the case when electrostatic interactions are absent, a drop of water surrounded by vapor of infinite extent is not stable at the triple point. This instability, that is a manifestation of the quantum fluctuations in the medium, will induce nucleation of ice in water, which will then grow in size indefinitely. This is a consequence of the finding here that the Lifshitz energy is minimized for large (micrometer size) radius of the ice ball and small (nanometer size) thickness of the water shell surrounding the ice. These results might be relevant to the formation of hail in thunderclouds. These results are tentative in that the self-energies are omitted. * Prachi.Parashar@jalc.edu † with inter-atomic forces. However, the astonishing feat of Casimir [10] was in showing that London dispersion forces, or the van der Waals interactions, were manifestations of the zero point energy.Casimir evaluated the energy of a planar cavity with perfectly conducting walls, an overly idealized system, that is obtained from the configuration of Fig. 1 when the regions labeled as ε 1 and ε 2 are perfect electrical conductors that are separated by vacuum in the background region labeled ε 3 . Lifshitz [11] generalized Casimir's result by evaluating the energy for a configuration of Fig. 1 consisting of two dielectric media of infinite extent separated by vacuum. The Lifshitz energy leads to the Casimir energy in the perfect conducting limit of the dielectric functions for the outer media. Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP) [12] extended these considerations for the case when the background region in the planar configuration of Fig. 1 is another uniform dielectric medium. The main idea underlying these groundbreaking works is that quantum fluctuations of fields in the media can be manifested in physical phenomena involving dielectrics. Among these, we point out that the configurations considered by Casimir and Lifshitz always lead to an attractive pressure (tending to decrease the thickness of the intervening medium). I...

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“…in terms of modified spherical Bessel functions of Eqs. (16) and generalized derivatives of of modified spherical Bessel functions in Eqs. (17) with…”

Section: Appendix: Lifshitz Interaction Energy For Concentric Spheresmentioning

confidence: 99%

“…To this end, we point out, though it has been surely known all along, that the energy for the configuration of Fig. 1 allows the decomposition [15,16]:…”

Section: Introductionmentioning

confidence: 99%

Role of zero point energy in promoting ice formation in a spherical drop of water

Parashar

Shajesh

Milton

et al. 2019

Phys. Rev. Research

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“…The first term of Eq. (A10) reproduces the leading term of the Casimir energy for two weakly interacting parallel plates [17,24].…”

Section: Discussionmentioning

confidence: 99%

“…Using Matsubara's formalism one [24] readily finds that the irreducible contribution to the Helmholtz free energy per unit area, f (1) , of a massless scalar field due to a semi-transparent flat plate of area A described by the potential interaction V (z) = λδ(z) is given by,…”

Section: An Isolated Flat Semi-transparent Platementioning

confidence: 99%

“…In the range λ,λ ≪ 2πT ≪ 1/a we have that In Matsubara's formalism [21] thermal Green's functions of a mode at temperature T are given by evaluating Euclidean Green's functions at the corresponding Matsubara frequency ξ n = 2πnT . We thus can draw on the literature for the Euclidean Green's function of a massless scalar in the presence of parallel semitransparent plates [14,17,24]. The physical solution to Eq.…”

Section: An Isolated Flat Semi-transparent Platementioning

confidence: 99%

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Field theoretic approach to roughness corrections

Schaden

2012

Phys. Rev. D

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We develop a systematic field theoretic description for the roughness correction to the Casimir free energy of parallel plates. Roughness is modeled by specifying a generating functional for correlation functions of the height profile, the two-point correlation function being characterized by the variance, σ 2 , and correlation length, ℓ, of the profile. We obtain the partition function of a massless scalar quantum field interacting with the height profile of the surface via a δ-function potential. The partition function of this model also is given by a holographic reduction to three coupled scalar fields on a two-dimensional plane. The original three-dimensional space with a flat parallel plate at a distance a from the rough plate is encoded in the non-local propagators of the surface fields on its boundary. Feynman rules for this equivalent 2 + 1-dimensional model are derived and its counter terms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction. The absolute separation, a eff , to a rough plate is measured to an equivalent plane that is displaced a distance ρ ∝ σ 2 /ℓ from the mean of its profile. This definition of the separation eliminates corrections to the free energy of order 1/a 4 eff and results in a unitary model. We derive an effective low-energy theory in the limit ℓ ≪ a. It gives the scattering matrix and equivalent planar surface of a very rough plate in terms of the single length scale ρ. The Casimir force on a rough plate is found to always weaken with decreasing correlation length ℓ. The two-loop approximation to the free energy interpolates between the free energy of the effective low-energy model and that of the proximity force approximation -the force on a very rough Dirichlet plate with σ 0.5ℓ being weaker than on a flat plate at any separation.

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Casimir energy of N magnetodielectric δ-function plates

Abhignan

2023

Phys. Scr.

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To investigate Casimir electromagnetic interaction in N bodies, we implement multiple δ-function plates with electric and magnetic properties. We use their optical properties to study the Casimir energy between the plates by implementing multiple scattering formalism. We initially solve Green’s functions for two and three plates configurations to obtain their reflection coefficients. Further, the coefficients are implemented in multiple scattering formalism, and a simple method was obtained to depict energy density distribution in the multiple scattering expansions using diagrammatic loops. The Casimir energy for N bodies depends on multiple scattering parameter ∆; this parameter was distributed into nearest neighbour scattering and next-to-nearest neighbour scattering terms represented by different loops depending on reflection, transmission and propagation distance. In this manner, the Casimir energy density was generalized to N plates by identifying a systematic pattern in the representation of diagrammatic loops.

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Many-body contributions to Green’s functions and Casimir energies

Cited by 17 publications

References 41 publications

Role of zero point energy in promoting ice formation in a spherical drop of water

Role of zero point energy in promoting ice formation in a spherical drop of water

Field theoretic approach to roughness corrections

Casimir energy of N magnetodielectric δ-function plates

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