Distance-Dependent Sign Reversal in the Casimir-Lifshitz Torque

Thiyam, Priyadarshini; Parashar, Prachi; Shajesh, K. V.; Malyi, Oleksandr I.; Boström, Mathias; Milton, Kimball A.; Brevik, Iver; Persson, Clas

doi:10.1103/physrevlett.120.131601

Cited by 24 publications

(26 citation statements)

References 39 publications

(32 reference statements)

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“…which immediately leads to the expression for the transverse electric scattering coefficients in Eqs. (14). The contribution from the transverse magnetic mode can be similarly factorized into where r H ij are the scattering coefficients for the transverse magnetic mode of an electromagnetic wave incident on interfaces a or b.…”

Section: Discussionmentioning

confidence: 99%

“…which leads leads to the expression for the transverse magnetic scattering coefficients in Eqs. (14). Thus, we obtain the expression for the Lizshitz interaction energy in terms of scattering coefficients to be…”

Section: Discussionmentioning

confidence: 99%

“…(13) then, in principle, involves the evaluation of the sums over the Matsubara mode number n and the angular momentum mode number l. Both these sums contribute negligibly for large values of n and l. However, the reflection coefficients in Eqs. (14) involve ratios of differences, and these differences get exceedingly small for larger values of l. Thus, one has to keep an excessive number of significant digits in the evaluation of the Bessel functions, which is computationally expensive. This difficulty is avoided by expressing the modified Bessel functions using (uniform) asymptotic expansions for large order [34,35].…”

Section: Asymptotic Expansionsmentioning

confidence: 99%

“…(27), instead of the exact expressions for the reflection coefficients in Eqs. (14). This involves a sum on the Matsubara mode n, a sum on the angular momentum mode l, and multiple sums on k to generate the energy.…”

Section: Numerical Proceduresmentioning

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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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Asymptotic Expansionsmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

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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“…An example is the limit of weak anisotropy, or more precisely, the limit of relatively small deviations from in-plane anisotropy. Although a treatment of the full anisotropic case exists [28], this is still a popular approximation [29][30][31]. This is valid for certain natural anisotropic materials such as calcite or quartz, but there is no reason to assume this must hold generally.…”

Section: Introductionmentioning

confidence: 99%

Maxwell eigenmode approach to the Casimir-Lifshitz torque

Broer

Liow

2019

Phys. Rev. A

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More than forty years ago, Barash published a calculation of the full retarded Casimir-Lifshitz torque for planar birefringent media with arbitrary degrees of anisotropy. An independent theoretical confirmation has been lacking since. We report a systematic and transparent derivation of the torque between two media with both electric and magnetic birefringence. Our approach, based on an eigenmode decomposition of Maxwell's equations, generalizes Barash's result for electrically birefringent materials, and can be generalized to a wide range of anisotropic materials and finite thickness effects. *

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Casimir‐Lifshitz Optical Resonators: A New Platform for Exploring Physics at the Nanoscale

Esteso,

Frustaglia,

Carretero‐Palacios

et al. 2023

Advanced Physics Research

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The Casimir‐Lifshitz force, FC − L, has become a subject of great interest to both theoretical and applied physics communities due to its fundamental properties and potential technological implications in emerging nano‐scale devices. Recent cutting‐edge experiments have demonstrated the potential of quantum trapping at the nano‐scale assisted by FC − L in metallic planar plates immersed in fluids through appropriate stratification of the inner dielectric media, opening up new avenues for exploring physics at the nano‐scale. This review article provides an overview of the latest results in Casimir‐Lifshitz based‐optical resonator schemes and their potential applications in fields such as microfluidic devices, bio‐nano and micro electromechanical systems (NEMS and MEMS), strong coupling, polaritonic chemistry, photo‐chemistry, sensing, and metrology. The use of these optical resonators provides a versatile platform for fundamental studies and technological applications at the nano‐scale, with the potential to revolutionize various fields and create new opportunities for research.

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Distance-Dependent Sign Reversal in the Casimir-Lifshitz Torque

Cited by 24 publications

References 39 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

Maxwell eigenmode approach to the Casimir-Lifshitz torque

Casimir‐Lifshitz Optical Resonators: A New Platform for Exploring Physics at the Nanoscale

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