Critical Casimir effect: Exact results

Dantchev, Daniel; Dietrich, S.

doi:10.1016/j.physrep.2022.12.004

Cited by 25 publications

(15 citation statements)

References 510 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among the available mean-field predictions (see ref. 16 for a comprehensive review) obtained as described above, we briefly discuss here those which turned out to be relevant for a qualitative understanding of the CCF in experimentally accessible systems, such as critical binary liquid mixtures and superfluids.…”

Section: Soft Matter Reviewmentioning

confidence: 99%

“…The important qualitative features of the resulting scaling function X Cas -confirmed by quantitative, accurate estimates based on MC simulations and by exact results in spatial dimension d = 2 (see, e.g., ref. 16)-are the following: (a) for (AE,AE) BCs the force is attractive for all (positive and negative) values of the scaling variable x (see the end of Section 2.2) and it attains its maximum strength below T c ; (b) for ðAE; ÇÞ BCs the force is repulsive for all values of the scaling variable x and it attains its maximum strength above T c ; (c) for a fixed value of the scaling variable x, the attraction for (AE,AE) BCs is generically weaker than the repulsion for ðAE; ÇÞ BCs. In all cases, the force vanishes exponentially for L c x.…”

Section: Soft Matter Reviewmentioning

confidence: 99%

“…More recently, certain specific aspects of CCFs have been reviewed, including their role in determining the phase behaviour 13 and assembly 14 of colloidal suspensions, their measurements involving optical trapping, 15 and the available exact analytical predictions. 16 Accordingly, our focus here is primarily on aspects which have not yet been covered in the above references. In order to keep the presentation focussed on the most relevant aspects of CCFs, the available literature will not be reviewed completely, but pertinent studies will be at least quoted, as guidance for the interested reader.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical Casimir forces in soft matter

Gambassi,

Dietrich

2024

Soft Matter

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Soft Matter Reviewmentioning

confidence: 99%

Section: Soft Matter Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Critical Casimir forces in soft matter

Gambassi,

Dietrich

2024

Soft Matter

Self Cite

View full text Add to dashboard Cite

show abstract

“…to equation (9). The first term [coming from ´R dxψ(x)] recovers Dω b (T, µ), the latter one is identified as ω s (T, µ, D) by virtue of equation (4).…”

Section: The Model and Its Solutionmentioning

confidence: 99%

“…The Casimir effect was first recognized [6] as a prediction of quantum electrodynamics in 1948, and since then was discussed in contexts as diverse as classical fluids, Bose-Einstein condensates, biological cells, and cosmology with a variety of methods encompassing experimental (e.g. [7,8]), analytical (see [9] for a recent review), and numerical (e.g. [10][11][12]) approaches.…”

Section: Introductionmentioning

confidence: 99%

Effective binding potential from Casimir interactions: the case of the Bose gas

Pruszczyk

Jakubczyk

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We consider the thermal Casimir effect in ideal Bose gases, where the dispersion relation involves both terms quadratic and quartic in momentum. We demonstrate that if macroscopic objects are immersed in such a fluid in spatial dimensionality $d \in \{3,7, 11, \dots \}$ and at the critical temperature $T_c$, the Casimir force acting between them is characterized by a sign which depends on the separation $D$ between the bodies and changes from attractive at large distances to repulsive at smaller separations. In consequence, an effective potential which binds the two objects at a finite separation arises. We demonstrate that for odd integer dimensionality $d \in \{3, 5, 7, \dots \}$, the Casimir energy is a polynomial of degree $(d-1)$ in $D^{-2}$. We point out a very special role of dimensionality $d=3$, where we derive a strikingly simple form of the Casimir energy as a function of $D$ at Bose-Einstein condensation. We discuss crossover between monotonous and oscillatory decay of the Casimir interaction above the condensation temperature.

show abstract

Casimir energy and modularity in higher-dimensional conformal field theories

Conghuan

Wang

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

An important problem in Quantum Field Theory (QFT) is to understand the structures of observables on spacetime manifolds of nontrivial topology. Such observables arise naturally when studying physical systems at finite temperature and/or finite volume and encode subtle properties of the underlying microscopic theory that are often obscure on the flat spacetime. Locality of the QFT implies that these observables can be constructed from more basic building blocks by cutting-and-gluing along a spatial slice, where a crucial ingredient is the Hilbert space on the spatial manifold. In Conformal Field Theory (CFT), thanks to the operator-state correspondence, we have a non-perturbative understanding of the Hilbert space on a spatial sphere. However it remains a challenge to consider more general spatial manifolds. Here we study CFTs in spacetime dimensions d > 2 on the spatial manifold T2 × ℝd−3 which is one of the simplest manifolds beyond the spherical topology. We focus on the ground state in this Hilbert space and analyze universal properties of the ground state energy, also commonly known as the Casimir energy, which is a nontrivial function of the complex structure moduli τ of the torus. The Casimir energy is subject to constraints from modular invariance on the torus which we spell out using PSL(2, ℤ) spectral theory. Moreover we derive a simple universal formula for the Casimir energy in the thin torus limit using the effective field theory (EFT) from Kaluza-Klein reduction of the CFT, with exponentially small corrections from worldline instantons. We illustrate our formula with explicit examples from well-known CFTs including the critical O(N) model in d = 3 and holographic CFTs in d ≥ 3.

show abstract

Critical Casimir effect: Exact results

Cited by 25 publications

References 510 publications

Critical Casimir forces in soft matter

Critical Casimir forces in soft matter

Effective binding potential from Casimir interactions: the case of the Bose gas

Casimir energy and modularity in higher-dimensional conformal field theories

Contact Info

Product

Resources

About