Related papers: Thermodynamic Casimir Effect in the large-n limit
Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately…
We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy…
A d-dimensional finite quantum model system confined to a general hypercubical geometry with linear spatial size L and ``temporal size'' 1/T (T - temperature of the system) is considered in the spherical approximation under periodic…
This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the…
Thermodynamic Casimir forces of film systems in the O$(n)$ universality classes with Dirichlet boundary conditions are studied below bulk criticality. Substantial progress is achieved in resolving the long-standing problem of describing…
Using exact calculations, we elucidate the significance of the surface (bound) states for the thermal Casimir interactions for an Ising strip with a finite width. The surface state arises whenever an imaginary wavenumber mode appears in the…
Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit of Casimir interactions…
The singular part of the finite-size free energy density $f_s$ of the O($n$) symmetric $\phi^4$ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet…
Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes $\mathfrak{B}_j, j=1,2$, are…
Critical dynamics in film geometry is analyzed within the field-theoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the so-called ordinary…
We consider the Casimir effect of a massive vector field between two semi-infinite dielectric slabs. We first derive the generalization of the Lifshitz formula that gives the Casimir interaction energy of two magnetodielectric slabs…
We consider the finite temperature Casimir stress acting on the boundary of a D>=3 dimensional cavity due to the vacuum fluctuations of electromagnetic fields. Both perfectly conducting and infinitely permeable boundary conditions are…
We study a coupled system that describes the interacting dynamics between a bulk field, confined to a finite region with timelike boundary, and a boundary observable. In our system the dynamics of the boundary observable prescribes…
The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate…
In this work I study the finite temperature Casimir effect caused by a complex and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. The Lorentz invariance breaking is caused by a constant space-like…
We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite…
The Casimir force between two ideal conducting surfaces is a special (zero temperature) limit of a more general theory due to Lifshitz. The temperature dependent theory includes correlations in coupled quantum and classical fluctuation…
We study fluctuation-induced interaction in confined fluids above the isotropic-lamellar transition. At an ideal continuous transition, the disjoining pressure has the asymptotic form $\Pi(d\to\infty)\approx -C k_BT q_0^2/d$, where $d$ is…
The $O(n)$ ${\phi}^4$ model on a slab $\mathbb{R}^{d-1}\times[0,L]$ bounded by free surfaces is studied for $2<d<4$ in the limit $n\to\infty$. The self-consistent potential $V(z)$ which the exact $n\to\infty$ solution of the model involves…
The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, are investigated. The system is confined to a…