We analyze the thermodynamic Casimir effect in strongly anisotropic
systems from the vectorial N\to\inftyN→∞
class in a slab geometry. Employing the imperfect (mean-field) Bose gas
as a representative example, we demonstrate the key role of spatial
dimensionality dd
in determining the character of the effective fluctuation-mediated
interaction between the confining walls. For a particular, physically
conceivable choice of anisotropic dispersion relation and periodic
boundary conditions, we show that the Casimir force at criticality as
well as within the low-temperature phase is repulsive for dimensionality
d\in (\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dotsd∈(52,4)∪(6,8)∪(10,12)∪…
and attractive for d\in (4,6)\cup (8,10)\cup \dotsd∈(4,6)∪(8,10)∪….
We argue, that for d\in\{4,6,8\dots\}d∈{4,6,8…}
the Casimir interaction entirely vanishes in the scaling limit. We
discuss implications of our results for systems characterized by
1/N>01/N>0
and possible realizations in the contexts of optical lattice systems and
quantum phase transitions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.