Title: A Brief Survey of Fluctuation-induced Interactions in Micro- and Nano-systems and One Exactly Solvable Model as Example

Abstract: Fluctuations exist in any material object $A$. If $A$ has non-zero temperature $T$, one speaks about thermal fluctuations. If $A$ is at very low $T$, the fluctuations are of quantum origin. Interesting effects appear if two bodies $A$ and $B$ are separated by a fluctuating medium $C$ (say a vacuum, or a fluid close to its {\it critical point}) when the fluctuations are long-ranged, i.e., they decay according to a power-law with the distance. Then the changes of fluctuations in $C$ due to the surfaces and constituents of $A$ are also felt by $B$, and \textit{vice versa}, which leads to a fluctuation induced force (FIF) between them. This force persists in addition to the direct influence of $A$ on $B$ (say, via gravity or Coulomb's force). These FIF's can be of attractive or repulsive character. They may play crucially important role on phenomena involving objects with length scale comparative with the Universe, as well as to the tiny objects relevant for MEMS and NEMS. In the current article we present some basic facts for the FIF and their diversity. Then on the example of one dimensional Ising model with a defect bond we present some new analytical results for such forces.