Karsh Limited Temperature Effect Related Research

The Casimir effect causes lots of attention of theoretical studyingsince it is found. The Casimir energy and force may change signdepending on geometry of the configuration and the type of boundaryconditions. The intensive study of different geometry type of boundaryconditions using quantum field theory shows that the Casimir forcearises not only in the presence of material boundaries, but also inspaces with non-Euclidean topology and depend on the topology ofspace-time. Many of the previous research focus on the Casimir effectat zero temperature. But it is hard to reach absolute zero in reality andactually all experimental measurements of the Casimir effect havebeen done at room temperature, so it is important to study theinfluence of temperature on the Casimir effect. In the last few years,great progress has been made in the experimental study of finitetemperature Casimir effect and there is a chance to verify thetheoretical result in experimental study.In this thesis, starting from the framework of Matsubara quantumfield theory at nonzero temperature, we study the arbitrary dimensionalfinite temperature Casimir effect by using zeta-function regularizationtechnique. We focus on three model: parallel planes; rectangularboxe;helix boundary condition. We get the exact results for Casimir freeenergy and Casimir pressure in (D+1)-dimensional space-time and givethe asymptotic expressions for low and high temperature limits. For finitetemperature Casimir effect in (D+1)-dimensional space-time, nopapers till now give the physical result. In the case of D=3, we get theresult that can be expressed in terms of the standard results in theliterature for parallel plates boundary. For rectangular box, we onlycalculate the case of box with the same length of sides in the interest ofsimplicity and point out some problems in the literature papers. On the basis of the study of Casimir effect for helix boundary condition,thisthesis consider the temperature correction. In this thesis we get theexpression of free energy and force for arbitrary temperature.The thesis is organized as follows. Sect.1introduces the startingpoint of Casimir effect and the experimental study. In Sect.2thezeta-functional regularization technique is demonstrated. Section3contains the general steps and method of calculating finite Casimireffect. In Sects.4we study the Casimir effect in three boundarycondition. Section5contains our conclusions and discussion.This thesis emphasize that the physical Casimir force should go tozero when the characteristic dimensions of the volume go to infinity. Thisis achieved by a subtraction of the free energy of the black bodyradiation within the volume and of other terms proportional to the totalarea of box surface and to the sum of the sides after performing thezeta-functional technique. And some of previous papers didn’t noticethat and the result is not satisfactory.