Response Of The Unruh-DeWitt Detector In Flat Spacetime With Nontrivial Topology

The flat spacetime with nontrivial topology is a kind of spacetime that is locally flat but not globally,for example,one spatial dimension is compactified S~1×R~3.Since nontrivial topology affects the spacetime distribution of quantum field,it may cause some important physical effects:the Casimir-like effect,the topological mass generation,and the photon's superluminal propagation,etc.The Unruh-De Witt(U-D)particle detector is a two-level detector which interacts with the surrounding massless scalar field in Minkowski spacetime,and produces spontaneous radiation and spontaneous absorption.Using the U-D detector,people can describe the main characteristics of the coupling between atom and dipole in simple mathematical forms.Therefore,the detector plays an important role in the research of topological structures such as the local effect of a gravitational field on the vacuum,Unruh radiation,and the event horizon of black hole.In this paper,we calculate the transition rate of the U-D detector linearly coupled with the massless scalar field in the compactified Minkowski spacetime,and explore the impact of spatial compactification on the spacetime symmetry by comparing the detector's transition properties of the compactified spacetime and that of the free spacetime.The first chapter introduces the related theoretical research results of the U-D detector.Firstly,it expounds the geometric concept of compactified Minkowski spacetime,the physical meaning of the topological structure of spacetime,and the physical phenomena caused by the spatial compactification.Secondly,the research progresses and applications of the U-D detector are summarized.Based on the research results in different spacetime backgrounds,the factors that affect the detector's transition behavior are introduced in detail.Then we explain how to calculate the transition rate of the U-D detector,and mainly describe the Wightman function of the scalar field.Finally,the research plan of this paper is outlined.By calculating the U-D detector's transition rate in different motion situations,the effect of spatial compactification on the response of the detector is studied.The second chapter focuses on the response of the inertial U-D detector.Three typical cases of the detector's motion is considered in the compactified Minkowski spacetime,i.e.,static,moving at a constant velocity only along the compact direction,moving at a constant velocity with nonzero components along the non-compact and the compact directions.Firstly,we derive the detector's transition rate based on the Wightman function,and find that by changing the spatial compactification length,the detector's velocity and the field structure,the detector's spontaneous emission processes can be enhanced or weakened at different degrees.For the static case,the detector's spontaneous emission rate depends on the compact length and the energy level spacing.For the case of only moving at a constant velocity in the compact direction,its spontaneous emission rate depends on the detector's velocity and the compact length.For the case of moving at a constant velocity with nonzero components along the non-compact and compact directions,its spontaneous emission rate depends on the components of velocity along the non-compact and compact directions,the compact length.Then we compare the results of the compactified spacetime with that of the free spacetime,and analyze the reason why the compactified spacetime breaks the equivalence of the inertial reference frame.Nextly,several extreme approximation cases is studied,the results show that when the compact length is much smaller than the detector's transition wavelength,the detector's spontaneous emission processes can be enhanced in the untwisted field,but it is nearly forbidden in the twisted field.And when the compact length is much larger than the detector's transition wavelength,or the detector's velocity is close to the speed of light,the effect of spatial compactification almost disappears,and the detector's transition rates in the untwisted and twisted fields return to the results of the free Minkowski spacetime.Finally,we also study the influence of the reference frame selection on the detector's transition rate,and find that the detector's transition rate is a Lorentz scalar.The third chapter studies the uniformly accelerated detector.We investigate and analyze the influence of uniformly accelerated motion on the Lamb shift and spontaneous excitation of the atom,and focus on the impact of accelerated motion of the atom on the vacuum fluctuations.Based on the results of previous research on the response of the detector with uniform acceleration in the compact direction,we further calculate the transition rate of the detector moving at a constant acceleration only along the non-compact direction.The results show that its spontaneous emission and spontaneous absorption rates depend on the compact length,the detector's acceleration and the field structure.According to the calculation results,the transition rate of the uniformly accelerated detector in compactified spacetime has an additional modifying factor compared with that of the free spacetime,so the spatial compactification will change the detector's transition process.In addition,when the compact length is much smaller than the detector's transition wavelength,both the processes of the dectector's spontaneous emission and spontaneous absorption can be enhanced in the untwisted field,but they are nearly forbidden in the twisted field.And when the compact length is much larger than the detector's transition wavelength,or the detector's acceleration is large enough,the detector's transition rates return to the results of the free Minkowski spacetime.Although this paper don't have much research on uniform acceleration,the relevant results are important for our research on the impact of non-inertial motion in topological spacetime.The fourth chapter summarizes the research work of this thesis,and outlines the modification to the transition rate of the inertial and uniformly accelerated detectors from the spatial compactification.Finally,the future related research work is introduced,including the response of the detector in the Mobius ring and Klein bottle spacetime,the detector's transition rate in the electromagnetic field,and the modification of non-uniformly accelerated motion to the transition rate,such as circular motion.