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This study extends the investigation of quantum dissipative effects of a cosmological scalar field by taking into account cosmic expansion and contraction.Cheung,Drewes,Kang,and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field in a recent work,where analytical expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interactions,and the work was conducted using Minkowski-space propagators in loop diagrams.In this work,we incorporate the Hubble expansion and contraction of the cosmic background and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly.Given that the Hubble parameter,H,attains a small but non-zero value,we carry out calculations to the first order in H.If we set H=0,all results match those in flat spacetime.Interestingly,we must integrate over the resonances,which in turn leads to an amplification of the effects of a non-zero H.This is an intriguing phenomenon,which cannot be uncovered in flat spacetime.The implications on particle creations in the early universe will be studied in a forthcoming study. 相似文献
3.
Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an -curvature condition. 相似文献
4.
Tobias Kirschbaum Dr. Frank Rominger Prof. Dr. Michael Mastalerz 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(64):14560-14564
Since a few years, the interest in negatively-curved fused polycyclic aromatic hydrocarbons (PAHs) has significantly increased. Recently, the first chiral negatively-curved PAH with the topology of a monkey saddle was introduced. Herein the synthesis of its triaza congener is reported. The influence of this CH↔N exchange on photophysical and electrochemical properties is studied as well as the isomerization process of the enantiomers. The aza analogue has a significantly higher inversion barrier, which makes it easier to handle at room temperature. All experimental results are underpinned by theoretical DFT calculations. 相似文献
5.
Timothy Buttsworth 《Mathematische Nachrichten》2019,292(4):747-759
Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g. 相似文献
6.
Rongmu YAN 《数学年刊B辑(英文版)》2020,41(3):451-464
In this paper, the author establishs a real-valued function on K¨ahler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K¨ahler manifolds, then they are holomorphically isometric. 相似文献
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In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity. 相似文献
9.
Yuxin Wang Huafei Sun Shoudong Huang Yang Song 《Mathematical Methods in the Applied Sciences》2020,43(2):486-511
This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system , (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that or does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that for any initial value in this set, then the zero solution of the system is asymptotically stable. 相似文献
10.
Abolhassan Mohammadi Tayeb Golanbari Haidar Sheikhahmadi Kosar Sayar Lila Akhtari M. A. Rasheed Khaled Saaidi 《中国物理C(英文版)》2020,44(9):095101-095101-13
In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria. 相似文献