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arXiv 1402.4557gr-qc
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宇宙学de Sitter空间中与时间相关的粒子产生和粒子数

Time dependent particle production and particle number in cosmological de Sitter space

Eric Greenwood

摘要:

本文用三种不同的方法:瞬时对角化、真空间的Bogolyubov变换和Unruh-de Witt探测器,研究了含时过程中产生的感生准粒子的占据数。这里我们考虑含时谐振子的哈密顿量,其质量和频率都随时间变化。我们用不变算子方法导出了诱导准粒子的占有数;在导出占有数的过程中,我们还指出并建立了泛函薛定谔形式主义、量子动力学方程和两个不同的等时Fock空间基之间的Bogolyubov变换之间的联系,并解释了不变算子在其中所起的作用。使用de Sitter时空的平坦FRW图,我们表明不同的方法导致不同的结果:瞬时对角化导致幂律分布,而Bogolyubov变换和Unruh-de Witt检测器都导致热分布。结果表明,瞬时对角化和Bogolyubov方法之间的差异的来源是事实上,有没有定义良好的粒子的概念,在真空中,由于发散项。在Bogolyubov方法中,这种发散项抵消导致热分布,而在瞬时对角化中没有这种抵消。然而,为了在通常的Bogolyubov方法中获得热分布,必须使用大质量极限。从物理学的角度来看,我们应该预期只有被允许进入视界的模式才是热的,因此在大质量极限下,这些模式完全在视界内,即使它们确实增长了,它们也会由于质量而保持在视界内。因此,不应该期望热分布,因为模式将没有机会热化。

英文摘要:

In this paper we consider the occupation number of induced quasi-particles produced during a time-dependent process using three-different methods: Instantaneous diagonalization, Bogolyubov transformation between two different vacua, and the Unruh-de Witt detector. Here we consider the Hamiltonian for a time-dependent Harmonic oscillator, with time-dependent mass and frequency. We derive the occupation number of the induced quasi-particles using the invariant operator method; in deriving the occupation number we also point out and make the connection between the Functional Schrödinger formalism, quantum kinetic equation, and Bogolyubov transformation between two different Fock space basis at equal times and explain the role in which the invariant operator plays. Using the flat FRW chart of de Sitter spacetime, we show that the different methods lead to different results: Instantaneous diagonalization leads to a power law distribution, while the Bogolyubov transformation and Unruh-de Witt detector both lead to thermal distributions. It is shown that the source of the discrepancy between the instantaneous diagonalization and Bogolyubov methods is the fact that there is no notion of well-defined particles in the out vacuum due to a divergent term. In the Bogolyubov method, this divergent term cancels leading to the thermal distribution, while in the instantaneous diagonalization there is no such cancelation. However, to obtain the thermal distribution in the usual Bogolyubov method, one must use the large mass limit. On physical grounds, one should expect that only the modes which have been allowed to sample the horizon would be thermal, thus in the large mass limit these modes are well within the horizon and, even though they do grow, they remain well within the horizon due to the mass. Thus one should not expect a thermal distribution since the modes won't have a chance to thermalize.

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