insight - Quantum Field Theory - # Stationary Quantum Field Dynamics in Circular and Drifted Rindler Motions

Core Concepts

The circular and drifted Rindler motions in Minkowski spacetime are two sides of the same coin, connected by a smooth deformation through parator motion. The effective temperature response of an Unruh-DeWitt detector coupled to a massless scalar field exhibits qualitative changes in this deformation, particularly in the regime where the detector's internal energy spacing is small.

Abstract

The paper analyzes the effective temperature response of an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski spacetime, focusing on the circular and drifted Rindler motions and their connection through parator motion.

Key highlights:

- Circular motion and drifted Rindler motion are shown to be smoothly connected through parator motion, which is a one-parameter subfamily of a two-parameter family of stationary motions.
- For drifted Rindler motion in 3+1 dimensions:
- In the large gap limit, the drift speed has a modest heating effect relative to the linear acceleration Unruh temperature.
- In the small gap limit, the drift speed has a mild cooling effect, by less than 10%, relative to the linear acceleration Unruh temperature.
- In the ultrarelativistic limit, the detailed balance temperature matches that of circular motion and parator motion.

- For drifted Rindler motion in 2+1 dimensions:
- In the large gap limit, the detailed balance temperature is the same as in 3+1 dimensions.
- In the small gap limit, the drift speed has a stronger cooling effect, with the detailed balance temperature approaching zero as the drift speed approaches unity.

- The smallness of the circular motion effective temperature for small internal energy spacings in 2+1 dimensions is traced to the weak decay of the Wightman function along the detector's trajectory, a phenomenon unique to 2+1 dimensions and therein to circular and parator motion.

To Another Language

from source content

arxiv.org

Stats

The proper acceleration a and torsion b for drifted Rindler motion are given by:
a = γ^2 / R
b = γ^2 v / R
The proper acceleration a and torsion b for circular motion are given by:
a = γ^2 v^2 / R
b = γ^2 v / R

Quotes

"The circular motion Killing vectors, the drifted Rindler Killing vectors and the parator Killing vectors form a smooth two-parameter family, given by (2.17) with a > 0 and b > 0, such that circular motion occurs for a < b, drifted Rindler motion occurs for a < b, and the two are joined by the parator one-parameter subfamily in which a = b."
"The smallness of the circular motion effective temperature for small internal energy spacings in 2+1 dimensions is traced to the weak decay of the Wightman function along the detector's trajectory, a phenomenon unique to 2+1 dimensions and therein to circular and parator motion."

Key Insights Distilled From

by Leo Parry, J... at **arxiv.org** 10-01-2024

Deeper Inquiries

The results presented in the paper can be extended to other types of stationary motions by considering the broader framework of stationary worldlines in Minkowski spacetime. Each type of stationary motion can be characterized by its own set of curvature invariants, such as proper acceleration, torsion, and hypertorsion. The analysis of the eﬀective temperature associated with these motions can be generalized by examining the response of the Unruh-DeWitt (UDW) detector to various stationary trajectories. For instance, motions that involve combinations of boosts and translations, or more complex trajectories that may not fit neatly into the categories of circular, drifted Rindler, or parator, can still be analyzed using similar techniques. The smooth deformation between these motions suggests that there exists a continuous spectrum of stationary motions, each with its own unique eﬀective temperature profile. This indicates that the underlying quantum field dynamics are sensitive to the specific characteristics of the motion, allowing for a rich variety of thermal responses depending on the trajectory of the observer.

The smooth deformation between circular and drifted Rindler motions has significant implications for the underlying quantum field dynamics. This relationship highlights the interconnectedness of different types of stationary motions and suggests that the quantum field's response can be continuously transformed as the observer's trajectory changes. The fact that circular motion can be viewed as a limit of drifted Rindler motion (and vice versa) implies that the quantum field dynamics are not only dependent on the acceleration but also on the specific trajectory taken by the observer. This smooth transition allows for the exploration of how the eﬀective temperature and the associated thermal effects evolve as one moves through different types of motion. Furthermore, it emphasizes the role of the Wightman function's decay properties in determining the thermal response, which can lead to new insights into the nature of particle creation and vacuum fluctuations in curved spacetimes. The implications extend to understanding how different trajectories can yield varying thermal signatures, potentially influencing experimental designs in analog gravity setups.

Yes, the unique behavior of circular and parator motions in 2+1 dimensions presents intriguing opportunities for practical applications of the Unruh effect, particularly in analog gravity experiments. The distinct thermal responses observed in these motions, especially the vanishing of the detailed balance temperature in the small gap limit, could be leveraged to create experimental setups that simulate the Unruh effect more effectively. In analog systems, such as Bose-Einstein condensates or superfluid helium, the ability to manipulate the effective spacetime geometry allows researchers to explore the thermal properties associated with these unique trajectories. The small internal energy spacing characteristic of 2+1 dimensions could lead to observable signatures of the Unruh effect, making it feasible to test theoretical predictions in a controlled environment. Additionally, the smooth transition between circular and parator motions could facilitate the design of experiments that dynamically alter the observer's trajectory, providing a platform to study the interplay between acceleration, temperature, and quantum field dynamics in real-time. This could enhance our understanding of fundamental concepts in quantum field theory and contribute to the development of new technologies based on quantum thermal effects.

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