Action (physics)

Summary

In physics, action is a scalar quantity describing how a physical system has changed over time (its dynamics). Action is significant because the equations of motion of the system can be derived through the principle of stationary action. In the simple case of a single particle moving with a constant velocity (uniform linear motion), the action is the momentum of the particle times the distance it moves, added up along its path; equivalently, action is twice the particle's kinetic energy times the duration for which it has that amount of energy. For more complicated systems, all such quantities are combined. More formally, action is a mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensions of energy × time or momentum × length, and its SI unit is joule-second (like the Planck constant h

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Using an isolated Milky Way-mass galaxy simulation, we compare results from nine state-of-the-art gravitohydrodynamics codes widely used in the numerical community. We utilize the infrastructure we have built for the AGORA High-resolution Galaxy Simulations Comparison Project. This includes the common disk initial conditions, common physics models (e. g., radiative cooling and UV background by the standardized package GRACKLE) and common analysis toolkit yt, all of which are publicly available. Subgrid physics models such as Jeans pressure floor, star formation, supernova feedback energy, and metal production are carefully constrained across code platforms. With numerical accuracy that resolves the disk scale height, we find that the codes overall agree well with one another in many dimensions including: gas and stellar surface densities, rotation curves, velocity dispersions, density and temperature distribution functions, disk vertical heights, stellar clumps, star formation rates, and Kennicutt-Schmidt relations. Quantities such as velocity dispersions are very robust (agreement within a few tens of percent at all radii) while measures like newly formed stellar clump mass functions show more significant variation (difference by up to a factor of similar to 3). Systematic differences exist, for example, between mesh-based and particle-based codes in the low-density region, and between more diffusive and less diffusive schemes in the high-density tail of the density distribution. Yet intrinsic code differences are generally small compared to the variations in numerical implementations of the common subgrid physics such as supernova feedback. Our experiment reassures that, if adequately designed in accordance with our proposed common parameters, results of a modern high-resolution galaxy formation simulation are more sensitive to input physics than to intrinsic differences in numerical schemes.

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Semiclassical analysis of the quantum instanton approximation

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We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to order-of-magnitude errors in the rate predictions. Nevertheless, semiclassical instanton theory remains accurate. We conclude that semiclassical instanton theory can be obtained directly from the semiclassical limit of the quantum instanton for symmetric systems. We suggest a modification of the quantum instanton approach which avoids sampling the spurious path and thus has a stronger connection to semiclassical instanton theory, giving numerically accurate predictions even for very asymmetric systems in the low temperature limit.

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