Potential well

Summary

A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to do due to entropy. Energy may be released from a potential well if sufficient energy is added to the system such that the local maximum is surmounted. In quantum physics, potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles; in these cases a particle may be imagined to tunnel through the walls of a potential well. The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (e.g., be a lake) without any water flowing away toward another, lower minimum (e.g. sea level). In the case of gravity, the region around a mass is a gravitational potential well, unless the density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself. A potential hill is the opposite of a potential well, and is the region surrounding a local maximum. Quantum confinement can be observed once the diameter of a material is of the same magnitude as the de Broglie wavelength of the electron wave function. When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials. A particle behaves as if it were free when the confining dimension is large compared to the wavelength of the particle. During this state, the bandgap remains at its original energy due to a continuous energy state. However, as the confining dimension decreases and reaches a certain limit, typically in nanoscale, the energy spectrum becomes discrete.

Official source

https://en.wikipedia.org/wiki/Potential_well

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Work fluctuations in the active Ornstein-Uhlenbeck particle model

Francesco Cagnetta

We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.

IOP Publishing Ltd2021

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Ginevra Favole

Halo assembly bias is the secondary dependence of the clustering of dark matter haloes on their assembly histories at fixed halo mass. This established dependence is expected to manifest itself on galaxy clustering, a potential effect commonly known as galaxy assembly bias. Using the IllustrisTNG300 magnetohydrodynamical simulation, we analyse the dependence of the properties and clustering of galaxies on the specific mass accretion history of their hosting haloes (sMAH). We first show that several halo and galaxy properties strongly correlate with the slope of the sMAH (beta) at fixed halo mass. Haloes with increasingly steeper beta increment their masses faster early on, and their hosted galaxies present larger stellar-to-halo mass ratios, lose their gas faster, reach the peak of their star formation histories at higher redshift, and become quenched earlier. We also demonstrate that beta provides a more stable link to these key galaxy formation properties than other broadly employed halo proxies, such as formation time. Finally, we measure the secondary dependence of galaxy clustering on beta at fixed halo mass. By tracing back the evolution of individual haloes, we show that the amplitude of the galaxy assembly bias signal for the progenitors of z = 0 galaxies increases with redshift, reaching a factor of 2 at z = 1 for haloes of M-halo = 10(11.)(5) -10(12) h(-1) M-circle dot. The measurement of the evolution of assembly bias along the merger tree provides a new theoretical perspective to the study of secondary bias. Our findings have also important implications for the generation of mock catalogues for upcoming cosmological surveys.

OXFORD UNIV PRESS2021

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IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

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