The possibility of Ads space evolved into ds space

This article proposes an educated guess. Since the extreme value of the doubt way of thinking represents the minimum (the breakdown or decline of something into random disorder) of an open (related to tiny, weird movements of atoms) system, we saw in the previous article that the extreme value of the doubt way of thinking can be smaller, which points to that (the breakdown or decline of something into random disorder) reduction acts on the (related to tiny, weird movements of atoms) system. It will happen in a sudden and unplanned way. We assume that the macro system and the micro system are closed systems, the system (the breakdown) increases to 0, the macro open system increases in (the breakdown or decline of something into random disorder), and the micro system decreases in (the breakdown or decline of something into random disorder). We know that Ads space can make up/be equal to Ads/CFT explanation (of why something works or happens the way it does), while ds space has serious (problems, delays, etc.) (experiments prove that the universe is ds space-time). Assuming that there is an unplanned reduction process in the tiny system, the Ads space can change into a ds space.

Correlated disorder in rainbow metamaterials for vibration attenuation

Metastructures are typically composed of periodic unit cells designed to present enhanced dynamic properties in which either single or multiple resonators are periodically distributed. Even though the periodic metamaterials can obtain bandgaps with outstanding vibration attenuation, the widths of bandgaps can still be narrow for some practical applications. Rainbow metamaterials have been proposed based on gradient or random profiles to provide further improved attenuation. Nonetheless, the effects of correlated random disorder on their attenuation performance remains an open challenge. This work presents an investigation on the effects of correlated disorder on the vibration attenuation of rainbow metamaterials. An analytical model using the transfer matrix approach is used to calculate the receptance functions in a finite length metastructure composed of evenly spaced non-symmetric resonators attached to a beam with Π-shaped cross-section, thus a multi-frequency metastructure. The correlated disorder is modelled using random fields and an analytical expression of the Karhunen-Loève expansion is used such that spatial correlation on the resonator properties is modified by various correlation lengths, i.e., the level of spatial smoothness. Individual samples of random fields are used to investigate the effects of the correlated disorder in the vibration attenuation of a multi-frequency metastructure. It is shown that the bandgap can be further widened when compared to uncorrelated disorder. The obtained results indicates that a combination of the gradient profile with some level of disorder, typically resulting from random fields with larger correlation lengths, tends to give improved vibration attenuation when compared to a optimized gradient rainbow metamaterial. It opens new and innovative ways for the design of broadband rainbow metastructures for vibration attenuation.

Thermalization in a Quantum Harmonic Oscillator with Random Disorder

We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.

Disorder in Quantum Many-Body Systems

Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.

Leviathan, Taxation, and Public Goods

In the context of the rationale and structure of group formation, Mancur Olson drew attention to the fact that despite problems of inefficiency in public- goods provision, and irregularity in pricing and burden sharing, individuals voluntarily form groups to provide themselves with public goods. This preoccupation with the economic incentives in groups that led him to imagine the origin of the state as an economic group with beginnings in anarchy distinguished by and plagued by roving banditry, with its random disorder and erratic tax theft. The roving bandit who had settled down to become a king or stationary bandit would become the next stage, succeeding anarchy and improving upon life for both bandit and subjects. This chapter recounts the main elements in the stationary bandit theory, together with a view of the economic structure of governance and its reciprocal relations with the social economy, and suggests routes for further application.