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- All Subjects: Quantum Mechanics
Description
The longstanding issue of how much time it takes a particle to tunnel through quantum barriers is discussed; in particular, the phenomenon known as the Hartman effect is reviewed. A calculation of the dwell time for two successive rectangular barriers in the opaque limit is given and the result depends on the barrier widths and hence does not lead to superluminal tunneling or the Hartman effect.
ContributorsMcDonald, Scott (Author) / Davies, Paul (Thesis director) / Comfort, Joseph (Committee member) / McCartney, M. R. (Committee member) / Barrett, The Honors College (Contributor)
Created2009-05
Description
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
A swarm describes a group of interacting agents exhibiting complex collective behaviors. Higher-level behavioral patterns of the group are believed to emerge from simple low-level rules of decision making at the agent-level. With the potential application of swarms of aerial drones, underwater robots, and other multi-robot systems, there has been increasing interest in approaches for specifying complex, collective behavior for artificial swarms. Traditional methods for creating artificial multi-agent behaviors inspired by known swarms analyze the underlying dynamics and hand craft low-level control logics that constitute the emerging behaviors. Deep learning methods offered an approach to approximate the behaviors through optimization without much human intervention.
This thesis proposes a graph based neural network architecture, SwarmNet, for learning the swarming behaviors of multi-agent systems. Given observation of only the trajectories of an expert multi-agent system, the SwarmNet is able to learn sensible representations of the internal low-level interactions on top of being able to approximate the high-level behaviors and make long-term prediction of the motion of the system. Challenges in scaling the SwarmNet and graph neural networks in general are discussed in detail, along with measures to alleviate the scaling issue in generalization is proposed. Using the trained network as a control policy, it is shown that the combination of imitation learning and reinforcement learning improves the policy more efficiently. To some extent, it is shown that the low-level interactions are successfully identified and separated and that the separated functionality enables fine controlled custom training.
This thesis proposes a graph based neural network architecture, SwarmNet, for learning the swarming behaviors of multi-agent systems. Given observation of only the trajectories of an expert multi-agent system, the SwarmNet is able to learn sensible representations of the internal low-level interactions on top of being able to approximate the high-level behaviors and make long-term prediction of the motion of the system. Challenges in scaling the SwarmNet and graph neural networks in general are discussed in detail, along with measures to alleviate the scaling issue in generalization is proposed. Using the trained network as a control policy, it is shown that the combination of imitation learning and reinforcement learning improves the policy more efficiently. To some extent, it is shown that the low-level interactions are successfully identified and separated and that the separated functionality enables fine controlled custom training.
ContributorsZhou, Siyu (Author) / Ben Amor, Heni (Thesis advisor) / Walker, Sara I (Thesis advisor) / Davies, Paul (Committee member) / Pavlic, Ted (Committee member) / Presse, Steve (Committee member) / Arizona State University (Publisher)
Created2020
Description
Scientific research encompasses a variety of objectives, including measurement, making predictions, identifying laws, and more. The advent of advanced measurement technologies and computational methods has largely automated the processes of big data collection and prediction. However, the discovery of laws, particularly universal ones, still heavily relies on human intellect. Even with human intelligence, complex systems present a unique challenge in discerning the laws that govern them. Even the preliminary step, system description, poses a substantial challenge. Numerous metrics have been developed, but universally applicable laws remain elusive. Due to the cognitive limitations of human comprehension, a direct understanding of big data derived from complex systems is impractical. Therefore, simplification becomes essential for identifying hidden regularities, enabling scientists to abstract observations or draw connections with existing knowledge. As a result, the concept of macrostates -- simplified, lower-dimensional representations of high-dimensional systems -- proves to be indispensable. Macrostates serve a role beyond simplification. They are integral in deciphering reusable laws for complex systems. In physics, macrostates form the foundation for constructing laws and provide building blocks for studying relationships between quantities, rather than pursuing case-by-case analysis. Therefore, the concept of macrostates facilitates the discovery of regularities across various systems. Recognizing the importance of macrostates, I propose the relational macrostate theory and a machine learning framework, MacroNet, to identify macrostates and design microstates. The relational macrostate theory defines a macrostate based on the relationships between observations, enabling the abstraction from microscopic details. In MacroNet, I propose an architecture to encode microstates into macrostates, allowing for the sampling of microstates associated with a specific macrostate. My experiments on simulated systems demonstrate the effectiveness of this theory and method in identifying macrostates such as energy. Furthermore, I apply this theory and method to a complex chemical system, analyzing oil droplets with intricate movement patterns in a Petri dish, to answer the question, ``which combinations of parameters control which behavior?'' The macrostate theory allows me to identify a two-dimensional macrostate, establish a mapping between the chemical compound and the macrostate, and decipher the relationship between oil droplet patterns and the macrostate.
ContributorsZhang, Yanbo (Author) / Walker, Sara I (Thesis advisor) / Anbar, Ariel (Committee member) / Daniels, Bryan (Committee member) / Das, Jnaneshwar (Committee member) / Davies, Paul (Committee member) / Arizona State University (Publisher)
Created2023