Perturbation Theory of Single Particle Spectrum of Antiferromagnetic Mott Insulating States in the Hubbard Models

In this work, we present an analytical framework for studying antiferromagnetic (AFM) Mott insulating states in the Hubbard model. We first derive an analytical solution for the single-particle Green's functions in the atomic limit. Within a second-order perturbation approach, we compute the ground state energy and show that the ground state is antiferromagnetically ordered. Then we derive an analytical solution for single-particle Green's functions when effects of the hopping term are considered in the N\'{e}el state. With the analytical solution, we compute and explain various properties of antiferromagnetic Mott insulators observed both experimentally and numerically: i) magnetic blueshift of the Mott gap; ii) spectral functions with features comparable to observations by angle-resolved photoemission spectroscopy on parental compounds of cuprate high $T_c$ superconductors. This work comprehends the electronic properties of antiferromagnetic Mott states analytically and provides a foundation for future investigations of doped antiferromagnetic Mott insulators, aiming for the mechanism of cuprates high-$T_c$ superconductivity.Comment: 4.5 pages, 2 figure

Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

Prompt-Specific Poisoning Attacks on Text-to-Image Generative Models

Data poisoning attacks manipulate training data to introduce unexpected behaviors into machine learning models at training time. For text-to-image generative models with massive training datasets, current understanding of poisoning attacks suggests that a successful attack would require injecting millions of poison samples into their training pipeline. In this paper, we show that poisoning attacks can be successful on generative models. We observe that training data per concept can be quite limited in these models, making them vulnerable to prompt-specific poisoning attacks, which target a model's ability to respond to individual prompts. We introduce Nightshade, an optimized prompt-specific poisoning attack where poison samples look visually identical to benign images with matching text prompts. Nightshade poison samples are also optimized for potency and can corrupt an Stable Diffusion SDXL prompt in <100 poison samples. Nightshade poison effects "bleed through" to related concepts, and multiple attacks can composed together in a single prompt. Surprisingly, we show that a moderate number of Nightshade attacks can destabilize general features in a text-to-image generative model, effectively disabling its ability to generate meaningful images. Finally, we propose the use of Nightshade` and similar tools as a last defense for content creators against web scrapers that ignore opt-out/do-not-crawl directives, and discuss possible implications for model trainers and content creators

Relieving the Impact of Transit Signal Priority on Passenger Cars through a Bilevel Model

Transit signal priority (TSP) is an effective control strategy to improve transit operations on the urban network. However, the TSP may sacrifice the right-of-way of vehicles from side streets which have only few transit vehicles; therefore, how to minimize the negative impact of TSP strategy on the side streets is an important issue to be addressed. Concerning the typical mixed-traffic flow pattern and heavy transit volume in China, a bilevel model is proposed in this paper: the upper-level model focused on minimizing the vehicle delay in the nonpriority direction while ensuring acceptable delay variation in transit priority direction, and the lower-level model aimed at minimizing the average passenger delay in the entire intersection. The parameters which will affect the efficiency of the bilevel model have been analyzed based on a hypothetical intersection. Finally, a real-world intersection has been studied, and the average vehicle delay in the nonpriority direction decreased 11.28 s and 22.54 s (under different delay variation constraint) compared to the models that only minimize average passenger delay, while the vehicle delay in the priority direction increased only 1.37 s and 2.87 s; the results proved the practical applicability and efficiency of the proposed bilevel model