On propagation of information in quantum many-body systems

We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the many-body evolution stays, up to small leaking probability tails, within a light cone of the support of the initial conditions. This estimate is used to prove the light-cone approximation of dynamics and Lieb-Robinson-type bound, which in turn yield the results above. Our conditions cover long-range interactions. The main results of this paper as well as some key steps of the proofs were first presented in [36].Comment: updated reference [36] M. Lemm, C. Rubiliani, I. M. Sigal, and J. Zhang, Information propagation in long-range quantum many-body systems, Phys. Rev. A, To appear (2023

An Unsupervised Approach for Discovering Relevant Tutorial Fragments for APIs

Developers increasingly rely on API tutorials to facilitate software development. However, it remains a challenging task for them to discover relevant API tutorial fragments explaining unfamiliar APIs. Existing supervised approaches suffer from the heavy burden of manually preparing corpus-specific annotated data and features. In this study, we propose a novel unsupervised approach, namely Fragment Recommender for APIs with PageRank and Topic model (FRAPT). FRAPT can well address two main challenges lying in the task and effectively determine relevant tutorial fragments for APIs. In FRAPT, a Fragment Parser is proposed to identify APIs in tutorial fragments and replace ambiguous pronouns and variables with related ontologies and API names, so as to address the pronoun and variable resolution challenge. Then, a Fragment Filter employs a set of nonexplanatory detection rules to remove non-explanatory fragments, thus address the non-explanatory fragment identification challenge. Finally, two correlation scores are achieved and aggregated to determine relevant fragments for APIs, by applying both topic model and PageRank algorithm to the retained fragments. Extensive experiments over two publicly open tutorial corpora show that, FRAPT improves the state-of-the-art approach by 8.77% and 12.32% respectively in terms of F-Measure. The effectiveness of key components of FRAPT is also validated.Comment: 11 pages, 8 figures, In Proc. of 39rd IEEE International Conference on Software Engineering (ICSE'17

On the microscopic propagation speed of long-range quantum many-body systems

We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is thermodynamically stable and holds all the way down to microscopic length scales. For this, we develop a novel multiscale rendition of the ASTLO (adiabatic spacetime localization observables) method. Our result opens the door to deriving the first thermodynamically stable Lieb-Robinson bounds on general local operators for these long-range interacting bosonic systems.Comment: 28 pages, 5 figures; v1->v2: relaxed decay assumption in main resul

Three Essays in Entrepreneurial Finance and Innovation:

Thesis advisor: Thomas ChemmanurMy doctoral dissertation consists of three chapters focused on topics in entrepreneurial finance and corporate innovation. In the first chapter, I analyze secondary market patent transactions from public assignors (seller firms) to assignees (buyer firms). I show that firms with higher innovation productivity (more able to innovate) but with lower production efficiency (less able to commercialize) are more likely to sell patents distant from their operations. Using a linked assignor-assignee dataset, I find that patents technologically closer to buyer than to seller firms are more likely to be sold in a patent transaction, implying gains from trading patents. I document that, in the three years following patent transactions, seller firms experience a positive and statistically significant improvement in their ROA and operating profitability. I find that the improvement in ROA and operating profitability is concentrated in seller firms which increase their R&D focus after patent transactions, suggesting that an increase in innovation focus is one of the channels driving these results. Consistent with this channel, I find that inventors who are either newly hired by or remaining in assignor firms over the three years subsequent to patent transactions have technological expertise more similar to those of assignor firms. In the second chapter, co-authored with Xi Chen, we study how venture capitalists (VCs) create value in the product market for the entrepreneurial firms backed by them. By constructing a novel dataset based on Nielsen Retail Scanner and VentureXpert, we document that, compared to non-VC-backed firms, VC-backed startups have more than doubled their sales and seized more nationwide market share in the five years following the first VC investment. A further decomposition indicates that VC-backed firms achieve the growth in sales and market share by lowering their product prices. In addition, subsequent to the first VC investment, VC-backed firms enlarge their product portfolios by introducing new products and establishing new product lines, and they expand their products to more stores and geographic locations. Using the limited partner return as an instrument for the supply of VC financing, we show that the above effects are causal. We document heterogeneous value creation effects of VC financing for firms with different market share and for firms with different geographic proximity to the lead VC investors. This suggests that, apart from providing capital, VCs also add value to startups by directing their marketing strategy and monitoring their operations. In the third chapter, co-authored with Thomas Chemmanur, Jiajie Xu, and Xiang Zheng, we analyze the effect of the composition of venture capital (VC) syndicates on value creation to the entrepreneurial firms they invest in. We hypothesize that VCs may learn about each other’s skills at value creation when they co-invest together in entrepreneurial firms, allowing for more efficient value creation when they co-invest in subsequent syndicates. Further, if VCs view syndication as a repeated game, this may generate incentives to co-operate to a greater extent with each other when investing together in a syndicate, reducing the probability of conflicts among VCs. We empirically analyze the implications of these hypotheses and find the following. First, prior collaboration between a lead VC and any of the VCs in a syndicate leads to greater short-term value creation, as evidenced by greater sales growth, employment growth, probability of patented innovation, and the quality of innovations generated during the three years subsequent to VC syndicate investment. Second, prior collaboration between the lead VC and at least one of the syndicate members leads to greater long-term value creation, as evidenced by the higher probability of a successful exit (IPO or acquisition). Third, if the prior collaboration is very successful (leading to an IPO exit resulting from the previous collaboration), then there is even greater value creation by the VC syndicate compared to the case where the prior collaboration was less successful. Finally, consistent with prior collaboration allowing VCs to learn about each other’s value creation skills and reducing potential conflicts among the VCs forming a syndicate, syndicates with prior collaboration between the lead VC and at least one syndicate member are characterized by more uniform syndicate compositions across financing rounds.Thesis (PhD) — Boston College, 2023.Submitted to: Boston College. Carroll School of Management.Discipline: Finance

Why do firms go public through debt instead of equity?

We analyze a sample of private firms that go public through an initial public debt offering (IPDO) as an alternative to going public through equity (IPO). Firms that choose the IPDO route are larger, more likely to be backed by a financial sponsor such as a venture capital or private equity firm, and less likely to face information asymmetry than traditional IPO firms. Only a quarter of these firms eventually conduct an IPO, but those who do face lower underpricing than their contemporaneous private peers who do not have public debt at the time of going public.Cambridge Endowment for Research in Finance (CERF

Diffraction limit of light in curved space

Overcoming diffraction limit is crucial for obtaining high-resolution image and observing fine microstructure. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years, how spatial curvature affect the diffraction limit is an attractive and important question. Here we investigate the issue of diffraction limit and optical resolution on two-dimensional curved spaces - surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of non-uniform strong gravitational effect by probing locally the optical resolution

A new semi-analytical flow model for multi-branch well testing in natural gas hydrates

This paper presents a new semi-analytical solution and the related methodology to analyze the pressure behavior of multi-branch wells produced from natural gas hydrates. For constant bottom-hole pressure production, the transient flow solution is obtained by Laplace transforms. The interference among various branches is investigated using the superposition principle. A simplified form of the proposed model is validated using published analytical solutions. The complete flow profile can be divided into nine distinct regimes: wellbore storage and skin, vertical radial flow, linear flow, pseudo-radial flow, composite flow, dissociated flow, transitional flow, improvement flow and stress-sensitive flow. A well’s multi-branch structure governs the vertical radial and the linear flow regimes. In our model, a dynamic interface divides the natural gas hydrates deposit into dissociated and non-dissociated regions. Natural gas hydrates formation properties govern the compositeeffect, dissociated, transitional, and improvement flow regimes. A dissociation coefficient governs the difference in flow resistance between dissociated and non-dissociated natural gas hydrates regions. The dissociated-zone radius affects the timing of these flow regimes. Conversion of natural gas hydrates to natural gas becomes instantaneous as the dissociation coefficient increases. The pressure derivative exhibits the same features as a homogeneous formation. The natural gas hydrates parameter values in the Shenhu area of the South China Sea cause the prominent dissociated flow regime to conceal the later transitional and improvement flow regimes. Due to the maximum practical well-test duration limitation, the first five flow regimes (through composite flow) are more likely to appear in practice than later flow regimes.Cited as: Chu, H., Zhang, J., Zhang, L., Ma, T, Gao Y., Lee, W. J. A new semi-analytical flow model for multi-branch well testing in natural gas hydrates. Advances in Geo-Energy Research, 2023, 7(3): 176-188. https://doi.org/10.46690/ager.2023.03.0