Ground state fluctuations in finite Fermi and Bose systems

We consider a small and fixed number of fermions (bosons) in a trap. The ground state of the system is defined at T=0. For a given excitation energy, there are several ways of exciting the particles from this ground state. We formulate a method for calculating the number fluctuation in the ground state using microcanonical counting, and implement it for small systems of noninteracting fermions as well as bosons in harmonic confinement. This exact calculation for fluctuation, when compared with canonical ensemble averaging, gives considerably different results, specially for fermions. This difference is expected to persist at low excitation even when the fermion number in the trap is large.Comment: 20 pages (including 1 appendix), 3 postscript figures. An error was found in one section of the paper. The corrected version is updated on Sep/05/200

On the Microcanonical Entropy of a Black Hole

It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient.Comment: 15 pages, 1 figur

On the Quantum Density of States and Partitioning an Integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For $N$ bosons in a one dimensional harmonic oscillator potential, it is well known that the asymptotic (N -> infinity) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of s-th powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d^2(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the $s=1$ case by our method, we generalize it to obtain a new formula for distinct restricted partitions.Comment: 17 pages including figure captions. 6 figures. To be submitted to J. Phys. A: Math. Ge

On the Claims of Weak Block Synchronization in Bitcoin

Recent Bitcoin attacks [CCS\u2721, CCS\u2721, ICDCS\u2719] commonly exploit the phenomenon of so-called weak block synchronization in Bitcoin. The attacks use two independently-operated Bitcoin monitors — i.e., Bitnodes and a system of customized supernodes — to confirm that block propagation in Bitcoin is surprisingly slow. In particular, Bitnodes constantly reports that around 30% of nodes are 3 blocks (or more) behind the blockchain tip and the supernodes show that on average more than 60% of nodes do not receive the latest block even after waiting for 10 minutes. In this paper, we carefully re-evaluate these controversial claims with our own experiments in the live Bitcoin network and show that block propagation in Bitcoin is, in fact, fast enough (e.g., most peers we monitor receive new blocks in about 4 seconds) for its safety property. We identify several limitations and bugs of the two monitors, which have led to these inaccurate claims about the Bitcoin block synchronization. We finally ask several open-ended questions regarding the technical and ethical issues around monitoring blockchain networks

Number Fluctuation in an interacting trapped gas in one and two dimensions

It is well-known that the number fluctuation in the grand canonical ensemble, which is directly proportional to the compressibility, diverges for an ideal bose gas as T -> 0. We show that this divergence is removed when the atoms interact in one dimension through an inverse square two-body interaction. In two dimensions, similar results are obtained using a self-consistent Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may be mapped on to a system of non-interacting particles obeying the Haldane-Wu exclusion statistics. We also calculate the number fluctuation from the ground state of the gas in these interacting models, and compare the grand canonical results with those obtained from the canonical ensemble.Comment: 11 pages, 1 appendix, 3 figures. Submitted to J. Phys. B: Atomic, Molecular & Optica

THÀNH PHẦN HÓA HỌC VÀ HOẠT TÍNH KHÁNG VI SINH VẬT GÂY BỆNH CỦA TINH DẦU TỪ VỎ BƯỞI DA XANH (Citrus maxima (Burm.) Merr.)

Pomelo is a Vietnam’s plant species with high nutritional and economic value. Besides, pomelo essential oil contains numerous compounds with high biological activity. The essential oil is extracted by using steam distillation, and its chemical composition is determined by means of GC-MS. The major components are limonene (91.19%), b-myrcene (2.92%), a-phellandrene (1.98%), and a-pinene (1.19%). The antimicrobial activity of essential oils is tested against pathogenic Gram-positive bacteria (Bacillus cereus, Staphylococcus aureus), Gram-negative bacteria (Escherichia coli), and Aspergillus flavus at different concentrations with the agar well diffusion method. This essential oil is active against B. cereus, S. aureus, and E. coli with inhibition diameter zones at 8.3–11.3, 10.3–18.7, and 9.0–11.7 mm, respectively, and inhibits A. flavus mold with 18.9–65.0% efficiency.Bưởi là loài cây không chỉ có giá trị cao về mặt dinh dưỡng mà còn có giá trị cao về mặt kinh tế và được trồng phổ biến ở Việt Nam. Ngoài ra, tinh dầu bưởi chứa nhiều hợp chất có hoạt tính sinh học cao. Tinh dầu bưởi được chiết xuất bằng phương pháp chưng cất lôi cuốn hơi nước và thành phần hóa học được phân tích bằng phương pháp GC-MS. Thành phần chính của tinh dầu gồm limonene (91,19%), b-myrcene (2,92%), a-phellandrene (1,98%) và a-pinene (1,19%). Hoạt tính kháng vi sinh vật của tinh dầu được khảo sát với vi khuẩn Gram dương (Bacillus cereus, Staphylococcus aureus), Gram âm (Escherichia coli) và nấm mốc Aspergillus flavus ở nồng độ 5, 10, 25 và 50% bằng phương pháp khuếch tán giếng thạch. Tinh dầu có khả năng kháng B. cereus, S. aureus và E. coli với đường kính vòng kháng khuẩn lần lượt là 8,3–11,3, 10,3–18,7 và 9,0–11,7 mm và ức chế sự phát triển của A. flavus (18,9–65,0%)

Off-Path TCP Exploits of the Mixed IPID Assignment

In this paper, we uncover a new off-path TCP hijacking attack that can be used to terminate victim TCP connections or inject forged data into victim TCP connections by manipulating the new mixed IPID assignment method, which is widely used in Linux kernel version 4.18 and beyond to help defend against TCP hijacking attacks. The attack has three steps. First, an off-path attacker can downgrade the IPID assignment for TCP packets from the more secure per-socket-based policy to the less secure hash-based policy, building a shared IPID counter that forms a side channel on the victim. Second, the attacker detects the presence of TCP connections by observing the shared IPID counter on the victim. Third, the attacker infers the sequence number and the acknowledgment number of the detected connection by observing the side channel of the shared IPID counter. Consequently, the attacker can completely hijack the connection, i.e., resetting the connection or poisoning the data stream. We evaluate the impacts of this off-path TCP attack in the real world. Our case studies of SSH DoS, manipulating web traffic, and poisoning BGP routing tables show its threat on a wide range of applications. Our experimental results show that our off-path TCP attack can be constructed within 215 seconds and the success rate is over 88%. Finally, we analyze the root cause of the exploit and develop a new IPID assignment method to defeat this attack. We prototype our defense in Linux 4.18 and confirm its effectiveness through extensive evaluation over real applications on the Internet

Number Fluctuation and the Fundamental Theorem of Arithmetic

We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state, resulting in a fluctuation of the ground state population. As a counter example, we take the quantum spectrum to be logarithms of the prime number sequence, and using the fundamental theorem of arithmetic, find that the ground state fluctuation vanishes exactly for all excitations. The use of the standard canonical or grand canonical ensembles, on the other hand, gives substantial number fluctuation for the ground state. This difference between the microcanonical and canonical results cannot be accounted for within the framework of equilibrium statistical mechanics.Comment: 4 pages, 4 figures. To be submitted to Phys. Rev. Let