Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We investigate the magnetic susceptibility $\chi(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $\chi(T)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay ($\xi = \infty$) we find a crossover at $\alpha^*=1.066$ between a phase with a divergent low-temperature susceptibility $\chi(T\rightarrow 0)$ for $\alpha > \alpha^*$ to a phase with a vanishing $\chi(T\rightarrow 0)$ for $\alpha < \alpha^*$. For finite cutoff lengths $\xi$, this crossover occurs at a smaller $\alpha^*(\xi)$. Additionally we study the localization of spin excitations for $\xi = \infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at $\alpha_c=\alpha^*$.Comment: 6 pages, 7 figure

The Adjudication and Enforcement of Rights After Brexit

This report records the inaugural meeting and roundtable of the Brexit and Rights Engagement Network (BREN) on Tuesday 3rd July 2018 at Edinburgh Law School. Attendees at the roundtable included network members, fellow academics, representatives of the Scottish Parliament, the Scottish Government, the Scottish Human Rights Commission, the Equality and Human Rights Commission, the legal professions, and NGOs. Two years after the EU Referendum and only a few days after the European Union (Withdrawal) Act 2018 (the 2018 Act) receiving Royal Assent, the Brexit and Rights Engagement Network met for the first time. The purpose of the roundtable was to ignite debate amongst legal scholars and policy makers, and others working in a rights environment relating to interpretation, adjudication and enforcement of rights in the lead up to, and following “Brexit Day,” (March 29, 2019). This report is split into two sections, Part A will consider the adjudication of EU rights, but also their enforcement under the 2018 Act and the Withdrawal Agreement, whilst ‘options for the future’ will be broached in Part B

Parity Violation in Neutrino Transport and the Origin of Pulsar Kicks

In proto-neutron stars with strong magnetic fields, the neutrino-nucleon scattering/absorption cross sections depend on the direction of neutrino momentum with respect to the magnetic field axis, a manifestation of parity violation in weak interactions. We study the deleptonization and thermal cooling (via neutrino emission) of proto-neutron stars in the presence of such asymmetric neutrino opacities. Significant asymmetry in neutrino emission is obtained due to multiple neutrino-nucleon scatterings. For an ordered magnetic field threading the neutron star interior, the fractional asymmetry in neutrino emission is about $0.006 (B/10^{14}G)$, corresponding to a pulsar kick velocity of about $200 (B/10^{14}G)$ km/s for a total radiated neutrino energy of $3\times 10^{53}$ erg.Comment: AASTeX, 10 pages including 2 ps figures; ApJ Letter in press (March 10, 1998). Shortened to agree with the published versio

Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.Comment: 4 pages, 2 figure

Competitive market for multiple firms and economic crisis

The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities (perfectly competitive markets obey Bose-Einstein statistics and purely monopolistic-competitive markets obey Boltzmann statistics) and that how interaction among firms influences the evolutionary of competitive markets. It has been widely accepted that perfect competition is most efficient. Our study shows that the perfectly competitive system, as an extreme case of competitive markets, is most efficient but not stable, and gives rise to economic crises as society reaches full employment. In the economic crisis revealed by our model, many firms condense (collapse) into the lowest supply level (zero supply, namely bankruptcy status), in analogy to Bose-Einstein condensation. This curious phenomenon arises because perfect competition (homogeneous competitions) equals symmetric (indistinguishable) investment direction, a fact abhorred by nature. Therefore, we urge the promotion of monopolistic competition (heterogeneous competitions) rather than perfect competition. To provide early warning of economic crises, we introduce a resolving index of investment, which approaches zero in the run-up to an economic crisis. On the other hand, our model discloses, as a profound conclusion, that the technological level for a long-run social or economic system is proportional to the freedom (disorder) of this system; in other words, technology equals the entropy of system. As an application of this new concept, we give a possible answer to the Needham question: "Why was it that despite the immense achievements of traditional China it had been in Europe and not in China that the scientific and industrial revolutions occurred?"Comment: 17 pages; 3 figure

Super and Sub-Poissonian photon statistics for single molecule spectroscopy

We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson-Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations, and obtain an exact analytical formula for the line shape and Mandel's Q parameter. The line shape exhibits well known behaviors, including motional narrowing when the stochastic modulation is fast, and power broadening. The Mandel parameter, describing the line shape fluctuations, exhibits a transition from a Quantum sub-Poissonian behavior in the fast modulation limit, to a classical super-Poissonian behavior found in the slow modulation limit. Our result is applicable for weak and strong laser field, namely for arbitrary Rabi frequency. We show how to choose the Rabi frequency in such a way that the Quantum sub-Poissonian nature of the emission process becomes strongest. A lower bound on $Q$ is found, and simple limiting behaviors are investigated. A non-trivial behavior is obtained in the intermediate modulation limit, when the time scales for spectral diffusion and the life time of the excited state, become similar. A comparison is made between our results, and previous ones derived based on the semi-classical generalized Wiener--Khintchine theorem.Comment: 14 Phys. Rev style pages, 10 figure

Modeling of Tyre-Clay Soil Interaction via Quasi-Static Moving Boundary Displacement Method

A vehicle mobility model has been developed using energy principles and a quasi-static moving boundary displacement method. For a given condition of both tyre and terrain characteristics, the model calculates the contact length, the slip rate, the traction efficiency and the drawbar pull. The effect of tread configuration is also included in calculating the slip rate. A numerical example is given to demonstrate the capability of the new developed mode. The model's predictions are also compared with the experimental results in the laboratory tests and a good agreement is obtained

Microwave resonance of the reentrant insulating quantum Hall phases in the 1st excited Landau Level

We present measurements of the real diagonal microwave conductivity of the reentrant insulating quantum Hall phases in the first excited Landau level at temperatures below 50 mK. A resonance is detected around filling factor $\nu=2.58$ and weaker frequency dependence is seen at $\nu=2.42$ and 2.28. These measurements are consistent with the formation of a bubble phase crystal centered around these $\nu$ at very low temperatures

Overall Evolution of Realistic Gamma-ray Burst Remnant and Its Afterglow

Conventional dynamic model of gamma-ray burst remnants is found to be incorrect for adiabatic blastwaves during the non-relativistic phase. A new model is derived, which is shown to be correct for both radiative and adiabatic blastwaves during both ultra-relativistic and non-relativistic phase. Our model also takes the evolution of the radiative efficiency into account. The importance of the transition from the ultra-relativistic phase to the non-relativistic phase is stressed.Comment: 9 pages, aasms4 style, 3 ps figures, minor changes, will be published in Chin. Phys. Let