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Imtheacht an Dá Nónmhar agus Tóraigheacht Taise Taoibhghile: an Early Modern Irish exemplary tale
Get PDFArgues that the fianaigheacht tale had an exemplary function. It was concerned with the relationships of vassals to their overlords and to one another and the proper place of the poet in society
A rigorous proof of the Bohr–van Leeuwen theorem in the semiclassical limit
Get PDFThe original formulation of the Bohr-van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from −∞ to ∞ what makes the free energy density magnetic-field-independent. When considering a classical (Maxwell-Boltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this article is to give, within the linear-response theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials
The BFSS model on the lattice
Get PDFWe study the maximally supersymmetric BFFS model at finite temperature and its bosonic relative. For the bosonic model in p + 1 dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including the phase transition. The mass becomes p^(1/3)λ^1/3 for large p, with λ the ’tHooft coupling. For p = 9 simulations of the model give m = (1.90 ± .01)λ^1/3 , which is also the mass gap of the Hamiltonian. We argue that there is no ‘sign’ problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when 1/α' corrections are included
Global symmetries of Yang-Mills squared in various dimensions
Get PDFTensoring two on-shell super Yang-Mills multiplets in dimensions D ≤ 10 yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) D with each dimension 3 ≤ D ≤ 10 we obtain formulae for the algebras g and h of the U-duality group G and its maximal compact subgroup H, respectively, in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product
Chaotic strings in a near Penrose limit of AdS5 × T1,1
Get PDFWe study chaotic motions of a classical string in a near Penrose limit of AdS_5 ×T^1,1 . It is known that chaotic solutions appear on R × T^1,1 , depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincaré sections. In comparison to the AdS_5 × T^1,1 case, we argue that no chaos lives in a near Penrose limit of AdS_5 ×S^5 , as expected from the classical integrability of the parent system
On the optical properties of carbon nanotubes. Part I. A general formula for the dynamical optical conductivity
Get PDFThis paper is the first one of a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNT). Produced by rolling up a graphene sheet, SWNT owe their intriguing properties to their cylindrical quasi-one-dimensional (quasi-1D) structure (the ratio length/radius is experimentally of order of 10^3 ). We model SWNT by circular cylinders of small diameters on the surface of which the conduction electron gas is confined by the electric field generated by the fixed carbon ions. The pair-interaction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi-1D structure, we introduce a 1D effective many-body Hamiltonian which is the starting-point of our analysis. To investigate the optical properties, we consider a perturbation by a uniform time-dependent electric field modeling an incident light beam along the longitudinal direction. By using Kubo’s method, we derive within the linear response theory an asymptotic expansion in the low-temperature regime for the dynamical optical conductivity at fixed density of particles. The leading term only involves the eigenvalues and associated eigenfunctions of the (unperturbed) 1D effective many-body Hamiltonian, and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT
