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It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $\mathrm{nm}$ is in random pure state then the average entropy subsystem $m$ where $m\ensuremath{\le}n$ ${S}_{m,n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\left(\ensuremath{\Sigma}{k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n+1}^{\mathrm{mn}}1/k\right)\ensuremath{-}(m\ensuremath{-}1)/2n$. In this Letter simple proof conjecture given.

The Abelian sandpile models feature a finite group G generated by the operators corresponding to particle addition at various sites. We study canonical decomposition of as product cyclic groups G=Z(d1)*Z(d2)*Z(d3)...*Z(dg), where g is least number generators G, and di multiple di+1. structure determined in terms toppling matrix Delta . construct scalar functions, linear height variables pile, that are invariant under any site. These invariants provide convenient coordinates label recurrent...

We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within conformal field theory framework. This convergent includes all subleading corrections Bekenstein-Hawking term.

We study the excitations of a massive Schwarzschild black hole mass M resulting from capture infalling matter described by massless scalar field. The near-horizon dynamics this system is governed Hamiltonian which related to Virasoro algebra and admits one-parameter family self-adjoint extensions parameter z∈R. density states can be expressed equivalently in terms z or M, leading consistent relation between these two parameters. corresponding entropy obtained as S=S(0)−32 logS(0)+C, where...

An observable influence of zero-point fluctuations the vacuum electromagnetic field on bound electrons is well known in hydrogen atom, where it produces Lamb shift. Here, we adapt an approach used to explain shift terms a slight expansion orbits due interaction with and apply assemblies $N$ that are modeled as independent atomically two-level systems. The effect stabilize collective ground-state energy, which leads prediction novel effects at room temperature for quasi-two-dimensional...

In this review, we summarize exact results for the three-dimensional BTZ black hole. We use rigorous mathematical to clarify general structure and properties of hole spacetime its microscopic description. particular, study formation by point particle collisions, leading an analytic determination Choptuik scaling parameter. also show that a `No Hair Theorem' follows immediately from theorem hyperbolic geometry, due Sullivan. A understanding Bekenstein-Hawking entropy, decay rate massless...

We give a detailed general description of recent geometrical discretization scheme and illustrate, by explicit numerical calculation, the scheme's ability to capture topological features. The is applied Abelian Chern-Simons theory leads, after necessary field doubling, an expression for discrete partition function in terms untwisted Reidemeister torsion various triangulation-dependent factors. evaluated computationally triangulations ${S}^{3}$ lens spaces. results confirm that triangulation...

The authors consider toppling distributions for the Abelian sandpile model in one dimension. They study avalanche mass and duration thermodynamic limit. also investigate their dependence on seeding distribution, which describes how sand is dropped. None of models shows criticality.

Compact torus injection into the Saskatchewan Torus-Modified [Phys. Fluids B 4, 3277 (1992)] tokamak discharges has triggered improved confinement characterized by an increase in electron density more than twofold, 30% reduction Hα radiation level, significant suppression of floating potential fluctuations and m=2 Mirnov oscillations. In this paper, we present detailed experimental setup results, as well extended theory explaining mechanism for triggering a compact injection.

We have considered the most general gauge invariant five-dimensional action of a second rank antisymmetric Kalb-Ramond tensor theory, including topological term form ${ϵ}^{ABLMN}{B}_{AB}{H}_{LMN}$ in Randall-Sundrum scenario. Such field ${B}_{AB}$ (whose rank-3 strength is ${H}_{LMN}$), which appears massless sector heterotic string assumed to coexist with gravity bulk. The third corresponding has well-known geometric interpretation as space-time torsion. only nontrivial classical solutions...

A novel feature of the H-mode induced by compact torus injection on STOR-M tokamak is observed. There almost no change in radial electric field profiles during and after L-H transition. The usual hypothesis E x B shear stabilization mechanism therefore unlikely to play a role this new microinstabilities parallel flow suggested as plausible cause for transition improved regime.

We obtain a bound-state spectrum of low-energy excitations near the Fermi points gapped graphene in presence charge impurity. The effects possible short-range interactions induced by impurity are modeled suitable boundary conditions. subcritical region effective Coulomb coupling is labeled parameter which characterizes conditions and determines inequivalent quantizations system. In supercritical we renormalization-group flow for coupling.

From the measurement of breakdown potentials in an electrodeless discharge a magnetic field values γH, Townsend's second coefficient field, have been calculated and curve between γH H has found to be hyperbolic nature, for three different pressure, 10 μ, 25 μ 57.5 varying from 0 60 gauss. Assuming expression derived by Sen Ghosh earlier paper,

We study the formation of Banados-Teitelboim-Zanelli black holes by collision point particles. It is shown that Gott time machine, originally constructed for case vanishing cosmological constant, provides a precise mechanism hole formation. As result, one obtains an exact analytic understanding Choptuik scaling.

We present a quantum analysis of the massless excitations in graphene with charge impurity. When effective exceeds certain critical value, spectrum is quantized and unbounded from below. The corresponding eigenstates are square-integrable at infinity have rapidly oscillatory behaviour short distance, which can be interpreted as fall to centre. Using cutoff regularization, we show that Coulomb interaction strength driven its value under renormalization group flow. In subcritical region, find...