Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Translation-symmetry protected topological orders on lattice

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

Spin and Charge Structure of the Surface States in Topological Insulators

We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The spin structure on surfaces other than the 111 surface has additional complexity because of a misalignment of the contributions coming from the two sublattices of the crystal. For these surfaces we expect new features to be seen in the spin-resolved ARPES experiments, caused by a non-helical spin-polarization of electrons at the individual sublattices as well as by the interference of the electron waves emitted coherently from two sublattices. We also show that the position of the Dirac crossing in spectrum of surface states depends on the orientation of the interface. This leads to contact potentials and surface charge redistribution at edges between different facets of the crystal.Comment: Use the correct spin operator. Changes affect the surface states spin structure, but not the spectru

Controlled MOCVD growth of Bi2Se3 topological insulator nanoribbons

Topological insulators are a new class of materials that support topologically protected electronic surface states. Potential applications of the surface states in low dissipation electronic devices have motivated efforts to create nanoscale samples with large surface-to-volume ratios and highly controlled stoichiometry. Se vacancies in Bi2Se3 give rise to bulk conduction, which masks the transport properties of the surface states. We have therefore developed a new route for the synthesis of topological insulator nanostructures using metalorganic chemical vapour deposition (MOCVD). MOCVD allows for control of the Se/Bi flux ratio during growth. With the aim of rational growth, we vary the Se/Bi flux ratio, growth time, and substrate temperature, and observe morphological changes which indicate a growth regime in which nanoribbon formation is limited by the Bi precursor mass-flow. MOCVD growth of Bi2Se3 nanostructures occurs via a distinct growth mechanism that is nucleated by gold nanoparticles at the base of the nanowire. By tuning the reaction conditions, we obtain either single-crystalline ribbons up to 10 microns long or thin micron-sized platelets.Comment: Related papers at http://pettagroup.princeton.ed

Nonclassical photon pairs generated from a room-temperature atomic ensemble

We report experimental generation of non-classically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated by a controllable time delay up to 2 microseconds. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.Comment: 4 pages, 2 figure

Erratum : Squeezing and entanglement delay using slow light

An inconsistency was found in the equations used to calculate the variance of the quadrature fluctuations of a field propagating through a medium demonstrating electromagnetically induced transparency (EIT). The decoherence term used in our original paper introduces inconsistency under weak probe approximation. In this erratum we give the Bloch equations with the correct dephasing terms. The conclusions of the original paper remain the same. Both entanglement and squeezing can be delayed and preserved using EIT without adding noise when the decoherence rate is small.Comment: 1 page, no figur