Exact Mapping Research Articles

Loop quantum gravity, exact holographic mapping, and holographic entanglement entropy

The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\Sigma$ with boundary $\partial\Sigma$ is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region $A$ and its complement $\bar{A}$ are specified on the boundary $\partial\Sigma$, we show that the boundary entanglement entropy $S(A)$ of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. $S(A)$ is proportional to the minimal area of the bulk surface attached to the boundary of $A$ in $\partial\Sigma$.

Virtual Mass of Any Shape of Body by using General Mapping Function

When an object is moving in acceleration with fluid interaction from surrounding, it possesses virtual mass (added mass) in which the total mass of object is higher than the original mass. The exact conformal mapping method was proposed to determine the virtual mass. However, it is difficult to determine the virtual mass for the body of random shape by using conformal mapping. Therefore the new concept of mapping function is proposed. It is based on Laurent series that has been proposed to map the body of random shape to a circle. The function of a body shape is expressed in Fourier series which is essential to determine the complex coefficients of mapping function (Laurent series). Proposed method is compared with exact conformal method (equilateral polygon) and the validity is confirmed.

Advanced Synthesis Technique for Unified Extracted Pole Filters

This paper proposes a novel and unified synthesis approach and design procedure for microwave filters with extracted pole and nonresonating node (NRN) technique. By introducing a general circuit topology, the traditional extracted pole and NRN filters can be unified to a general prototype. With the new design process, the exact mapping relationship between the electromagnetic (EM) model of the pole producing element and the circuit model can be achieved. All the physical dimensions of the filter structure can be obtained by a fully analytical approach. No full EM optimization or adjustment is needed in the filter design. A three pole TE $_{\mathrm { {101}}}$ mode waveguide filter with one finite transmission zero is designed to illustrate the new procedure. In addition, a seven-pole TE $_{\mathrm { {011}}}$ mode filter with four finite transmission zeros covering all three possible types of arrangements is designed and fabricated to demonstrate the versatility of the proposed method. The simulated and measured results verified the efficiency and the accuracy of the proposed design method.

Many-terminal Majorana island: From topological to multichannel Kondo model

We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multi-channel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter $K$ in the leads that is effectively doubled. For strong interaction, $K=1/2$, the intermediate fixed point of the standard multi-channel Kondo model is exactly recovered. It evolves with $K$ and connects to strong coupling in non-interacting case $K=1$, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multi-channel Kondo state.

TSS-EMOTE, a refined protocol for a more complete and less biased global mapping of transcription start sites in bacterial pathogens.

BackgroundBacteria rely on efficient gene regulatory mechanisms to switch between genetic programs when they are facing new environments. Although this regulation can occur at many different levels, one of the key steps is the initiation of transcription. Identification of the first nucleotide transcribed by the RNA polymerase is therefore essential to understand the underlying regulatory processes, since this provides insight on promoter strength and binding sites for transcriptional regulators, and additionally reveals the exact 5’ untranslated region of the transcripts, which often contains elements that regulate translation.ResultsHere we present data from a novel TSS-EMOTE assay (Transcription Start Specific Exact Mapping Of Transcriptome Ends) to precisely map the transcription initiation sites of four entire transcriptomes. TSS-EMOTE is a variation of the dRNA-seq method, which has been combined with the EMOTE protocol, in order to increase detection of longer transcripts and limit biases introduced by PCR amplification of the Illumina sequencing library. Using TSS-EMOTE, 2018 promoters were detected in the opportunistic pathogen Staphylococcus aureus, and detailed consensus sequences could be obtained for the RNA polymerase recognition elements (e.g. sigma factor binding sites). The data also revealed a 94 nt median length of the 5’ untranslated region in S. aureus, giving important insights for future work on translational regulation. Additionally, the transcriptomes of three other opportunistic pathogens, Staphylococcus epidermidis, Acinetobacter baumannii and Enterobacter aerogenes, were examined, and the identified promoter locations were then used to generate a map of the operon structure for each of the four organisms.ConclusionsMapping transcription start sites, and subsequent correlation with the genomic sequence, provides a multitude of important information about the regulation of gene expression, both at the transcriptional and translational level, by defining 5’ untranslated regions and sigma-factor binding sites. We have here mapped transcription start sites in four important pathogens using TSS-EMOTE, a method that works with both long and 3’-phosphorylated RNA molecules, and which incorporates Unique Molecular Identifiers (UMIs) to allow unbiased quantification.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-3211-3) contains supplementary material, which is available to authorized users.

On the numerical study of percolation and epidemic critical properties in networks

The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of these dynamics in a network a number of subtleties must be taken into account in order to correctly estimate the transition point and the associated critical properties. We expose these subtleties and identify the different quantities which play the role of criticality detector in the two dynamics.

Exact quantum field mappings between different experiments on quantum gases

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact solutions. Here we present an exact result which holds even when no exact solutions can be found: a class of spacetime mappings of different experiments onto each other, as long as the gas particles interact via two-body potentials which possess a scaling property that most real interactions do possess. Since our result is an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics, it is otherwise general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. Practical applications of this mapping include perfect simulation of non-trivial experiments with other experiments which may be easier to perform.

Holographic duality between(2+1)-dimensional quantum anomalous Hall state and(3+1)-dimensional topological insulators

In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.

Integral imaging system using an adaptive lens array.

We produced an adaptive lens array composed of multiple flat lens arrays arranged in a curved shape with an adjustable radius of curvature, in order to overcome the hardware problem of the conventional flat or curved lens array-based systems. The manufactured adaptive lens array is applied to an integral imaging system. The gap mismatch that occurs when using a curved lens array is resolved by computing the exact display mapping position of element images through each lens. The results of the experiment demonstrate that the adaptive lens array-based integral imaging system successfully generated elemental images according to the curvature transformation of the adaptive lens array, and they were reconstructed as 3D images.

Quantum centipedes: collective dynamics of interacting quantum walkers

We consider the quantum centipede made of N fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of N. Some analytical results are obtained for arbitrary N by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large-N limit.

Dark-soliton-like excitations in the Yang–Gaudin gas of attractively interacting fermions

Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin- Fermi gas with attractive delta-function interactions in one-dimension with the exactly solvable Yang–Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks–Girardeau gas. The prospects for experimental observations are briefly discussed.

Crystallization of spin superlattices with pressure and field in the layered magnet SrCu2(BO3)2.

An exact mapping between quantum spins and boson gases provides fresh approaches to the creation of quantum condensates and crystals. Here we report on magnetization measurements on the dimerized quantum magnet SrCu2(BO3)2 at cryogenic temperatures and through a quantum-phase transition that demonstrate the emergence of fractionally filled bosonic crystals in mesoscopic patterns, specified by a sequence of magnetization plateaus. We apply tens of Teslas of magnetic field to tune the density of bosons and gigapascals of hydrostatic pressure to regulate the underlying interactions. Simulations help parse the balance between energy and geometry in the emergent spin superlattices. The magnetic crystallites are the end result of a progression from a direct product of singlet states in each short dimer at zero field to preferred filling fractions of spin-triplet bosons in each dimer at large magnetic field, enriching the known possibilities for collective states in both quantum spin and atomic systems.

VIRTUAL MASS OF REGULAR POLYGON AT ANGLE OF ATTACK

In case of the accelerating motion like a sinusoidal motion, the virtual mass effect should be taken into account in equation of motion. Generally speaking we should find the appropriate mapping functions while they are restricted in some functions. To the author's knowledge, the virtual mass of the regular polygon is not shown by the exact solution, while the regular polygon is used as a sectional shape of the structure like a building, a membrance of a structure and so on. It is shown that the virtual mass of an regular polygon has been calculated by using the exact conformal mapping, in which the angle of attack is taken into account. Results show that it is not dependent from the angle of attack except the flat plat (n=2). It means, although the body shape is not a point symmetry, there is no dependence of angle of attack on virtual mass except the flat plate.

Application mapping onto mesh-based network-on-chip using constructive heuristic algorithms

Application mapping is an important part of network-on-chip (NoC) design, it tries to map the application onto a NoC-based platform. Because mapping an application onto the mesh architecture is NP-hard, there is no known algorithm for solving this problem in polynomial time. In this study, we propose a new application mapping algorithm for mapping an application onto the mesh topology NoC architecture to minimize the energy consumption. We compare the proposed algorithm with some previously proposed algorithm and exact mapping technique. Our experiments on multimedia benchmarks show that the proposed mapping algorithm obtains the same solutions as the optimal solutions that are generated by IPL on most of cases. On random benchmarks containing higher number of cores, we use less execution time to find better solution than CastNet and NMAP in large-scale mesh-based NoC.

Phase diagram and entanglement of two interacting topological Kitaev chains

A superconducting wire described by a $p$-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.

Semiclassical electron transport at the edge of a two-dimensional topological insulator: Interplay of protected and unprotected modes

We study electron transport at the edge of a generic disordered two-dimensional topological insulator, where some channels are topologically protected from backscattering. Assuming the total number of channels is large, we consider the edge as a quasi-one-dimensional quantum wire and describe it in terms of a non-linear sigma model with a topological term. Neglecting localization effects, we calculate the average distribution function of transmission probabilities as a function of the sample length. We mainly focus on the two experimentally relevant cases: a junction between two quantum Hall (QH) states with different filling factors (unitary class) and a relatively thick quantum well exhibiting quantum spin Hall (QSH) effect (symplectic class). In a QH sample, the presence of topologically protected modes leads to a strong suppression of diffusion in the other channels already at the scales much shorter than the localization length. On the semiclassical level, this is accompanied by the formation of a gap in the spectrum of transmission probabilities close to unit transmission, thereby suppressing shot noise and conductance fluctuations. In the case of a QSH system, there is at most one topologically protected edge channel leading to weaker transport effects. In order to describe `topological' suppression of nearly perfect transparencies, we develop an exact mapping of the semiclassical limit of the one-dimensional sigma model onto a zero-dimensional sigma model of a different symmetry class, allowing us to identify the distribution of transmission probabilities with the average spectral density of a certain random-matrix ensemble. We extend our results to other symmetry classes with topologically protected edges in two dimensions.

The origin of the criticality in meme popularity distribution on complex networks.

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

Density matrix renormalization group study of the Anyon-Hubbard model

Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ. We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.

Exact holographic mapping in free fermion systems

In this paper, we shall perform a detailed analysis of the Exact Holographic Mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free-fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. Our analytic results allow us to study the asymptotic properties that are difficult to probe numerically, such as the near horizon regime of the black hole geometry. We shall also explore a few interesting but hitherto unexplored bulk geometries, such as that corresponding to a boundary critical fermion with nontrivial dynamic critical exponent. Our analytic framework also allows us to study the holographic mapping of some of these boundary theories in dimensions 2+1 or higher.

Surface phase defects induced downstream laser intensity modulation in high-power laser facility

Optics surface phase defects induced intensity modulation in high-power laser facility for inertial confinement fusion research is studied. Calculations and experiments reveal an exact mapping of the modulation patterns and the optics damage spot distributions from the surface phase defects. Origins are discussed during the processes of optics manufacturing and diagnostics, revealing potential improvements for future optics manufacturing techniques and diagnostic index, which is meaningful for fusion level laser facility construction and its operation safety.