Speeding up the spread of quantum information in chaotic systems

We explore the effect of introducing mild nonlocality into otherwise local, chaotic quantum systems, on the rate of information spreading and associated rates of entanglement generation and operator growth. We consider various forms of nonlocality, both in 1-dimensional spin chain models and in holographic gauge theories, comparing the phenomenology of each. Generically, increasing the level of nonlocality increases the rate of information spreading, but in lattice models we find instances where these rates are slightly suppressed.

Optical conductivities in triple fermions with different monopole charges

We investigate the linear optical conductivities of the newly-discovered triple-component semimetals. Due to the exactly flat band, the optical conductivity relates to the transition between the zero band and the conduction band directly reflecting the band structure of the conduction electrons in contrast to the other materials. For the low-energy models with various monopole charges, the diagonal conductivities show strong anisotropy. The ω-dependence of interband conductivities for a general low-energy model is deduced. The real part of the interband σ_xx always linearly depends on the optical frequency, while the one of σ_zz is proportional to ω^{2/n-1}. This can be a unique fingerprint of the monopole charge. For the lattice models, there also exists the optical anomalous Hall conductivity, where a sign change may appear. The characteristic frequencies of the kink structures are calculated, strictly. Our work will help us to establish the basic picture of linear optical response in topological triple-component semimetals and identify them from other materials.

Estimating the Designability of Protein Structures

The total number of amino acid sequences that can fold to a target protein structure, known as "designability", is a fundamental property of proteins that contributes to their structure and function robustness. The highly designable structures always have higher thermodynamic stability, mutational stability, fast folding, regular secondary structures, and tertiary symmetries. Although it has been studied on lattice models for very short chains by exhaustive enumeration, it remains a challenge to estimate the designable quantitatively for real proteins. In this study, we designed a new deep neural network model that samples protein sequences given a backbone structure using sequential Monte Carlo method. The sampled sequences with proper weights were used to estimate the designability of several real proteins. The designed sequences were also tested using the latest AlphaFold2 and RoseTTAFold to confirm their foldabilities. We report this as the first study to estimate the designability of real proteins.

A Novel (2, 3)-Threshold Reversible Secret Image Sharing Scheme Based on Optimized Crystal-Lattice Matrix

The (k, n)-threshold reversible secret image sharing (RSIS) is technology that conceals the secret data in a cover image and produces n shadow versions. While k (kn) or more shadows are gathered, the embedded secret data and the cover image can be retrieved without any error. This article proposes an optimal (2, 3) RSIS algorithm based on a crystal-lattice matrix. Sized by the assigned embedding capacity, a crystal-lattice model is first generated by simulating the crystal growth phenomenon with a greedy algorithm. A three-dimensional (3D) reference matrix based on translationally symmetric alignment of crystal-lattice models is constructed to guide production of the three secret image shadows. Any two of the three different shares can cooperate to restore the secret data and the cover image. When all three image shares are available, the third share can be applied to authenticate the obtained image shares. Experimental results prove that the proposed scheme can produce secret image shares with a better visual quality than other related works.

4-dimensional lattice models for the quantum range

Some finite subspace models L are presented for quantum structures which replace the use of countable infinite Hilbert space H dimensions. A maximal Boolean sublattice, called block, is 24, where its four atoms directly above 0εL, base vectors of H in 24 are drawn as four points on an interval. Blocks can overlap in one or two atoms. Different kinds of operators can map one block onto another and interpretations are given such that subspaces can carry on their base vector tuple real, complex or quaternionic numbers, energies, symmetries and generate coordinate lines. Describing states of physical systems is done using L and its applications for dynamical modelling. They don‘t need the infinte dimensional vectors of H. L has in the first model 11 blocks and 24 atoms (figure 1). They correspond to the 24 elements of the tetrahedral S4 symmetry. S4 arises from a spin-line rgb-graviton whirl operator with center at the tip of a tetrahedron and a nucleon triangle base with three quarks as vertices. The triangles factor group D3 of S4 is due to the CPT Klein normal subgroup Z2 x Z2 of S4 . It has a strong interaction SI rotor for the nucleons inner dynamics which is used for integrating functions, exchanging energies of nucleon with its environment and setting barycentrical coordinates in the triangle. At their intersection B as barycenter sets a Higgs boson or field the rescaled quark mass of a nucleon. Each factor class of one element from D3 assigns to it a color charge, a coordinate, an energy vector and a symmetry. Symmetries attached can be different according to interactions involved. Every atom of L has then a specific character with different properties.Three characters are added to octonian base vectors, listed by their indices as n = 0,1,…,7, and named for the atoms of L as na, nb, nc. The structure and element attributes of the finite subspace lattices L are desribed in many examples and models which technical constructed run macroscopically. Several models are described below. Example, the color charge whirl as rgb-graviton projection operator maps the block 2c3b5a6a to 0a1a2a3a. The symmetries change dimension from 3x3- to 2x2-matrices. From SU(3) are λ1 on 3b mapped to the SU(2) x-coordinate Pauli matrix σ1, from λ2 on 5a to σ2 y-coordinate and from λ3 on 6a to σ3 z-coordinate of real Euclidean space R³. The SU(3) matrices have complex w3 = z +ict, w2 = (iy,f), w1 = (x,m) coordinates. In figure 3 is shown how a rotation of two proton tetrahedrons for fusion changes the two linearly independent wj vectors to the 1-dimensional x,y,z base vectors. In deuteron then on one coordinate line sit with Cooper paire u-d-quarks at the ends the Heisenberg coupled energy or space vector rays 15 (x,m), m mass measured in kg, x in meter, 23 (iy,E(rot)), E(rot) rotational energy measured in Joule J, y in meter, 46 (ict,f), t time measured in seconds, f = 1/∆t frequency s inverse time interval measured in Hz. The six color charges are red r on +x as octonian coordinate 1, green g on +y as 2 , blue b on -z as 6, turquoise on -x as 5, magenta on -y as 3, yellow on +z as 4..

Pricing Exotic Options Using Some Lattice Procedures

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically. GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40