Topological insulator and quantum memory

Measurements done on the quantum systems are too specific. Contrary to their classical counterparts, quantum measurements can be invasive and destroy the state of interest. Besides, quantumness limits the accuracy of measurements done on quantum systems. Uncertainty relations define the universal accuracy limit of the quantum measurements. Relatively recently, it was discovered that quantum correlations and quantum memory might reduce the uncertainty of quantum measurements. In the present work, we study two different types of measurements done on the topological system. Namely, we discuss measurements done on the spin operators and the canonical pair of operators: momentum and coordinate. We quantify the spin operator's measurements through the entropic measures of uncertainty and exploit the concept of quantum memory. While for the momentum and coordinate operators, we exploit the improved uncertainty relations. We discovered that quantum memory reduces the uncertainties of spin measurements. On the hand, we proved that the uncertainties in the measurements of the coordinate and momentum operators depend on the value of the momentum and are substantially enhanced at small distances between itinerant and localized electrons (the large momentum limit). We note that the topological nature of the system leads to the spin-momentum locking. The momentum of the electron depends on the spin and vice versa. Therefore, we suggest the indirect measurement scheme for the momentum and coordinate operators through the spin operator. Due to the factor of quantum memory, such indirect measurements in topological insulators have smaller uncertainties rather than direct measurements

Combinatorics of Lax Objects in Bethe Ansatz

Algebraic Bethe Ansatz, also known as quantum inverse scattering method, is a consistent tool based on the Yang-Baxter equation which allows to construct Bethe Ansatz exact solutions. One of the most important objects in algebraic Bethe Ansatz is a monodromy matrix M̂, which is defined as an appropriate product of so-called Lax operators L̂ (local transition operators). Monodromy matrix as well as each of Lax operators acts in the tensor product of the quantum space with an auxiliary space ℂ². Thus M̂, when written in the standard basis of auxiliary space, consists of four elements Â, B̂, Ĉ, D̂, which are the operators acting in quantum space , where B̂ and Ĉ are step operators and the remaining generate all constants of motion. In this work a consistent method of construction of the Bethe Ansatz eigenstates in terms of objects â, b̂, ĉ, d̂ i.e. matrix elements of the Lax operators in the auxiliary space is proposed

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

We analyse the number field-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime field ℚ of rationals of degree $2^3$ and $2^4$, respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

We analyse the number field-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime field ℚ of rationals of degree $2^3$ and $2^4$, respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem

The influence of sonication and silver nanoparticles doped on viscoelastic structure of agarose gel

The paper presents result of experimental measurements of viscoelastic properties of agarose gel after sonication and with silver nanoparticles doped. Researches were conducted using a HAAKE MARS 2 rheometer (Thermo Electron Corporation, Karlsruhe, Germany), with serrated plate-plate measuring geometry. Viscoelastic properties of samples were measured with oscillation tests at constant deformation rate 0.1%, and frequency 1 Hz in the temperature range from 278 to 348 K. It was presented that using the sonication before solidification of gel results in increases of the storage modulus and complex viscosity of the solidified gel. It was also presented that when silver nanoparticles are doped into agarose gel, storage modulus and complex viscosity start to decrease at lower temperature