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Combinatorics of Lax Objects in Bethe Ansatz

100%

Stagraczyński R.

Acta Physica Polonica A

2015

vol. 128

issue 2

216-218

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 𝓗 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 𝓗, 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

45%

Banaszak G., Barańczuk S., Lulek T., Milewski J., Stagraczyński R.

Acta Physica Polonica A

2012

vol. 121

issue 5-6

1111-1114

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

27%

Żyła G., Stompor M., Kopańska M., Stagraczyński R., Fal J., Traciak J., Trybus M., Wolski S., Zawlik I., Cebulski J., Konefał-Janocha M., Cholewa M.

Acta Physica Polonica A

2017

vol. 132

issue 1

152-154

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.

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3 Acta Physica Polonica A

1 2017

1 2015

1 2012

3 Stagraczyński R.

1 Banaszak G.

1 Barańczuk S.

1 Cebulski J.

1 Cholewa M.

1 Fal J.

1 Konefał-Janocha M.

1 Kopańska M.

1 Lulek T.

1 Milewski J.

1 Stompor M.

1 Traciak J.

1 Trybus M.

1 Wolski S.

1 Zawlik I.

1 Żyła G.

Search results

Combinatorics of Lax Objects in Bethe Ansatz

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

The Influence of Sonication and Silver Nanoparticles Doped on Viscoelastic Structure of Agarose Gel