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    Wyświetlanie 1-9 z 9
    Tytuł:
    Matrix Representation of Constants of Motion for One-Dimensional Heisenberg Magnet
    Autorzy:
    Jakubczyk, P.
    Labuz, M.
    Lulek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/1402564.pdf
    Data publikacji:
    2015-08
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    75.10.Jm
    Opis:
    We demonstrate an exact diagonalization of the one-dimensional Heisenberg magnet in terms of algebraic Bethe Ansatz. We point out, by a polynomial expansion of the transfer matrix with respect to spectral parameter, a complete set of observables for classification of all eigenstates. We introduce an application of our approach on the example of the Heisenberg magnet consisting of four qubits, including its constants of motion, density matrices and complete classification of eigenstates.
    Źródło:
    Acta Physica Polonica A; 2015, 128, 2; 176-178
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Combinatorics of Lax Objects in Bethe Ansatz
    Autorzy:
    Stagraczyński, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/1402580.pdf
    Data publikacji:
    2015-08
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    75.10.Jm
    Opis:
    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.
    Źródło:
    Acta Physica Polonica A; 2015, 128, 2; 216-218
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Construction of three-qubit Kochen-Specker sets
    Autorzy:
    Toh, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1070549.pdf
    Data publikacji:
    2016-03
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    03.65.Ta
    42.50.Dv
    Opis:
    Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of quantum mechanics. Parity proof is one of the many different approaches applied to prove Kochen-Specker theorem for quantum system with different dimensionality. This method of proof requires Kochen-Specker sets that were composed of an odd number of bases and an even number of projectors. In most of the cases, the number of Kochen-Specker sets produced is large and its production is generally aided by computer calculation. However, manual generation of the Kochen-Specker sets are also reported previously for qutrit and two-qubit systems. We put forward the first and surprisingly simple method to generate manually Kochen-Specker sets, with respect to the Mermin pentagram, that can be used for the parity proof of the Kochen-Specker theorem in a state space of eight-dimensional three-qubit system.
    Źródło:
    Acta Physica Polonica A; 2016, 129, 3; 273-277
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geometric Phase for Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems
    Autorzy:
    Mendaš, I.
    Burić, N.
    Popović, D.
    Prvanović, S.
    Radonjić, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1204876.pdf
    Data publikacji:
    2014-08
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    03.65.Vf
    07.05.Dz
    Opis:
    Geometric phase for novel analytical solutions (Barnes and Das Sarma) of time-dependent two-level quantum systems is discussed, specifically for a general single-axis driving term, which is represented by a function J(t) in the Hamiltonian, and its corresponding evolution operator. It is demonstrated how general results for corresponding phases (total, dynamic and geometric) can be obtained. Using a specific case, it was found that over time in which the driving field is appreciably different from zero, the corresponding geometric phase changes (in the specific example by Δ β ≈ 0.8 radians) thus enabling detection. The results are relevant to qubit control and to quantum computing applications.
    Źródło:
    Acta Physica Polonica A; 2014, 126, 3; 670-672
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some Exact Results in the One-Dimensional Attractive Hubbard Model
    Autorzy:
    Jakubczyk, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1402562.pdf
    Data publikacji:
    2015-08
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    75.10.Pq
    03.65.Aa
    03.65.Fd
    Opis:
    The one-dimensional attractive Hubbard model (Ułl 0) is discussed for the chains of N nodes and the same number of electrons, where N-1 of them have the same spin projection, assuming periodic boundary conditions and the half-filling case. Based on the analysis of the eigenvalue problem we provided the general analytical expression for the eigenvalues, for any number N. This formula implies the existence of two elementary particles with mutually dependent momenta on the ring with N sites the same number of electrons including N-1 of the same spin projection.
    Źródło:
    Acta Physica Polonica A; 2015, 128, 2; 170-172
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Translating Concepts of State Transfer to Spin-1 Chains
    Autorzy:
    Wieśniak, M.
    Dutta, A.
    Ryu, Junghee
    Powiązania:
    https://bibliotekanauki.pl/articles/1402299.pdf
    Data publikacji:
    2015-07
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    03.67.-a
    03.67.Hk
    Opis:
    State transfer is a well-known routine for various systems of spins-1/2. Still, it is not well studied for chains of spins of larger magnitudes. In this contribution we argue that while perfect state transfer may seem unnatural in spin-1 systems, it is still feasible for arrays of V-type three-level atoms. Tomography of such 1D array is also shown to be possible by acting on one atom from such an array.
    Źródło:
    Acta Physica Polonica A; 2015, 128, 1; 3-5
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring
    Autorzy:
    Banaszak, G.
    Barańczuk, S.
    Lulek, T.
    Milewski, J.
    Stagraczyński, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/1427165.pdf
    Data publikacji:
    2012-05
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Aa
    73.21.-b
    85.35.Be
    89.70.Eg
    Opis:
    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.
    Źródło:
    Acta Physica Polonica A; 2012, 121, 5-6; 1111-1114
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Universal Sequence of the Ground States and Energy Level Ordering in Frustrated Antiferromagnetic Rings with a Single Bond Defect
    Autorzy:
    Antkowiak, M.
    Florek, W.
    Kamieniarz, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1032629.pdf
    Data publikacji:
    2017-04
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    75.10.Jm
    75.10.Hk
    75.50.Xx
    03.65.Aa
    Opis:
    The universal sequence of the ground states for antiferromagnetic frustrated rings with the odd number of the local spins s and a single bond defect α described by the isotropic Heisenberg Hamiltonian is discussed. The Lieb-Mattis energy level ordering in a pentanuclear ring is revealed and the arising magnetisation steps are demonstrated.
    Źródło:
    Acta Physica Polonica A; 2017, 131, 4; 890-892
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Random Unitary Matrices Associated to a Graph
    Autorzy:
    Kondratiuk, P.
    Życzkowski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1399055.pdf
    Data publikacji:
    2013-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    02.10.Yn
    03.65.Aa
    03.67.Mn
    05.45.Mt
    05.45.Pq
    Opis:
    We analyze composed quantum systems consisting of k subsystems, each described by states in the n-}dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order $n^2$. The global evolution operator is represented by a unitary matrix of size N = n^{k}. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to the Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size n^2 one can construct a fair approximation of large random unitary matrices of size $n^{k}$. Graph-structured random unitary matrices investigated here allow one to define the corresponding structured ensembles of random pure states.
    Źródło:
    Acta Physica Polonica A; 2013, 124, 6; 1098-1105
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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