Relevant bibliographies by topics / Heisenberg spin equation

Academic literature on the topic 'Heisenberg spin equation'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Heisenberg spin equation"

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SCHIEF, W. K. "Nested toroidal flux surfaces in magnetohydrostatics. Generation via soliton theory." Journal of Plasma Physics 69, no. 6 (November 25, 2003): 465–84. http://dx.doi.org/10.1017/s0022377803002472.

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It is shown that the classical magnetohydrostatic equations of an infinitely conducting fluid reduce to the integrable potential Heisenberg spin equation subject to a Jacobian condition if the magnitude of the magnetic field is constant along individual magnetic field lines. Any solution of the constrained potential Heisenberg spin equation gives rise to a multiplicity of magnetohydrostatic equilibria which share the magnetic field line geometry. The multiplicity of equilibria is reflected by the local arbitrariness of the total pressure profile. A connection with the classical Da Rios equations is exploited to establish the existence of associated helically and rotationally symmetric equilibria. As an illustration, Palumbo's ‘unique’ toroidal isodynamic equilibrium is retrieved.
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Muminov, Khikmat, and Yousef Yousefi. "Semiclassical Description of Anisotropic Magnets for Spin." Advances in Condensed Matter Physics 2012 (2012): 1–3. http://dx.doi.org/10.1155/2012/749764.

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Nonlinear equations describing one-dimensional non-Heisenberg ferromagnetic model are studied by the use of generalized coherent states in a real parameterization. Also, dissipative spin wave equation for dipole and quadruple branches is obtained if there is a small linear excitation from the ground state.
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NEPOMECHIE, RAFAEL I. "A SPIN CHAIN PRIMER." International Journal of Modern Physics B 13, no. 24n25 (October 10, 1999): 2973–85. http://dx.doi.org/10.1142/s0217979299002800.

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Yousefi, Yousef, and Khikmat Kh Muminov. "Semiclassical Modeling of Isotropic Non-Heisenberg Magnets for Spin and Linear Quadrupole Excitation Dynamics." Physics Research International 2013 (March 27, 2013): 1–4. http://dx.doi.org/10.1155/2013/634073.

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Equations describing one-dimensional non-Heisenberg model are studied by use of generalized coherent states in real parameterization, and then dissipative spin wave equation for dipole and quadrupole branches is obtained if there is a small linear excitation from the ground state. Finally, it is shown that for such exchange-isotropy Hamiltonians, optical branch of spin wave is nondissipative.
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MUNIRAJA, GOPAL, and M. LAKSHMANAN. "MOTION OF SPACE CURVES IN THREE-DIMENSIONAL MINKOWSKI SPACE $R_1^{3}$, SO(2,1) SPIN EQUATION AND DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION." International Journal of Geometric Methods in Modern Physics 07, no. 06 (September 2010): 1043–49. http://dx.doi.org/10.1142/s0219887810004701.

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We consider the dynamics of moving curves in three-dimensional Minkowski space [Formula: see text] and deduce the evolution equations for the curvature and torsion of the curve. Next by mapping a continuous SO(2,1) Heisenberg spin chain on the space curve in [Formula: see text], we show that the defocusing nonlinear Schrödinger equation(NLSE) can be identified with the spin chain, thereby giving a geometrical interpretation of it. The associated linear eigenvalue problem is also obtained in a geometrical way.
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Schief, W. K., and C. Rogers. "The Euler Equations of Spatial Gasdynamics and the Integrable Heisenberg Spin Equation." Studies in Applied Mathematics 128, no. 4 (December 9, 2011): 407–19. http://dx.doi.org/10.1111/j.1467-9590.2011.00539.x.

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Gutkin, Eugene. "Heisenberg-Ising spin chain and the nonlinear schrödinger equation." Reports on Mathematical Physics 24, no. 1 (August 1986): 121–27. http://dx.doi.org/10.1016/0034-4877(86)90046-7.

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ZEE, A. "NON-ABELIAN FLUX AND SPIN LIQUID STATES." Modern Physics Letters B 05, no. 20 (August 30, 1991): 1339–48. http://dx.doi.org/10.1142/s0217984991001635.

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We describe in the Heisenberg anti-ferromagnet in two and three dimensional spaces non-Abelian flux states about which the low energy excitations obey the Dirac equation. A gap in the energy spectrum may be opened. These states describe spin liquids.
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Chen, Ai-Hua, and Fan-Fan Wang. "Darboux Transformation and Exact Solutions of the Continuous Heisenberg Spin Chain Equation." Zeitschrift für Naturforschung A 69, no. 1-2 (February 1, 2014): 9–16. http://dx.doi.org/10.5560/zna.2013-0067.

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In this paper, we give the N-fold Darboux transformation (DT) for the continuous Heisenberg spin chain which describes the motion of the isotropic ferromagnets in the complex case. By using this DT, we get N-soliton solutions and a new exact solution of the spin chain from a trivial seed solution and a plane wave seed solution, respectively.
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De-Gang, Zhang, and Liu Jie. "A higher-order deformed Heisenberg spin equation as an exactly solvable dynamical equation." Journal of Physics A: Mathematical and General 22, no. 2 (January 21, 1989): L53—L54. http://dx.doi.org/10.1088/0305-4470/22/2/002.

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Dissertations / Theses on the topic "Heisenberg spin equation"

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Grice, Glenn Noel Mathematics UNSW. "Constant speed flows and the nonlinear Schr??dinger equation." Awarded by:University of New South Wales. Mathematics, 2004. http://handle.unsw.edu.au/1959.4/20509.

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This thesis demonstrates how the geometric connection between the integrable Heisenberg spin equation, the nonlinear Schr??dinger equation and fluid flows with constant velocity magnitude along individual streamlines may be exploited. Specifically, we are able to construct explicitly the complete class of constant speed flows where the constant pressure surfaces constitute surfaces of revolution. This class is undoubtedly important as it contains many of the specific cases discussed earlier by other authors.
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Goomanee, Salvish. "Rigorous Approach to Quantum Integrable Models at Finite Temperature." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN039/document.

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Cette thèse développe un cadre rigoureux qui permet de démontrer des représentations exactes associées à divers observables de la chaîne XXZ de Heisenberg de spin 1/2 à température finie. Il a était argumenté dans la littérature que l’énergie libre par site ou les longueurs de corrélations admettent des représentations intégrales où les intégrandes sont exprimées en termes de solutions d’équations intégrales non-linéaires. Les dérivations de ces représentations reposaient sur divers conjectures telles que l’existence d’une valeur propre de la matrice de transfert quantique, real, non-dégénérée, de module maximale, de l’échangeabilitée de la limite du volume infinie et du nombre de Trotter à l’infinie, de l’existence et de l’unicité des solutions des equation intégrales non-linéaires auxiliaires et finalement de l’identification des valeurs propers de la matrice de transfert quantiques avec les solutions de l’équations intégrales non-linéaires. Nous démontrons toutes ces conjectures dans le regime de haute température. Nôtre analyse nous permet aussi de démontrer que pour ces température suffisamment élevées, il est possible d’avoir une description d’un certain sous-ensemble de valeurs propres sous-dominante de la matrice de transfert quantique décrite en terme de solutions d’une chaîne de spin-1 de taille finie
This thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length
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Books on the topic "Heisenberg spin equation"

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Boudreau, Joseph F., and Eric S. Swanson. Quantum spin systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0022.

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The quantum mechanical underpinnings of magnetism are explored via the Heisenberg model of antiferromagnetism. The Lanczos algorithm is developed and applied to obtain ground state properties of the anisotropic antiferromagnetic Heisenberg spin chain. In particular, the phase diagram for the system magnetization is determined. A quantum Monte Carlo method that is appropriate for discrete systems is also presented. The method leverages the similarity between the Schrödinger equation and the diffusion equation to compute energy levels. The formalism necessary to compute ground state matrix elements is also developed. Finally, the method is tested with an application to the spin chain.
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Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. The Atomistic Spin Dynamics Equation of Motion. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.003.0004.

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From the information obtained in DFT, in particular the magnetic moments and the Heisenberg exchange parameters, one has the possibility to make a connection to atomistic spin-dynamics. In this chapter the essential features of this connection is described. It is also discussed under what length and time-scales that this approach is a relevant approximation. The master equation of atomistic spin-dynamics is derived, and discussed in detail. In addition we give examples of how this equation describes the magnetization dynamics of a few model systems.
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Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. Atomistic Spin Dynamics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.001.0001.

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The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and should be used. The contents involve a description of density functional theory both from a fundamental viewpoint as well as a practical one, with several examples of how this theory can be used for the evaluation of ground state properties like spin and orbital moments, magnetic form-factors, magnetic anisotropy, Heisenberg exchange parameters, and the Gilbert damping parameter. This book also outlines how interatomic exchange interactions are relevant for the effective field used in the temporal evolution of atomistic spins. The equation of motion for atomistic spin-dynamics is derived starting from the quantum mechanical equation of motion of the spin-operator. It is shown that this lead to the atomistic Landau-Lifshitz-Gilbert equation, provided a Born-Oppenheimer-like approximation is made, where the motion of atomic spins is considered slower than that of the electrons. It is also described how finite temperature effects may enter the theory of atomistic spin-dynamics, via Langevin dynamics. Details of the practical implementation of the resulting stochastic differential equation are provided, and several examples illustrating the accuracy and importance of this method are given. Examples are given of how atomistic spin-dynamics reproduce experimental data of magnon dispersion of bulk and thin-film systems, the damping parameter, the formation of skyrmionic states, all-thermal switching motion, and ultrafast magnetization measurements.
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Book chapters on the topic "Heisenberg spin equation"

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Makhankov, V. G., A. V. Makhankov, A. T. Maksudov, and Kh Kh Muminov. "Two-Dimensional Classical Attractors in the Spin Phase Space of the S = 1 Easy-Axis Heisenberg Ferromagnet." In Nonlinear Evolution Equations and Dynamical Systems, 185–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76172-0_40.

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Eckle, Hans-Peter. "Bethe Ansatz for the Anisotropic Heisenberg Quantum Spin Chain." In Models of Quantum Matter, 502–44. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0014.

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This chapter verifies the conjecture for the wave function, the Bethe ansatz wave function, of the anisotropic Heisenberg quantum spin chain by examining first the cases for one, two, and three spin deviations. The equations determining the quasi- momenta are the Bethe ansatz equations, now obtained from the coordinate Bethe ansatz. The Bethe ansatz equations derive from the eigenvalue equation in combination with boundary conditions, here periodic boundary conditions. These quasi-momenta also determine the energy eigenvalue. However, solving the Bethe ansatz equations to obtain a particular state requires more considerations. New variables, called rapidities, are useful. The consideration of the thermodynamic limit then allows to extract information about the ground state and low-lying excitations of the anisotropic quantum spin chain from the Bethe ansatz equations. Furthermore, complex solutions of the Bethe ansatz equations, called strings, are considered.
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Eckle, Hans-Peter. "Finite Heisenberg Quantum Spin Chain." In Models of Quantum Matter, 667–86. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0020.

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The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.
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Eckle, Hans-Peter. "Thermodynamics of the Isotropic Heisenberg Quantum Spin Chain." In Models of Quantum Matter, 641–54. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0018.

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This chapter presents the extension of the Bethe ansatz to finite temperature, the thermodynamic Bethe ansatz, for the antiferromagnetic isotropic Heisenberg quantum spin chain, the XXX quantum spin chain. It discusses how the added complications of this model arise from the more complicated structure of excitations of the quantum spin chain, the complex string excitations, which have to be included in the Bethe ansatz thermodynamics. It derives the integral equations of the thermodynamic Bethe ansatz for the XXX quantum spin chain and mentions explicit formulas for the free energy of the quantum spin chain and some interesting physical quantities, especially making contact with predictions of conformal symmetry.
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Eckle, Hans-Peter. "Six-Vertex Model." In Models of Quantum Matter, 454–73. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0011.

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This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter relations, the six-vertex model is diagonalized and the Bethe ansatz equations are derived. The Hamiltonian of the Heisenberg quantum spin chain is obtained from the transfer matrix for a special value of the spectral parameter together with an infinite set of further conserved quantum operators. By the diagonalization of the transfer matrix the exact solution of the one-dimensional quantum spin chain Hamiltonian has automatically also been obtained, which is given by the same Bethe ansatz equations.
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Eckle, Hans-Peter. "Mathematical Tools." In Models of Quantum Matter, 657–66. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0019.

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Chapter 19 introduces the mathematical techniques required to extract analytic infor- mation from the Bethe ansatz equations for a Heisenberg quantum spin chain of finite length. It discusses how the Bernoulli numbers are needed as a prerequisite for the Euler– Maclaurin summation formula, which allows to transform finite sums into integrals plus, in a systematic way, corrections taking into account the finite size of the system. Applying this mathematical technique to the Bethe ansatz equations results in linear integral equations of the Wiener–Hopf type for the solution of which an elaborate mathematical technique exists, the Wiener–Hopf technique.
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Steel, Duncan G. "Two-State Systems: The Atomic Operators." In Introduction to Quantum Nanotechnology, 274–88. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895073.003.0016.

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In the digital world, the concepts of on and off or high and low or 0 and 1 are common classical two-state systems. Quantum systems can be similarly configured, as we saw in Chapter 9 with the demonstration of Rabi oscillations. Two-state or few-state systems are so important that a powerful algebra has been developed to study and explore these systems. A similar algebra emerged from the algebra developed for spin ½ particles. While Chapter 10 discussed the spinors and spin matrices and the corresponding Pauli matrices, in this chapter the corresponding commutators are determined for the various atomic operators first introduced in Chapter 15. We then move to the Heisenberg picture including the operators for the vacuum field. The Heisenberg equations of motion are derived following the rules in Chapter 8 when a classical electromagnetic field is present and then in the presence of the quantum vacuum to include the effects of decay. This provides the first means of handling the return of an excited population back to the ground state which is very challenging to deal with in the amplitude picture. This chapter is enormously important because it sets the stage for much more advanced studies in advanced texts that determine the impact of fluctuations of the field and correlations measured from single photon emitters.
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