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Journal articles on the topic 'Heisenberg spin equation'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

POPŁAWSKI, NIKODEM J. "GEOMETRIZATION OF ELECTROMAGNETISM IN TETRAD-SPIN-CONNECTION GRAVITY." Modern Physics Letters A 24, no. 06 (February 28, 2009): 431–42. http://dx.doi.org/10.1142/s0217732309030151.

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The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic fields is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational principle with the tetrad and spin connection as dynamical variables and show that, in this approach, the field equations are the Einstein–Maxwell equations if we relate the electromagnetic potential to the trace of the spin connection. We also show that, as in the Ponomarev–Obukhov formulation, the generally covariant Dirac Lagrangian gives rise to the standard spinor source for the Einstein–Maxwell equations, while the spinor field obeys the nonlinear Heisenberg–Ivanenko equation with the electromagnetic coupling. We generalize that formulation to spinors with arbitrary electric charges.

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12

Douvagai, Yaouba Amadou, Gambo Betchewe, Alphonse Houwe, Mustafa Inc, Serge Y. Doka, and Bandar Almohsen. "Dynamic behaviors for a (2 + 1)-dimensional inhomogenous Heisenberg ferromagnetic spin chain system." Modern Physics Letters B 35, no. 15 (March 19, 2021): 2150251. http://dx.doi.org/10.1142/s0217984921502511.

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We investigate a (2 + 1)-dimensional nonlinear Schrodinger equation (NLSE), which describes the spin dynamics of (2 + 1)-dimensional inhomogeneous Heisenberg ferromagnetic spin chain (IHFSC) with bilinear and anisotropic interactions in the semiclassical limit. Miscellaneous new solitons solutions are obtained through the generalized Riccati equation mapping method (GREMM). Moreover, the effects of homogeneity on the soliton propagation and interaction are discussed. The derived structure of the obtain solutions offers a rich platform to better understand the nonlinear dynamics in the ferromagnetic materials.

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13

BRACKEN, PAUL. "AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 20, no. 07 (March 20, 2005): 1503–14. http://dx.doi.org/10.1142/s0217751x0502104x.

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The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

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14

Porsezian, K., K. M. Tamizhmani, and M. Lakshmanan. "Geometrical equivalence of a deformed heisenberg spin equation and the generalized nonlinear schrödinger equation." Physics Letters A 124, no. 3 (September 1987): 159–60. http://dx.doi.org/10.1016/0375-9601(87)90243-x.

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15

Aliyu, Aliyu Isa, Yongjin Li, Mustafa Inc, Dumitru Baleanu, and Ali S. Alshomrani. "Solitons and complexitons to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model." International Journal of Modern Physics B 33, no. 30 (December 10, 2019): 1950368. http://dx.doi.org/10.1142/s0217979219503685.

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This paper investigates the ([Formula: see text])-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified [Formula: see text]-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.

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16

TANG, BING, DE-JUN LI, KE HU, and YI TANG. "INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY." International Journal of Modern Physics B 27, no. 25 (September 12, 2013): 1350139. http://dx.doi.org/10.1142/s0217979213501397.

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Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

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17

BRACKEN, PAUL. "SPIN MODEL EQUATIONS, CONNECTIONS WITH INTEGRABLE SYSTEMS AND APPLICATIONS TO MAGNETIC VORTICES." International Journal of Modern Physics B 17, no. 25 (October 10, 2003): 4525–37. http://dx.doi.org/10.1142/s0217979203023045.

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It is shown how the Landau–Lifshitz model can be related to a nonlinear Schrödinger equation. In two space dimensions, the continuous Heisenberg model and more generally, the nonlinear sigma models are described by gauged Cherns–Simons field theories.

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18

Quispel, G. R. W. "The anisotropic Heisenberg spin chain and the derivative nonlinear Schrodinger equation." Journal of Physics A: Mathematical and General 20, no. 16 (November 11, 1987): L1069—L1070. http://dx.doi.org/10.1088/0305-4470/20/16/006.

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19

Rizvi, Syed Tahir Raza, Aly R. Seadawy, Ishrat Bibi, and Muhammad Younis. "Chirped and chirp-free optical solitons for Heisenberg ferromagnetic spin chains model." Modern Physics Letters B 35, no. 08 (January 15, 2021): 2150139. http://dx.doi.org/10.1142/s0217984921501396.

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In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions.

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20

Ciftja, Orion, Marshall Luban, Mark Auslender, and James H. Luscombe. "Equation of state and spin-correlation functions of ultrasmall classical Heisenberg magnets." Physical Review B 60, no. 14 (October 1, 1999): 10122–33. http://dx.doi.org/10.1103/physrevb.60.10122.

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21

Ma, Yu-Lan, Bang-Qing Li, and Ying-Ying Fu. "A series of the solutions for the Heisenberg ferromagnetic spin chain equation." Mathematical Methods in the Applied Sciences 41, no. 9 (February 27, 2018): 3316–22. http://dx.doi.org/10.1002/mma.4818.

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22

Sulaiman, Tukur Abdulkadir, Tolga Aktürk, Hasan Bulut, and Haci Mehmet Baskonus. "Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation." Journal of Electromagnetic Waves and Applications 32, no. 9 (December 27, 2017): 1093–105. http://dx.doi.org/10.1080/09205071.2017.1417919.

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23

VAN HIEU, NGUYEN, and NGUYEN HUNG SON. "TWO-PARTICLE GREEN FUNCTIONS OF ITINERANT ELECTRONS WITH HEISENBERG MAGNETIC INTERACTION." International Journal of Modern Physics B 04, no. 15n16 (December 1990): 2307–17. http://dx.doi.org/10.1142/s0217979290001078.

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The equation in the ladder approximation was derived for the two-particle Green function of the itinerant electrons with the Heisenberg ferromagnetic and antiferromagnetic interaction. The general form of its solution was found. The existence of the pole in this solution is related to the condensation of the bound pairs in the corresponding spin state. The condition for the pole determines the critical temperature T c . The effective interaction between the mobile holes due to the mobile hole-localized spin coupling in the two-band Hubbard model was also studied.

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24

BALAKRISHNAN, RADHA. "TWO-BRANCH ENERGY OF MAGNETIC SURFACES AND CONNECTION WITH ANHOLONOMY." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 2083–91. http://dx.doi.org/10.1142/s0217979200001229.

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For general boundary conditions, we show that the energy H of a classical Heisenberg ferromagnetic spin system on a curved surface satisfies the inequality H≥|Γ|. Here Γ is a certain geometric phase or anholonomy associated with the spin vector field. This is a generalization of the well known Bogomol'nyi inequality H≥4πQ (Q=integer). For a wide variety of curved surfaces, seeking solutions with certain symmetries, we find that the variational equation δH=0 can be reduced to a sine-Gordon equation with a geometry-dependent parameter. Soliton lattice solutions of this equation are analyzed. It is shown that both H and Γ develop two branches each, all of which merge at the one-soliton limit. This branching is interpreted as a topological transition of the spin textures that occurs at the one-soliton point.

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25

Haouam, Ilyas. "The Non-Relativistic Limit of the DKP Equation in Non-Commutative Phase-Space." Symmetry 11, no. 2 (February 14, 2019): 223. http://dx.doi.org/10.3390/sym11020223.

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The non-relativistic limit of the relativistic DKP equation for both of zero and unity spin particles is studied through the canonical transformation known as the Foldy–Wouthuysen transformation, similar to that of the case of the Dirac equation for spin-1/2 particles. By considering only the non-commutativity in phases with a non-interacting fields case leads to the non-commutative Schrödinger equation; thereafter, considering the non-commutativity in phase and space with an external electromagnetic field thus leads to extract a phase-space non-commutative Schrödinger–Pauli equation; there, we examined the effect of the non-commutativity in phase-space on the non-relativistic limit of the DKP equation. However, with both Bopp–Shift linear transformation through the Heisenberg-like commutation relations, and the Moyal–Weyl product, we introduced the non-commutativity in phase and space.

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26

BOOS, H. E., V. E. KOREPIN, and F. A. SMIRNOV. "EMPTINESS FORMATION PROBABILITY AND QUANTUM KNIZHNIK-ZAMOLODCHIKOV EQUATION." International Journal of Modern Physics A 19, supp02 (May 2004): 57–81. http://dx.doi.org/10.1142/s0217751x04020312.

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We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.

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27

Radha, R., and V. Ramesh Kumar. "Gauge equivalence of the Gross–Pitaevskii equation and the equivalent Heisenberg spin chain." Physica Scripta 76, no. 5 (September 21, 2007): 431–35. http://dx.doi.org/10.1088/0031-8949/76/5/004.

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28

Bulut, Hasan, Tukur Abdulkadir Sulaiman, and Haci Mehmet Baskonus. "Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation." Superlattices and Microstructures 123 (November 2018): 12–19. http://dx.doi.org/10.1016/j.spmi.2017.12.009.

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29

Nian-ning, Huang. "A Variant form of the Takhtajan Equation for the Heisenberg Isotropic Spin Chain." Communications in Theoretical Physics 5, no. 2 (March 1986): 149–52. http://dx.doi.org/10.1088/0253-6102/5/2/149.

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30

Bakıcıerler, Gizel, Suliman Alfaqeih, and Emine Mısırlı. "Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation." Physica A: Statistical Mechanics and its Applications 582 (November 2021): 126255. http://dx.doi.org/10.1016/j.physa.2021.126255.

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31

Du, Xia-Xia, Bo Tian, Chen-Rong Zhang, and Su-Su Chen. "Nonlinear localized waves for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation." Physica Scripta 96, no. 7 (May 12, 2021): 075217. http://dx.doi.org/10.1088/1402-4896/abfd62.

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32

ALCARAZ, FRANCISCO C. "EXACT STEADY STATES OF ASYMMETRIC DIFFUSION AND TWO-SPECIES ANNIHILATION WITH BACK REACTION FROM THE GROUND STATE OF QUANTUM SPIN MODELS." International Journal of Modern Physics B 08, no. 25n26 (November 1994): 3449–61. http://dx.doi.org/10.1142/s0217979294001445.

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We calculated the exact probability distribution of the equilibrium state of some dynamical models in d-dimensional hypercubic lattices (d≥1). In these models we have asymmetric diffusion or two-species annihilation with back reaction A+B↔Ø. Our results are derived by exploring the relationship between the master equation and the Hamiltonian of quantum spins. The models we study are related to the spin-S Heisenberg model.

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33

KOLOKOLOV, I. V. "A FUNCTIONAL INTEGRATION METHOD FOR QUANTUM SPIN SYSTEMS AND ONE-DIMENSIONAL LOCALIZATION." International Journal of Modern Physics B 10, no. 18n19 (August 30, 1996): 2189–215. http://dx.doi.org/10.1142/s0217979296001008.

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A number of problems in statistical physics can be reformulated in terms of a two-state system evolving in a random field. The corresponding evolution operator can be written in the form of time-ordered operator exponential. Functional formalism allows us to rewrite the latter as a product of usual matrix exponentials using a nonlinear change of functional integration variables. In this review I present this formalism applied to two physical systems the quantum Heisenberg magnet and one-dimensional quantum mechanics in a spatially random potential. First, I derive a representation of the partition function of a quantum Heisenberg ferromagnet as a functional integral over number valued fields (a real one and a complex one) free of constraints. The fields of integration as functions of time obey initial conditions instead of the usual periodic boundary conditions. This is a manifestation of the finite-dimensionality of the space of spin states. In the subsequent sections I study the one-dimensional localization problem. The change of functional integration variables gives simultaneously explicit expressions for the averaging weight and for the Green function of the stationary Schrödinger equation. It allows to compute density correlators of arbitrary orders. The generalization to the case of different energy correlators (Berezinskii-Gor’kov equations) is considered too. In the present review such technical points as regularizations of functional integrals and transformations are discussed in more details than in the original papers.

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34

Sağlam Özkan, Yeşim. "The generalized exponential rational function and Elzaki–Adomian decomposition method for the Heisenberg ferromagnetic spin chain equation." Modern Physics Letters B 35, no. 12 (February 17, 2021): 2150200. http://dx.doi.org/10.1142/s0217984921502006.

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In this paper, the Heisenberg ferromagnetic spin chain equation, which is a model with different magnetic interactions in the classical and semiclassical limits, is investigated using the generalized exponential rational function method. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. A plurality of the exact solution is obtained by using the relevant method. Physical interpretations of some obtained solutions are also included. Particularly, upon choosing appropriate parameters, various plots are depicted. We achieve also a numerical solution corresponding to the initial value problem by the Elzaki–Adomian decomposition method and give comparative results in a table. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.

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35

Makhankov, A. V., and V. G. Makhankov. "Spin Coherent States, Holstein-Primakoff Transformations for Heisenberg Spin Chain Models, and Status of the Landau-Lifshits Equation." physica status solidi (b) 145, no. 2 (February 1, 1988): 669–78. http://dx.doi.org/10.1002/pssb.2221450233.

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36

Antipov, A. G., and I. V. Komarov. "The isotropic Heisenberg chain of arbitrary spin by direct solution of the Baxter equation." Physica D: Nonlinear Phenomena 221, no. 2 (September 2006): 101–9. http://dx.doi.org/10.1016/j.physd.2006.07.014.

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37

Lakshmanan, M. "On the higher-order deformed Heisenberg spin equation as an exactly solvable dynamical system." Journal of Physics A: Mathematical and General 22, no. 21 (November 7, 1989): 4735–36. http://dx.doi.org/10.1088/0305-4470/22/21/034.

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38

Ma, Yu-Lan. "Lump wave phase transition for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation." Optik 231 (April 2021): 166505. http://dx.doi.org/10.1016/j.ijleo.2021.166505.

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39

KUZEMSKY, A. L. "SPECTRAL PROPERTIES OF THE GENERALISED SPIN-FERMION MODELS." International Journal of Modern Physics B 13, no. 20 (August 10, 1999): 2573–605. http://dx.doi.org/10.1142/s0217979299002538.

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In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the Irreducible Green's Functions (IGF) approach. Examples are generalised d–f model and Kondo–Heisenberg model. The calculations of the quasiparticle excitation spectra with damping for these models has been performed in the framework of the equation-of-motion method for two-time temperature Green's Functions within a non-perturbative approach. A unified scheme for the construction of Generalised Mean Fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation has been generalised in order to include the presence of the two interacting subsystems of localised spins and itinerant electrons. A general procedure is given to obtain the quasiparticle damping in a self-consistent way. This approach gives the complete and compact description of quasiparticles and show the flexibility and richness of the generalised spin-fermion model concept.

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40

Peña Lara, D., J. A. Plascak, and J. Ricardo de Souza. "Multicritical Points from Mean Field Renormalization Group." International Journal of Modern Physics B 12, no. 18 (July 20, 1998): 1813–21. http://dx.doi.org/10.1142/s0217979298001046.

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The mean field renormalization group method is extended to study tri-critical phenomena. By taking into account the third-order terms in the expansion of the magnetizations of the different clusters with respect to the symmetry breaking fields, together with the scaling assumption of the magnetization at a first-order fixed point, one additional equation is obtained which locates, in an unique manner, the tricritical point. This approach is applied in the study of the classical spin-σ Blume–Capel model and the quantum spin-1/2 anisotropic Heisenberg model in the presence of a transverse field as well as with Dzyaloshinsky–Moriya interactions.

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41

Davidović, Dragomir. "Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation." Quantum 4 (September 21, 2020): 326. http://dx.doi.org/10.22331/q-2020-09-21-326.

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Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.

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42

Jia, Hui-Xian, and Dong-Ming Shan. "Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation." Zeitschrift für Naturforschung A 72, no. 11 (October 26, 2017): 1071–75. http://dx.doi.org/10.1515/zna-2017-0227.

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AbstractIn this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

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43

Deng, Lin-Fang, He-Yao Zhang, and Chao-Yun Long. "Solution of the Dirac equation with exponential-type potential under the GUP." International Journal of Modern Physics A 36, no. 01 (January 10, 2021): 2150005. http://dx.doi.org/10.1142/s0217751x21500056.

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In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

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44

Rogers, C., T. Ruggeri, and W. K. Schief. "On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200487. http://dx.doi.org/10.1098/rspa.2020.0487.

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A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction in the classical limit. In the general 3+1-dimensional case, it is demonstrated that Synge’s geometric characterization of the pressure being constant along streamlines encapsulates a three-dimensional extension of an integrable Heisenberg spin equation.

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Tuszyński, J. A., and J. M. Dixon. "A Quantum Field Theoretical Analysis of Spin-Half Metamagnetism." International Journal of Modern Physics B 11, no. 12 (May 20, 1997): 1445–62. http://dx.doi.org/10.1142/s0217979297000733.

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A number of metallic compounds such as FeRh, Mn3GaC , and FeCl2 exhibit the interesting property of metamagnetism, i.e. the presence of order–order magnetic-phase transitions. The microscopic Hamiltonian that is commonly used to describe this class of system is of Heisenberg type with competing exchange interactions between the nearest- and next-nearest neighbours. Starting from this quantum Hamiltonian, through several transformations, it is possible to obtain an effective second-quantized Hamiltonian which has a two-body interaction term. A recent method of analyzing such Hamiltonians is then applied based on exact calculations for the corresponding nonlinear equation of motion. This is followed by quantization about the classical solutions. Stability conditions imposed on the classical solutions agree with earlier results.

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de Vries, Pedro, and Hans De Raedt. "Solution of the time-dependent Schrödinger equation for two-dimensional spin-1/2 Heisenberg systems." Physical Review B 47, no. 13 (April 1, 1993): 7929–37. http://dx.doi.org/10.1103/physrevb.47.7929.

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Lado, F., E. Lomba, and J. J. Weis. "Integral equation and simulation studies of the Heisenberg spin fluid in an external magnetic field." Physical Review E 58, no. 3 (September 1, 1998): 3478–89. http://dx.doi.org/10.1103/physreve.58.3478.

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Bashar, Md Habibul, S. M. Rayhanul Islam, and Dipankar Kumar. "Construction of traveling wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation." Partial Differential Equations in Applied Mathematics 4 (December 2021): 100040. http://dx.doi.org/10.1016/j.padiff.2021.100040.

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Song, N., W. Zhang, P. Wang, and Y. K. Xue. "Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation." Journal of Function Spaces 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/6910926.

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The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.

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Onodera, Eiji. "The initial-value problem for a fourth-order dispersive closed curve flow on the 2-sphere." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 6 (August 14, 2017): 1243–77. http://dx.doi.org/10.1017/s0308210516000470.

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A closed curve flow on the 2-sphere evolved by a fourth-order nonlinear dispersive partial differential equation on the one-dimensional flat torus is studied. The governing equation arises in the field of physics in relation to the continuum limit of the Heisenberg spin chain systems or three-dimensional motion of the isolated vortex filament. The main result of the paper gives the local existence and uniqueness of a solution to the initial-value problem by overcoming loss of derivatives in the classical energy method and the absence of the local smoothing effect. The proof is based on the delicate analysis of the lower-order terms to find out the loss of derivatives and on the gauged energy method to eliminate the obstruction.

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