Journal articles: 'Ginzburg-Landau theory; Mean-field model'

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DAVIS, R. L. "SUPERFLUID FIELD THEORY." International Journal of Modern Physics A 08, no. 28 (November 10, 1993): 5005–21. http://dx.doi.org/10.1142/s0217751x9300196x.

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The very low temperature dynamics of an isotropic superfluid is derived from a repulsive bosonic field theory. The field theory is a fully dynamical generalization of the Ginzburg-Landau theory, which at zero temperature has semiclassical superfluid solutions. It is shown that supercurrent quenching occurs above some intrinsic critical velocity. The speed of first sound is calculated and the Landau criterion for a maximum superfluid velocity is derived. At finite temperature, the thermodynamic potential is computed, the order parameter and gap equations are derived, the origin of the Landau two-fluid model is identified and the thermomechanical effect is explained. This theory successfully describes many of the features of 4He well below the critical temperature, as well as relativistic generalizations.

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Bonora, L., A. A. Bytsenko, M. Chaichian, and A. E. Gonçalves. "Elliptic genera and q-series development in analysis, string theory, and N=2 superconformal field theory." International Journal of Modern Physics A 34, no. 33 (November 30, 2019): 1950226. http://dx.doi.org/10.1142/s0217751x19502269.

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In this paper, we examine the Ruelle-type spectral functions [Formula: see text], which define an overall description of the content of the work. We investigate the Gopakumar–Vafa reformulation of the string partition functions, describe the [Formula: see text] Landau–Ginzburg model in terms of Ruelle-type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in [Formula: see text] theories, construct the functional equations for [Formula: see text], and analyze the modular transformation laws for the elliptic genus of the Landau–Ginzburg model and study their properties in details.

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FUCHS, JÜRGEN, and MAXIMILIAN KREUZER. "ON THE LANDAU–GINZBURG DESCRIPTION OF $(A_1^{(1)})^{\oplus N}$ INVARIANTS." International Journal of Modern Physics A 09, no. 08 (March 30, 1994): 1287–304. http://dx.doi.org/10.1142/s0217751x94000583.

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We search for a Landau–Ginzburg interpretation of nondiagonal modular invariants of tensor products of minimal n = 2 superconformal models, looking in particular at automorphism invariants and at some exceptional cases. For the former we find a simple description as Landau–Ginzburg orbifolds, which reproduces the correct chiral rings as well as the spectra of various Gepner type models and orbifolds thereof. On the other hand, we are able to prove for one of the exceptional cases that this conformal field theory cannot be described by an orbifold of a Landau–Ginzburg model with respect to a manifest linear symmetry of its potential.

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DZHUNUSHALIEV, VLADIMIR, and DOUGLAS SINGLETON. "GINZBURG–LANDAU EQUATION FROM SU(2) GAUGE FIELD THEORY." Modern Physics Letters A 18, no. 14 (May 10, 2003): 955–65. http://dx.doi.org/10.1142/s0217732303010776.

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The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

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Tuyen, Le Thi Cam, Bui Duc Tinh, Le Minh Thu, Nguyen Quang Hoc, and Nguyen Khac Man. "Fluctuation diamagnetic susceptibility in type-II superconductors under magnetic field." International Journal of Modern Physics B 34, no. 04 (December 20, 2019): 2050007. http://dx.doi.org/10.1142/s0217979220500071.

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Strong fluctuation effects were found in both low- and high-field regimes by recent measurements of magnetization on [Formula: see text] (LCCO) single crystals. The low-field fluctuation diamagnetic susceptibility data could not be fitted by simple Gaussian fluctuation theory using the lowest Landau level (LLL) approximation because of the slightly nonlinear behavior around the mean-field transition temperature [Formula: see text]. Self-consistent calculation of fluctuation diamagnetic susceptibility in high-temperature superconductors, based on the Ginzburg–Landau (GL) two-dimensional model and including all Landau levels, is presented. Our results are valid for arbitrary values of the magnetic field not too close to [Formula: see text]. The results agree well with the experimental data in a wide region around [Formula: see text], including both below and above [Formula: see text].

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Lim, Kok Geng, Khian Hooi Chew, Lye Hock Ong, and Makoto Iwata. "Recent Advances in Application of Landau-Ginzburg Theory for Ferroelectric Superlattices." Solid State Phenomena 232 (June 2015): 169–95. http://dx.doi.org/10.4028/www.scientific.net/ssp.232.169.

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Ferroelectric superlattices with polarization perpendicular to the surface or interface are studied within the framework of the Landau-Ginzburg theory. An interface energy is introduced in the free energy to describe the effect of mixing and local polarization coupling at interface. Internal electric field is considered in the model. For superlattices grown on substrate, the influence of substrate on the properties of ferroelectric superlattices is required. This brief review is a sequel to the previous review article [1], which summarizes the recent development in Landau-Ginzburg theory developed for studying ferroelectric superlattices over approximately the last three years.

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Contreras, Andres, and Xavier Lamy. "Persistence of superconductivity in thin shells beyond Hc1." Communications in Contemporary Mathematics 18, no. 04 (May 3, 2016): 1550047. http://dx.doi.org/10.1142/s0219199715500479.

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In Ginzburg–Landau theory, a strong magnetic field is responsible for the breakdown of superconductivity. This work is concerned with the identification of the region where superconductivity persists, in a thin shell superconductor modeled by a compact surface [Formula: see text], as the intensity [Formula: see text] of the external magnetic field is raised above [Formula: see text]. Using a mean field reduction approach devised by Sandier and Serfaty as the Ginzburg–Landau parameter [Formula: see text] goes to infinity, we are led to studying a two-sided obstacle problem. We show that superconductivity survives in a neighborhood of size [Formula: see text] of the zero locus of the normal component [Formula: see text] of the field. We also describe intermediate regimes, focusing first on a symmetric model problem. In the general case, we prove that a striking phenomenon we call freezing of the boundary takes place: one component of the superconductivity region is insensitive to small changes in the field.

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DI GREZIA, ELISABETTA, SALVATORE ESPOSITO, and ADELE NADDEO. "QUANTUM PHASE EXCITATIONS IN GINZBURG–LANDAU SUPERCONDUCTORS." International Journal of Modern Physics B 20, no. 06 (March 10, 2006): 737–45. http://dx.doi.org/10.1142/s021797920603353x.

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We give a straightforward generalization of the Ginzburg–Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb–Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity. A physical scenario behind the model proposed, which can be directly tested by experiments, is envisaged.

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DZHUNUSHALIEV, VLADIMIR, DOUGLAS SINGLETON, and DANNY DHOKARH. "Effective Abelian-Higgs Theory from SU(2) gauge field theory." International Journal of Modern Physics A 20, no. 15 (June 20, 2005): 3481–87. http://dx.doi.org/10.1142/s0217751x05026807.

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In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU (2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

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BULAEVSKII, L. N. "MACROSCOPICAL THEORY OF LAYERED SUPERCONDUCTORS." International Journal of Modern Physics B 04, no. 11n12 (September 1990): 1849–77. http://dx.doi.org/10.1142/s0217979290000905.

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The macroscopical Ginzburg-Landau models with effective-mass tensor and Josephson coupling of the layers are used to describe the magnetic properties of layered superconductors (dichalcogenides of transition metals and intercalated compounds, organic superconductors and high-Tc copper oxide compounds). In the framework of such models the magnetic critical fields, Abrikosov lattice, torque, Josephson oscillations, Gaussian fluctuations are considered and the validity of mean field theory in the model with Josephson coupling is discussed. The layeredcompounds with different superconducting layers are also studied including the dependence of critical temperature on the strength of coupling and temperature dependence of magnetic anisotropy. The experimental data of high-Tc superconductors are discussed to show that in Bi- and Tl-compounds the conditions of Josephson coupling of layers is fulfilled.

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Calza, T. C. A., F. L. Cardoso, L. G. Cardoso, and C. A. Linhares. "Compatibility between the Ginzburg–Landau model and finite-temperature quantum field theory." Modern Physics Letters A 31, no. 40 (December 6, 2016): 1650227. http://dx.doi.org/10.1142/s0217732316502278.

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The formalism of finite-temperature quantum field theory, as developed by Matsubara, is applied to a Hamiltonian of N scalar fields with a quartic self-interaction at large N. A renormalized expression in the lowest quantum approximation is obtained for the squared mass m2 of the field, as a function of the temperature T, from which we study the process of spontaneous symmetry breaking. We find that in a range of values around the critical temperature Tc, the squared mass can be approximated by a linear relation m2 [Formula: see text] (T − Tc). We thus demonstrate the compatibility of the finite-temperature formalism for scalar fields, in the vicinity of criticality, with respect to the Ginzburg–Landau model. We also discuss the effects caused by the presence of a chemical potential and of an external magnetic field applied to the finite-temperature system, which however do not affect the linearity of the relation between the squared mass and the temperature.

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BERGLUND, PER, BRIAN GREENE, and TRISTAN HÜBSCH. "CLASSICAL VS. LANDAU-GINZBURG GEOMETRY OF COMPACTIFICATION." Modern Physics Letters A 07, no. 20 (June 28, 1992): 1855–69. http://dx.doi.org/10.1142/s0217732392001567.

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We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis based on exact and spectral sequences. General arguments ensure that the Landau-Ginzburg chiral ring copes with such a situation by having a non-trivial contribution from twisted sectors. Beyond the expected final agreement between the mathematical and physical approaches, we find a direct correspondence between the analysis of each, thus giving a more complete mathematical understanding of twisted sectors. Furthermore, this approach shows that physical reasoning based upon spectral flow arguments for determining the spectrum of Landau-Ginzburg orbifold models finds direct mathematical justification in Koszul complex calculations and also that careful point-field analysis continues to recover surprisingly much of the stringy features.

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BINDER, KURT, SUBIR K. DAS, and JÜRGEN HORBACH. "SURFACE-DIRECTED SPINODAL DECOMPOSITION: LATTICE MODEL VERSUS GINZBURG–LANDAU THEORY." Modern Physics Letters B 23, no. 04 (February 10, 2009): 549–65. http://dx.doi.org/10.1142/s0217984909018886.

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When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglected (true for the late stages of phase separation). In contrast, a local kinetic molecular field theory can take full account of nonlinearities and of rapid concentration variations, and thus has a much wider validity. This enables the detailed study of phase separation processes in thin films of solid binary alloys. However, the extension to spinodal decomposition in fluid binary systems (which can be simulated by brute force large scale molecular dynamics methods, of course) remains an unsolved challenge.

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DI GREZIA, E., S. ESPOSITO, and G. SALESI. "A GENERALIZATION OF THE GINZBURG–LANDAU THEORY TO p-WAVE SUPERCONDUCTORS." Modern Physics Letters B 22, no. 18 (July 20, 2008): 1709–16. http://dx.doi.org/10.1142/s0217984908016406.

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We succeed in building up a straightforward theoretical model for spin-triplet p-wave superconductors, by introducing a second-order parameter and a nonlinear interaction between the two mean fields in the Ginzburg–Landau theory. Such interaction breaks the isotropy of the original medium and allows pairs of electrons to arrange into S = 1 Cooper pairs. The present model predicts a thermodynamical and magnetic behavior analogous to that observed in conventional s-wave superconductors.

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Matsui, Tetsuo. "U(1) Gauge Theory as a Collective Field Theory for Hubbard Model." International Journal of Modern Physics B 02, no. 05 (October 1988): 613–23. http://dx.doi.org/10.1142/s0217979288000433.

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I construct a collective field theory for Hubbard model of high Tc superconductivity, using a path-integral method in the third quantized (slave boson) form. It is a U(1) gauge invariant theory consisting of a U(1) gauge field and a Higgs scalar. The gauge field stands for resonating valence bonds and describes a (short range) antiferro-paramagnet phase transition by a condensation machanism. The Higgs scalar represents spinless holes carrying electric charges. Through the confining gauge force, there formed bounded hole pairs on each link, which correspond to the vector mesons in lattice QCD. A superconducting phase is to be described by a condensation of a gauge invariant order parameter for these hole pairs, and to be compared with the color confining chirally broken phase in QCD. A Ginzburg-Landau theory for the vector hole-pair field is proposed.

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Ding, Heng Min, and Lv Chun Pu. "Thermal Kinetics Phase Field Model for the Metals' Solidification - Mathematic Derivation of the Dendrite Growth Phase Field Variable Diffusion Model." Applied Mechanics and Materials 364 (August 2013): 614–18. http://dx.doi.org/10.4028/www.scientific.net/amm.364.614.

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Phase field equations for simulation of dendritic growth have a history of nearly twenty years. The existing phase field equations are directly derived through the Ginzburg-Landau equations. However, though widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. In this paper, with the solid fraction as a phase field variables in the field, based on thermodynamics and heat transfer theory, author gives a rigorous scientific phase variable diffusion model of the pure metal solidification and its derivation process.

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MUKAIDA, HISAMITSU, and YOSHINORI SAKAMOTO. "RENORMALIZATION GROUP FOR THE PROBABILITY DISTRIBUTION OF MAGNETIC IMPURITIES IN A RANDOM-FIELD ϕ4 MODEL." International Journal of Modern Physics B 18, no. 06 (March 10, 2004): 919–48. http://dx.doi.org/10.1142/s021797920402446x.

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Extending the usual Ginzburg–Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New parameters corresponding to the extra ϕ4 coupling constants in the replica Hamiltonian are introduced. Although they do not affect the critical phenomena near the upper critical dimension, they can when dimensions are lowered.

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Balatsky, Alexander. "Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory." International Journal of Modern Physics B 06, no. 05n06 (March 1992): 765–88. http://dx.doi.org/10.1142/s0217979292000463.

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In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-½ semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-½ semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to SU(2)k=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of “spin rigidity” of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacements. We argue that topological structure of SU(2)k=1 Chern-Simons theory unambiguously dictates semion statistics of spinons.

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HUANG, HAI. "FIELD-THEORETICAL CALCULATIONS ON THE HALDANE GAP OF QUASI-ONE-DIMENSIONAL HEISENBERG ANTIFERROMAGNETS." International Journal of Modern Physics B 23, no. 31 (December 20, 2009): 5789–800. http://dx.doi.org/10.1142/s0217979209053898.

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One-dimensional Heisenberg antiferromagnets can be described by the O (3) nonlinear σ-model (NLσM). We give a review on zero temperature and finite temperature Haldane gaps obtained from this model. Based on the coupled-chain theory, we derive the finite temperature Haldane gap for triangular antiferromagnet RbNiCl 3. The Néel temperature is obtained as 11 K. In order to treat the anisotropy in crystal Ni ( C 2 H 8 N 2)2 NO 2( ClO 4), we relax the constraint of the NLσM and compute the finite temperature Haldane gap using a Ginzburg–Landau mean field approach. The comparison with the experimental data is discussed.

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WANG, L., H. S. LIM, and C. K. ONG. "DETERMINATIONS OF UPPER CRITICAL FIELDS IN CONTINUOUS GINZBURG–LANDAU MODEL." International Journal of Modern Physics C 15, no. 06 (July 2004): 783–807. http://dx.doi.org/10.1142/s0129183104006297.

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Novel procedures to determine the parallel upper critical field Bc2 (one-dimensional, 1D) have been proposed within a continuous Ginzburg–Landau model. Unlike conventional methods, where Bc2 is obtained through the determination of the smallest eigenvalue of an appropriate eigen equation, the square of the magnetic field is treated as eigenvalue problems by two procedures so that the upper critical field can be directly deduced. The two procedures proposed are extended to determine the upper critical field in the c–a crystal plane (two-dimensional, 2D) with an arbitrary angle θ tilted from the c-axis. The calculated Bc2 from the two procedures are consistent with each other in both 1D and 2D cases. Moreover, the values of Bc2 near the direction parallel to the layers obtained in the 2D case well approximate the counterparts in the 1D case. The properties of the calculated Bc2 are in reasonably good agreement with existing theories and experiments. The profiles of the order parameters associated with Bc2 for both 1D and 2D cases are Gaussian-like, further validating the methodology proposed.

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Huo, Fei, and Ji Wei Zhao. "Phase-Field Simulation of Interface Effect during Grain Nucleation." Advanced Materials Research 490-495 (March 2012): 3339–43. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.3339.

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In this paper, a phase field model based on Ginzburg-Landau theory is used to analyze the topological phenomena during grain growth. The simulation results show that two topological transformations exist during the grain growth—Neighbor Switching and Grain Annihilation; and we have found different kinds of topological events during the disappearance of a grain: direct vanishing of trilateral grain and pentagonal grain, as well as neighbor switching，which are right with classical topological theory and Euler formula. The simulation results are similar with experiments.

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KIOMETZIS, MICHAEL, and ADRIAAN M. J. SCHAKEL. "LANDAU DESCRIPTION OF THE SUPERCONDUCTING PHASE TRANSITION." International Journal of Modern Physics B 07, no. 25 (November 15, 1993): 4271–88. http://dx.doi.org/10.1142/s0217979293003668.

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Focusing on an order parameter that signals the breakdown of a global symmetry, we employ a dual formulation of the Ginzburg-Landau model to obtain a Landau description of the phase transition of three-dimensional type-II superconductors at zero magnetic field. In the superconducting phase the dual theory is a complex |ψ|4 theory interacting via a shielded Coulomb potential mediated by a massive vector mode which may be pictured as representing the magnetic field. In the normal, high-temperature phase the vector mode decouples and the theory reduces to a pure |ψ|4 theory with a broken global U(1) symmetry. The resulting massless Goldstone mode represents the photon. The phase transition between the two phases is continuous with critical exponents given by those of a superfluid with reversed temperature axis.

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Xiang, Xingfei. "Radially symmetric solutions for a limiting form of the Ginzburg—Landau model." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143, no. 1 (January 30, 2013): 185–203. http://dx.doi.org/10.1017/s0308210511000825.

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We obtain a solution, the L∞-norm of which is greater than ⅓√3, to the semilinear system arising in the mathematical theory of superconductivity when the domain is a disc or the exterior of a disc in ℝ2. We obtain an estimate of the critical field for the arbitrary penetration depth and determine the critical field as the penetration depth goes to zero when the domain is a disc. We prove that the L∞-norm of the symmetric solutions on the inner boundary is greater than that of the outer boundary when the domain Ω is an annulus. Stability of the solutions is also studied.

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Gil, Mariusz, and Stanisław Wędrychowicz. "Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/692879.

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We study the existence of mild solutions to the time-dependent Ginzburg-Landau ((TDGL), for short) equations on an unbounded interval. The rapidity of the growth of those solutions is characterized. We investigate the local and global attractivity of solutions of TDGL equations and we describe their asymptotic behaviour. The TDGL equations model the state of a superconducting sample in a magnetic field near critical temperature. This paper is based on the theory of Banach space, Fréchet space, and Sobolew space.

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Askerzade, I. "Specific heat jump of two-band superconductor KFe2As2 using Ginzburg-Landau theory." Materials Science-Poland 32, no. 3 (September 1, 2014): 465–69. http://dx.doi.org/10.2478/s13536-014-0212-2.

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AbstractIn this study specific heat jump using two-gap Ginzburg-Landau (GL) theory has been calculated. In contrast to the previous approaches, we have taken into account intergradient order parameters interaction in the GL free energy functional. The thermodynamic magnetic field revealed nonlinear temperature dependence due to interband interaction between order parameters and their gradients. The calculations showed that the specific heat jump in two-order parameter superconductors was smaller than that of single-order parameter superconductors. It has been shown that such a model is in good agreement with experimental data for KFe2As2 superconductors.

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Askerzade, I. N., and R. T. Tagiyeva Askerbeyli. "Fluctuation conductivity in two-band superconductor SmFeAsO0.8F0.2." Materials Science-Poland 33, no. 3 (September 1, 2015): 644–48. http://dx.doi.org/10.1515/msp-2015-0060.

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Abstract In this study we have calculated the fluctuation conductivity near critical temperature of SmFeAsO0.8F0.2 superconductor using two-band Ginzburg-Landau theory. It was illustrated that in the absence of external magnetic field, the two-band model reduced to a single effective band theory with modified temperature dependences. The calculations revealed three-dimensional character of fluctuations of conductivity in the new Fe-based superconductor SmFeAsO0.8F0.2. It has been shown that such a model is in good agreement with experimental data for this compound.

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Alavi, S. A., and V. Dehghani. "Back shifted Fermi gas model with temperature dependent pairing energy: Thermal properties of 98Mo." International Journal of Modern Physics E 25, no. 09 (September 2016): 1650065. http://dx.doi.org/10.1142/s0218301316500658.

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The effect of using a temperature dependent pairing term in back-shifted Fermi-gas (BSFG) formula of nuclear level density has been studied. We have used the mean order parameter formula of modified Ginzburg–Landau (MGL) theory as a simple possible choice for temperature dependency of the pairing term. The level density and heat capacity of [Formula: see text]Mo have been calculated with this formalism and compared with the experimental data. We observed good agreement between the heat capacity of this model and the experimental data.

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WANG, JIE, and TONG-YI ZHANG. "PHASE FIELD STUDY OF POLARIZATION VORTEX IN FERROELECTRIC NANOSTRUCTURES." Journal of Advanced Dielectrics 02, no. 02 (April 2012): 1241002. http://dx.doi.org/10.1142/s2010135x12410020.

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Ferroelectric nanostructures are attracting considerable attention due to their unusual physical properties and potential applications in memory devices and nanoelectromechanical systems. It has been found that low-dimensional ferroelectrics, such as ferroelectric nanodots, ferroelectric nanotubes and ferroelectric thin films, exhibit polarization vortices or vortex-like domain structures due to the strong depolarization field and the size effect. The polarization vortex is regarded as a new toroidal order in ferroelectrics which is different from the rectilinear order of polarization. The vortex states of polarization are bistable and can be switched from one state to the other, which holds the potential application in next generation ferroelectric memories. This paper briefly reviews the recent work on the phase field studies of polarization vortex in ferroelectric nanostructures. The homogeneous bulk thermodynamics of ferroelectrics is first introduced based on the Landau–Devonshire theory. To describe the inhomogeneous polarization distribution in ferroelectrics, the phase field model including interface thermodynamics is then presented in the form of time-dependent Ginzburg–Landau equations.

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Chen, Hui, and Tai Min Cheng. "Phenomenological Model for Pyroelectric Effects of Nano Graded Ferroelectric Films." Applied Mechanics and Materials 110-116 (October 2011): 3358–63. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.3358.

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In order to improve the pyroelectric properties of nanograded ferroelectric films (NGFF), and provide a theoretical reference for practical applications, the generalized Ginzburg-Landau-Denvonshire (GLD) theory is adopted to investigate the pyroelectric properties of the NGFF. A function is introduced to characterize the local structure in nanograded films. Influence of the local structure, film thickness and external electric field on the polarization distribution and pyroelectric properties are mainly discussed. The numerical results show that parameterand film thickness are two very important factors that influence the film properties, larger values lead to smaller spontaneous polarization and lower pyroelectric peak. Different directions of the external electric field can lead to greatly different effects on pyroelectric behaviors, whose effects is to expand the working temperature region, or else, change the order of phase transition.

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Higgs, Peter. "My Life as a Boson: The Story of "The Higgs"." Asia Pacific Physics Newsletter 01, no. 02 (September 2012): 50–51. http://dx.doi.org/10.1142/s2251158x12000264.

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The story begins in 1960, when Nambu, inspired by the BCS theory of superconductivity, formulated chirally invariant relativistic models of interacting massless fermions in which spontaneous symmetry breaking generates fermionic masses (the analogue of the BCS gap). Around the same time Jeffrey Goldstone discussed spontaneous symmetry breaking in models containing elementary scalar fields (as in Ginzburg-Landau theory). I became interested in the problem of how to avoid a feature of both kinds of model, which seemed to preclude their relevance to the real world, namely the existence in the spectrum of massless spin-zero bosons (Goldstone bosons). By 1962 this feature of relativistic field theories had become the subject of the Goldstone theorem.

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Ichinose, Ikuo, and Tetsuo Matsui. "A New Approach to the Dynamics of Holes and Spins." International Journal of Modern Physics B 05, no. 01n02 (January 1991): 191–206. http://dx.doi.org/10.1142/s0217979291000134.

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We briefly review our recent approach towards the physics of the Hubbard t-J model. It is characterized by (i) path-integral quantization of electrons in the slave boson and fermion representation, (ii) integration over spin degrees of freedom on the odd lattice sites around the short-range antiferromagnetic order, and (iii) introduction of auxiliary collective field describing the hole pairs on nearest-neighbour links as an order parameter of superconductivity. The results obtained so far include (A) derivation of the CP1+ Dirac-fermion theory as the low-energy effective field theory in the superconducting state, (B) derivation of the U(1) lattice gauge theory with Higgs coupling as the Ginzburg-Landau theory of hole pairs, and (C) some discussions on the phase structure based on the nonlinear sigma model renormalized by holes and the solvable one-pair model.

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DAVIS, R. L. "SPINNING VORTICES IN TYPE II SUPERCONDUCTORS." Modern Physics Letters A 05, no. 12 (May 20, 1990): 955–63. http://dx.doi.org/10.1142/s0217732390001062.

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A field-theoretical model displaying macroscopic type II superconductivity involves electromagnetic and antisymmetric tensor gauge fields interacting in a special background. Vortex lines are represented by Kalb-Ramond strings, and the force law for a vortex in a supercurrent follows naturally. It is shown by a duality transformation that this theory is equivalent to the low-energy sector of a spontaneously broken abelian Higgs model, but the existence of a charged background changes the nature of the symmetry breaking. As a result, it is not Neilsen-Olesen solutions but rather the spinning vortices which describe the macroscopic properties of flux tubes in a superconductor. The relationship with Ginzburg-Landau theory is briefly discussed.

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XIE, X. C., H. A. FERTIG, and S. DAS SARMA. "THEORY OF PAIRING IN THE ANYON MODEL." Modern Physics Letters B 04, no. 20 (November 10, 1990): 1265–71. http://dx.doi.org/10.1142/s0217984990001598.

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We study the semion pairing problem in the fermion representation by considering a semion as a fermion with a flux tube of ϕ=ϕ0/2. We solve analytically the problem of a pair of semions in a semion gas by treating the rest of the semions in the mean field approximation. We find that a bound pair forms that consists of two fermions from the two lowest Landau levels and a flux tube with ϕ=ϕ0.

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Lu, Jun-Wang, Ya-Bo Wu, Jian Xiao, Cui-Juan Lu, and Mo-Lin Liu. "Holographic superconductors in IR modified Hořava–Lifshitz gravity." International Journal of Modern Physics A 31, no. 19 (July 7, 2016): 1650110. http://dx.doi.org/10.1142/s0217751x16501104.

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In the probe limit, we study the holographic [Formula: see text]- and [Formula: see text]-wave superconductors in the IR modified Hořava–Lifshitz gravity and obtain the effect of the gravity parameter [Formula: see text] on the condensate and the AC conductivity. Concretely, for the two models, the increasing [Formula: see text] makes the superconductor phase transition more difficult. Moreover, at the critical point, both systems undergo a second-order phase transition as expected from the mean field theory, and the superfluid density decreases with the temperature linearly, which is consistent with the Ginzburg–Landau theory. Meanwhile, the analytical results back up the numerical results. What is more, in the superconducting phase, the ratio of the energy gap to the critical temperature, i.e. [Formula: see text], decreases with the increasing [Formula: see text]. In addition, our results generalize the previous work on holographic superconductors in Hořava–Lifshitz gravity to some extent.

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MIAO, BING. "ON THE STRUCTURE OF STATISTICAL FIELD THEORY OF POLYMERS." International Journal of Modern Physics B 27, no. 07 (March 10, 2013): 1361009. http://dx.doi.org/10.1142/s0217979213610092.

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We examine several widely used statistical field theoretic methods in theoretical polymer physics. A systematic derivation for the polymer field theoretic model is given within the framework of the effective Landau theory. After constructing the field theoretic model, we perform a perturbative expansion of the model, and then the mean-field approximation and the Gaussian fluctuation approximation are introduced into the treatment of the model in order. We also outline a derivation for the self-consistent Hartree theory in polymer physics within a variational scheme. The applications of these methods are also discussed accordingly.

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Dhote, Rakesh, Hector Gomez, Roderick Melnik, and Jean Zu. "Phase Field Dynamic Modelling of Shape Memory Alloys Based on Isogeometric Analysis." Advances in Science and Technology 78 (September 2012): 63–68. http://dx.doi.org/10.4028/www.scientific.net/ast.78.63.

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Shape Memory Alloys (SMAs) exhibit complex behaviors as a result of their constituent phases and microstructure evolution. In this paper, we focus on the numerical simulations of microstructure evolution in SMAs using a phase-field model for the two dimensional square-to-rectangular martensitic phase transformations. The phase-field model, based on the Ginzburg-Landau theory, has strong non-linearity, thermo-mechanical coupling, and higher-order differential terms and presents substantial challenges for numerical simulations. The isogeometric analysis, developed in this paper using the rich NURBS basis functions, offers several advantages in solving such complex problems with higher-order partial differential equations as the problem at hand. To our best knowledge, we report here for the first time the use of the new method in the study of microstructure evolution in SMAs. The numerical experiments of microstructure evolution have been carried out on the FePd SMA specimen. The results are in good agreement with those previously reported in the literature.

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PATIL, D. V., K. N. PREMNATH, D. DESAI, and SANJOY BANERJEE. "ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH." International Journal of Modern Physics C 25, no. 01 (December 2, 2013): 1340018. http://dx.doi.org/10.1142/s0129183113400184.

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In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO 4 solution.

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Curecheriu, Lavinia-Petronela. "Tunability modeling and experiments for BaTiO3-based solid solutions." Processing and Application of Ceramics 1, no. 1-2 (2007): 23–27. http://dx.doi.org/10.2298/pac0702023c.

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In this paper, the electric field dependence of the dielectric constant in some BaTiO3-based ferroelectrics is theoretically described by means of the Landau-Ginzburg-Devonshire (LGD) theory and its? approximations valid for low polarizations (Johnson?s equation and even-power relation) when the sample is in its ferroelectric state and by a model considering random non-interacting dipolar units in a double well potential for the paraelectric state. High-voltage tunability data were obtained at room temperature for BaZr0.10Ti0.90O3 and Ba0.70Sr0.30TiO3 ceramics. The data were well fitted by using the Johnson?s approximation for the ferroelectric-relaxor BaZr0.10Ti0.90 O3 and satisfactory for the Ba0.70Sr0.30TiO3 ceramics, close to its ferro-para phase transition. For the last one, the non-interacting dipolar units model allows to determine the average dipolar moment.

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39

Modanese, Giovanni. "Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current." Mathematics 6, no. 9 (September 4, 2018): 155. http://dx.doi.org/10.3390/math6090155.

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In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein–Gordon wavefunctions, as special cases; and in turn for non-relativistic quantum field theory and for the Schrödinger and Ginzburg–Landau equations, regarded as low energy limits. Quantum mechanics, however, is wider than quantum field theory, as an effective model of reality. For instance, fractional quantum mechanics and Schrödinger equations with non-local terms have been successfully employed in several applications. The non-locality of these formalisms is strictly related to the problem of time in quantum mechanics. We explicitly compute, for continuum wave packets, the terms of the fractional Schrödinger equation and the non-local Schrödinger equation by Lenzi et al. that break local current conservation. Additionally, we discuss the physical significance of these terms. The results are especially relevant for the electromagnetic coupling of these wavefunctions. A connection with the non-local Gorkov equation for superconductors and their proximity effect is also outlined.

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Fabrizio, M., B. Lazzari, and A. Morro. "Thermodynamics of Nonlocal Electromagnetism and Superconductivity." Mathematical Models and Methods in Applied Sciences 13, no. 07 (July 2003): 945–69. http://dx.doi.org/10.1142/s0218202503002787.

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This paper provides a thermodynamic theory, of electromagnetic undeformable media, which incorporates nonlocal effects. The laws of thermodynamics are taken to keep their standard form when applied to a whole body. If a sub-body is involved, then an additional term is allowed which accounts for possible fluxes of energy and entropy due to exchanges between the sub-body and the remaining part of the body. The divergence of such fluxes plays the role of localization residual. Next superconductivity is framed within the nonlocal theory. The nondissipativity of the theory follows without requiring any ad hoc condition. Also, the Ginzburg–Landau theory is considered as a model of phase transition. The pertinent equations are shown to be given by a free energy function of the magnetic field and of the modulus of a standard complex parameter. This approach has the advantage that the theory is apparently gauge-invariant. Further, as a generalization, the theory for time-dependent fields is elaborated.

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WOJTCZAK, L., and J. H. RUTKOWSKI. "MODIFIED VAN DER WAALS MODEL FOR SURFACE-MELTING DISCUSSION." Surface Review and Letters 02, no. 06 (December 1995): 773–85. http://dx.doi.org/10.1142/s0218625x95000704.

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The thermodynamic potential governing the surface-melting, considered in terms of the crystallinity and its profile is related to the Gibbs free-energy functional, leads to van der Waals equation of state. The presented construction allows us to determine the mean-field coefficients by their reference to material constants. The model is applied to the surface-melting discussion within the Landau-type mean-field theory of phase-transitions. In particular, the surface-melting temperature is estimated and temperature dependence of the surface liquid-like layer thickness profile is obtained.

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Guo, Hong, Fu-Wen Shu, Jing-He Chen, Hui Li, and Ze Yu. "A holographic model of d-wave superconductor vortices with Lifshitz scaling." International Journal of Modern Physics D 25, no. 02 (February 2016): 1650021. http://dx.doi.org/10.1142/s0218271816500218.

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We study analytically the [Formula: see text]-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results imply that holographic [Formula: see text]-wave superconductor is indeed a type II one even for different Lifshitz scaling. This is the same as the conventional [Formula: see text]-wave superconductors in the Ginzburg–Landau (GL) theory. Our results also indicates that the dynamical exponent [Formula: see text] cannot affect the droplet solutions, and the vortex lattice solutions receive its effects only in the radial part. This naively implies that it does not have direct influence on the shape of vortex lattice even after the higher-order corrections are taken into consideration (away from the phase transition point [Formula: see text]). However, it has effects on the upper critical magnetic field [Formula: see text] through the fact that a larger [Formula: see text] results in a smaller [Formula: see text] and therefore influences the size (characterized by [Formula: see text]) of the vortex lattices. Furthermore, close comparisons between our results and those of the GL theory reveal the fact that the upper critical magnetic field [Formula: see text] is inversely proportional to the square of the superconducting coherence length [Formula: see text], regardless of the anisotropy between space and time.

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Kushnir, Vasiliy N., Serghej L. Prischepa, Michela Trezza, Carla Cirillo, and Carmine Attanasio. "Superconducting Order Parameter Nucleation and Critical Currents in the Presence of Weak Stray Fields in Superconductor/Insulator/Ferromagnet Hybrids." Coatings 11, no. 5 (April 25, 2021): 507. http://dx.doi.org/10.3390/coatings11050507.

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The stray fields produced by ferromagnetic layers in Superconductor/Insulator/Ferromagnet (S/I/F) heterostructures may strongly influence their superconducting properties. Suitable magnetic configurations can be exploited to manipulate the main parameters of the hybrids. Here, the nucleation of the superconducting phase in an external magnetic field that periodically oscillates along the film width is studied on the base of the numerical solution of the linearized system of Usadel equations. In addition, the effect of the magnetic configuration of the F-layer on the temperature dependence of the critical current density, Jc(T), is investigated in the framework of the Ginzburg–Landau phenomenological theory on the base of the oscillating model of a stray field. By following this approach, the Jc(T) dependence of a Nb/SiO2/PdNi trilayer is reproduced for different magnetic configurations of the PdNi layer.

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YONEYA, TAMIAKI. "ACTION PRINCIPLE, VIRASORO STRUCTURE AND ANALYTICITY IN NONPERTURBATIVE TWO-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 07, no. 17 (July 10, 1992): 4015–38. http://dx.doi.org/10.1142/s0217751x92001794.

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The consequences of symmetry properties of a previously proposed action principle which describes the theory space of two-dimensional gravity are investigated. The string equation corresponding to the double scaling limit of the one-matrix model with general polynomial potential is expressed as a bilinear equation for the τ function of the KP hierarchy. The Virasoro condition for the τ function is then shown to be a Ward-like identity derived from the string equation corresponding to a conformal symmetry of the action principle. The possibility of a Ginzburg-Landau type integral representation of the τ function as a version of noncritical closed string field theory in less-than-one-dimensional space-time is discussed. Finally, the role of analyticity with respect to the eigenvalue of the puncture operator in interpreting the action principle is emphasized.

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Ichinose, Ikuo, and Tetsuo Matsui. "Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example." Modern Physics Letters B 28, no. 22 (August 30, 2014): 1430012. http://dx.doi.org/10.1142/s0217984914300129.

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Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory (LGT) developed in high-energy physics is quite a useful tool to understand physics of these systems. Knowledge of LGT is to become a necessary item even for condensed matter physicists. In the first part of this paper, we present a concise review of LGT for the reader who wants to understand its basics for the first time. For illustration, we choose the Abelian Higgs model, a typical and quite useful LGT, which is the lattice version of the Ginzburg–Landau model interacting with a U(1) gauge field (vector potential). In the second part, we present an account of the recent progress in the study of ferromagnetic superconductivity (SC) as an example of application of LGT to topics in condensed matter physics. As the ferromagnetism (FM) and SC are competing orders with each other, large fluctuations are expected to take place and therefore nonperturbative methods are required for theoretical investigation. After we introduce a LGT describing the FMSC, we study its phase diagram and topological excitations (vortices of Cooper pairs) by Monte Carlo simulations.

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KAWAKATSU, T., M. DOI, and R. HASEGAWA. "DYNAMIC DENSITY FUNCTIONAL APPROACH TO PHASE SEPARATION DYNAMICS OF POLYMER SYSTEMS." International Journal of Modern Physics C 10, no. 08 (December 1999): 1531–40. http://dx.doi.org/10.1142/s0129183199001315.

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Slow dynamics of complex domain structures in phase separating polymer systems is investigated with the use of the self-consistent field (SCF) dynamic density functional (DDF) technique where the free energy of the system is calculated using the path integral formalism of the polymer chain conformation. We apply this technique to micellization of block copolymers and to phase separation of polymer blends containing block copolymers as a compatibilizer. In order to study the late stage of the phase separation processes more efficiently, we adopt the so-called Ginzburg–Landau approach, where a phenomenological model free energy functional is used. Numerical results of this approach is quantitatively compared with the results of the SCF approach.

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Li, Jing, Tingting Quan, Wei Zhang, and Wei Deng. "The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/841891.

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The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be aZ2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given.

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Hoffmann, Michael, Prasanna Venkatesan Ravindran, and Asif Islam Khan. "Why Do Ferroelectrics Exhibit Negative Capacitance?" Materials 12, no. 22 (November 13, 2019): 3743. http://dx.doi.org/10.3390/ma12223743.

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The Landau theory of phase transitions predicts the presence of a negative capacitance in ferroelectric materials based on a mean-field approach. While recent experimental results confirm this prediction, the microscopic origin of negative capacitance in ferroelectrics is often debated. This study provides a simple, physical explanation of the negative capacitance phenomenon—i.e., ‘S’-shaped polarization vs. electric field curve—without having to invoke the Landau phenomenology. The discussion is inspired by pedagogical models of ferroelectricity as often presented in classic text-books such as the Feynman lectures on Physics and the Introduction of Solid State Physics by Charles Kittel, which are routinely used to describe the quintessential ferroelectric phenomena such as the Curie-Weiss law and the emergence of spontaneous polarization below the Curie temperature. The model presented herein is overly simplified and ignores many of the complex interactions in real ferroelectrics; however, this model reveals an important insight: The polarization catastrophe phenomenon that is required to describe the onset of ferroelectricity naturally leads to the thermodynamic instability that is negative capacitance. Considering the interaction of electric dipoles and saturation of the dipole moments at large local electric fields we derive the full ‘S’-curve relating the ferroelectric polarization and the electric field, in qualitative agreement with Landau theory.

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BOYER, DENIS, and DAVID ROMEU. "MODELING GRAIN BOUNDARIES IN SOLIDS USING A COMBINED NONLINEAR AND GEOMETRICAL METHOD." International Journal of Modern Physics B 19, no. 27 (October 30, 2005): 4047–56. http://dx.doi.org/10.1142/s0217979205032607.

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The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg–Landau-like) description of crystalline phases based on symmetries and some fairly general stability arguments. This method allows a very detailed description of defects at the lattice scale with virtually no tunning parameters, unlike the usual phase-field methods. The model equations are directly inspired from those used in a very different physical context, namely, the formation of periodic patterns in systems out-of-equilibrium (e.g. Rayleigh–Bénard convection, Turing patterns). We apply the formalism to the study of symmetric tilt boundaries. Our results are in quantitative agreement with those predicted by a recent crystallographic theory of grain boundaries based on a geometrical quasicrystal-like construction. These results suggest that frustration and competition effects near a defect in crystalline arrangements have some universal features, of interest in solids or other periodic phases.

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Kornyshev, A. A., D. A. Kossakowski, and S. Leikin. "Landau Theory of a System with Two Bilinearly Coupled Order Parameter sin External Field: Exact Mean Field Solution, Critical Properties and Isothermal Susceptibility." Zeitschrift für Naturforschung A 50, no. 9 (September 1, 1995): 789–94. http://dx.doi.org/10.1515/zna-1995-0901.

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Abstract We present simple description of a system with two bilinearly coupled order parameters in external field based on an exact mean-field solution of the Landau Hamiltonian. It reproduces the qualitative form of the "field-temperature" phase diagram given by a molecular-field model and by more sophisticated theories and experiments on metamagnets. The solution gives the same critical exponents as the molecular-field theory, but it is not restricted to the magnetic systems only and it is easier to handle, since it formulates the results in explicit analytical form. The susceptibility in this model does not diverge at the second order transition line (far from a higher order critical point separating the second and first order transition lines), but jumps down from the lower temperature wing to the higher temperature one. The jump amplitude is proportional to the square of the field in small fields and diverges in large fields close to the higher order critical point.

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Journal articles on the topic 'Ginzburg-Landau theory; Mean-field model'

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