Ginzburg Theory Research Articles

Viscosity of a sheared correlated (near-critical) model fluid in confinement

Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau–Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green–Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness L. In addition, at the critical point the viscosity is proportional to , where is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.

Dielectric properties of ferroelectric composites (NaNO2)0.95/(PbTiO3)0.05

ABSTRACTThe temperature and frequency dependences of dielectric properties of the ferroelectric composite (NaNO2)0,95/(PbTiO3)0,05 near the phase transition of sodium nitrite have been studied. A significant increase in the real part of the dielectric constant at low frequencies and its strong decrease with increasing frequency were discovered. The temperature hysteresis of phase transition is about 1.5 K. The dielectric constant upon cooling from the paraelectric phase to 273 K is less than during heating, while a similar dependence is observed for conductivity. The results are analyzed in the Landau – Ginzburg theory framework.

The Making of the Brave Sheep or … the Laboratory as the Unlikely Space of Attunement to Animal Emotions

Cohen (2003) argued that animals, humans, and objects must be appraised together as they form various, temporary clusters of active beings. In this article, drawing on material semiotics and actor-network theory insights, I look at one such temporary cluster of animal scientists and sheep brought together in a specific experiment and a set of animal science practices dedicated to exploring sheep emotions. This experiment was carried out at an animal science farm and laboratory of the National Institute of Agricultural Research in Clermont Ferrand, France, as part of a project on farm animals’ emotions (EmoFarm, 2010–2015). Here, I argue, the laboratory can be seen as an unlikely space of attunement to farm animals’ emotions, and the sheep body, to borrow from Latour, is what leaves a dynamic trajectory by which she learns to register and become sensitive to what the world is made of (Latour 2004, 205). By looking at this temporary cluster of active beings and what they produce, I engage in a conversation with Agamben’s (2009) theory of signatures and Ginzburg’s (1989) signatorial method.

Application Of Shape Memory Alloy In Harvesto-Absorber System

Abstract This paper presents a conception of the harvester-absorber system consisting of two parts. The first is the pendulum attached to the main system (oscillator), which is suspended on the linear damper and the nonlinear spring made of shape memory alloy. The spring is modelled as a polynomial function based on Landau–Ginzburg theory of phase transitions (similar as ferroelectric and ferromagnets). The obtained results show, that SMA element can increase harvesting energy level, while the absorber effect can be impaired (but not loss). Additionally, introducing SMA element causes changes in dynamics, introduces a new unstable solutions and bifurcations. The analysis was done by classical integration and continuation solution methods.

Piezoelectric properties of rhombohedral ferroelectric materials with phase transition

The temporal evolution of domain structure and its piezoelectric behavior of ferroelectric material BaTiO 3 during the transition process from rhombohedral to tetragonal phase under an applied electric field have been studied by employing Landau–Ginzburg theory and the phase-field method. The results obtained show that, during the transformation process, the intermediate phase was monoclinic MA phase, and several peak values of piezoelectric coefficient appeared at the stage where obvious change of domain pattern occurred. In addition, by comparing the cases of applied electric field with different frequencies, it was found that the maximum piezoelectric coefficient obtained decreased with increasing frequency value. These results are of great significance in tuning the properties of engineering domains in ferroelectrics, and could provide more fundamentals to the design of ferroelectric devices.

Dielectric investigation of the composites based on thiourea

The composites of thiourea and lithium niobate as well as lead titanate and barium titanate (thiourea fraction was 0.90 for all cases) have been studied by dielectric spectroscopy close to structural phase transitions in thiourea. It was found that the hysteresis increased and the temperature of ferroelectric phase transition from phase I to phase II decreased for all compositions investigated in comparison with the same properties of polycrystalline thiourea. The largest lowering of the phase transition temperature was observed for the thiourea and barium titanate composite. The results are analyzed within the framework of Landau–Ginzburg theory.

Truncated conformal space approach for 2D Landau–Ginzburg theories

We study the spectrum of Landau–Ginzburg theories in 1 + 1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a Φ2 theory (i.e. a free massive boson) in this framework. We then turn to Φ4 in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of Φ4 where kink excitations together with their bound states are present. We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of Φ6 Landau–Ginzburg theory, again finding agreement.

Effect of composition and interface intermixing on polarization behaviors of BaTiO3 /(Ba,Sr)TiO3 superlattices

We have developed a thermodynamic model based on the Landau–Ginzburg theory to study the effect of composition and interface intermixing on ferroelectric properties of BaTiO3/BaxSr1−xTiO3 (BT/BST) superlattices. Dependence of the lattice parameter and the substrate-induced misfit strain of BST layer in BT/BST superlattices on Ba/Sr content are obtained. Effect of composition and interface intermixing on ferroelectricity of superlattices are examined by investigating the modulated profiles of polarization and the mismatch in polarization at interface. Our study reveals that the polarization behaviors of BT/BST superlattices can be manipulated by varying the Ba/Sr content in BST layer without changing the period thickness of superlattices. The effect of Ba/Sr content on polarization behavior of BT/BST superlattices is stronger than the effect of interface intermixing on polarization of the superlattices.

Intrinsic Ferroelectric Coercive Field Calculation for BZT Films Doped by Indium and Lanthanum

The intrinsic coercive field is predicted by using Landau Ginzburg theory of ferroelectricity. A routine program created on Delphi platform is used to make simulation of the calculation of hysteresis loops and intrinsic coercive field. There are shifting in the values of intrinsic ferroelectric field of BZT on adding the zirconium composition, and the maximum intrinsic coercive field of BZT is found at 0.25 mol zirconium. The calculation shows that the best intrinsic coercive field is found at 1 mol % dopant.

Field and Frequency Dependence of the Dynamic Hysteresis in Lead Zirconate Titanate Solid Solutions

Dynamic hysteresis of Nb‐doped Pb(Zr1−xTix)O3 (PZT, 0.20 ≤ x ≤ 0.60) ceramics were studied systemically at different field (E) and frequency (f). The hysteresis loops were strongly dependent on E and f. The measured coercive fields (Ec0) were far lower than the calculated values based on the Landau–Ginzburg theory, and increased dramatically from the rhombohedral phase to the tetragonal phase while had less variation with composition in the same phase. With increasing E or f for each composition, three types of loops were observed: linear, minor, and saturated loops. The cross fields (E0), cross polarizations (P0), and hysteresis areas (<A>) showed different variation regularities with f. Similar varying curves were observed for all PZT ceramic samples by normalizing E0, P0, and <A> with E/Ec0, which indicated the same polarization switching for different domain structures. Further analyses revealed that the switching processes can be divided into three stages: space charge polarization, domain switching, and steady state. The first and second stage occurred at ~0.5 and ~1.5 E/Ec0, respectively. These results would be very helpful to further understand the polarization switching of ferroelectric ceramics.

Exotic symmetric space over a finite field, I

Let V be a 2n-dimensional vector space over an algebraically closed field k with ch k ≠ 2. Let G = GL(V) and H = Sp2n be the symplectic group obtained as H = G θ for an involution θ on G. We also denote by θ the induced involution on \( \mathfrak{g} \) = Lie G. Consider the variety G/H × V on which H acts naturally. Let \( \mathfrak{g}_{\mathrm{nil}}^{{-\theta }} \) be the set of nilpotent elements in the -1 eigenspace of θ in \( \mathfrak{g} \). The role of the unipotent variety for G in our setup is played by \( \mathfrak{g}_{\mathrm{nil}}^{{-\theta }} \) × V, which coincides with Kato’s exotic nilpotent cone. Kato established, in the case where k = C, the Springer correspondence between the set of irreducible representations of the Weyl group of type C n and the set of H-orbits in \( \mathfrak{g}_{\mathrm{nil}}^{{-\theta }} \) × V by applying Ginzburg theory for affine Hecke algebras. In this paper we develop a theory of character sheaves on G/H × V, and give an alternate proof for Kato’s result on the Springer correspondence based on the theory of character sheaves.

Charge and spin fractionalization in strongly correlated topological insulators

We construct an effective topological Landau–Ginzburg theory that describes general SU(2) incompressible quantum liquids of strongly correlated particles in two spatial dimensions. This theory characterizes the fractionalization of quasiparticle quantum numbers and statistics in relation to the topological ground-state symmetries, and generalizes the Chern–Simons, BF (‘background field’) and hierarchical effective gauge theories to an arbitrary representation of the SU(2) symmetry group. We mainly focus on fractional topological insulators with time-reversal symmetry, which are treated as SU(2) generalizations of the quantum Hall effect.

Triviality of the Aharonov–Bohm interaction in a spatially confining vacuum

This paper explores long-range interactions between magnetically charged excitations of the vacuum of the dual Landau–Ginzburg theory (DLGT) and the dual Abrikosov vortices present in the same vacuum. We show that, in the London limit of DLGT, the corresponding Aharonov–Bohm-type interactions possess such a coupling that the interactions reduce to a trivial factor of e2πi×(integer). The same analysis is done in the SU(N c)-inspired [U(1)] $^{N_{\mathrm{c}}-1}$ -invariant DLGT, as well as in DLGT extended by a Chern–Simons term. It is furthermore explicitly shown that the Chern–Simons term leads to the appearance of knotted dual Abrikosov vortices.

The response functions of self-dual Josephson junction arrays near the quantum phase transition

The dynamics of a self-dual Josephson junction array near its quantum transition is studied by means of a mutual U(1) × U(1) Chern–Simons Landau–Ginzburg theory. It is shown that disorder scalar fields, which become gapless at the critical point, generate intrinsic dissipation in the system. The electromagnetic response functions of the system and the longitudinal and Hall conductivities are analyzed in different regimes. In the presence of commensurate charge and magnetic frustration, the condensation of bound electric and magnetic disorder fields leads to finite universal longitudinal and transverse resistivities satisfying a relation akin to that found in the QHE in two-dimensional electron systems.

About Ginzburg–Landau, and a bit on others

This note is a brief history of how the theory of Ginzburg and Landau came to be. Early publications on the macroscopic theory of superconductivity are reviewed in detail. Discussions that the two co-authors had with their colleagues and between themselves are described. The 1952 review by V L Ginzburg is discussed, in which a number of well-defined requirements on the yet-to-be-developed microscopic theory of superconductivity were formulated, constituting what J Bardeen called the 'Ginzburg energy gap model'.

Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg–Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrodinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.

Ferroelectric transistors with improved characteristics at high temperature

We report on the temperature dependence of ferroelectric metal-oxide-semiconductor (MOS) transistors and explain the observed improved characteristics based on the dielectric response of ferroelectric materials close to the Curie temperature. The hysteretic current-voltage static characteristics of a fully depleted silicon-on-insulator transistor, with 40 nm vinylidene fluoride trifluorethylene, and 10 nm SiO2 gate stack, are measured from 300 to 400 K. In contrast with conventional MOS field effect transistors (MOSFETs), the subthreshold swing and the transconductance show, respectively, a minimum and a maximum near the Curie temperature (355 K) of the ferroelectric material. A phenomenological model is proposed based on the Landau–Ginzburg theory. This work demonstrates that a MOSFET with a ferroelectric layer integrated in the gate stack could have nondegraded or even improved subthreshold swing and transconductance at high temperature even though the hysteresis window is reduced. As a consequence, we suggest that for ferroelectric transistors with appropriately designed Curie temperatures, the performance degradation of logic or analog circuits, nowadays operating near 100 °C, could be avoided.

Phase transitions in TlH2PO4 and TlD2PO4 crystals: lattice dynamical treatment

Lattice dynamics simulation ofTlH2PO4 andTlD2PO4 crystals was performed within the semi-phenomenological atomistic model in the high temperatureP 21/b 2/c 21/n structural phase. Combining the results of phenomenological Landau–Ginzburg theory andlattice dynamics simulation, it was shown that the ferroelastic phase transition inTlH2PO4 occurs due to the bilinear interaction between the softB3g opticand B1u acoustic modes. According to our simulation, the hydrogenH1 atoms placed on the shorter hydrogen bonds play the key role in the ferroelastic phase transition inTlH2PO4, whereasthe D2 atoms located on the longer hydrogen bonds exert the main effect on the antiferroelectric phase transitionin TlD2PO4 crystal.

High-Field Study of Strong Magnetoelectric Coupling in Single-Domain Crystals of BiFeO3

Magnetic and dielectric properties of single-domain crystals of BiFeO 3 were studied in pulsed magnetic fields up to 55 T. At low temperatures, metamagnetic transitions accompanied with sharp changes in electric polarization ( P ) were observed at around 18 T. The angular dependence of the transition field coincides with that of the transition from the cycloidal state to the canted antiferromagnetic spin state studied in the framework of the Landau–Ginzburg theory incorporated with the Lifshitz-like invariant. The parasitic P component caused by the cycloidal spin structure amounts to 210±30 µC/m 2 in terms of the projected component on the pseudocubic principal axis, which can be controlled by applying magnetic fields at least up to 500 K. This result indicates that the microscopic magnetoelectric coupling in BiFeO 3 is not weak: In fact, it is rather strong as compared to that in the canonical multiferroic material TbMnO 3 .

Enhancement of dielectric and ferroelectric properties in ferroelectric superlattices

I studied theoretically the enhancement of remanent polarization and dielectric permittivity of interfacial-coupled ferroelectric superlattices based on the Landau–Ginzburg theory. Our model adopts the Landau–Khalatnikov equation to describe hysteresis behavior and takes the time-dependent space-charge-limited conductivity into account to investigate the ferroelectric and dielectric properties of ferroelectric superlattices. The results are in good agreement with recent experimental observations on the enhancement of remanent polarization and permittivity of BaTiO 3/SrTiO 3 superlattices and heterolayered Pb(Zr,Ti)O 3 thin films.