Showing papers on "Landau theory published in 2002"
TL;DR: In this paper, global in time classical solutions near Maxwellians are constructed for the Landau equation in a periodic box and generalized generalized Landau equations, which describes grazing collisions in a dilute gas.
Abstract: The Landau equation, which was proposed by Landau in 1936, is a fundamental equation to describe collisions among charged particles interacting with their Coulombic force In this article, global in time classical solutions near Maxwellians are constructed for the Landau equation in a periodic box Our result also covers a class of generalized Landau equations, which describes grazing collisions in a dilute gas
353 citations
TL;DR: In this article, a three-dimensional Landau theory of stress-induced martensitic phase transformations is presented, which accounts for the principal features of martensite transformations in shape memory alloys and steels, namely, stress-strain curves with constant transformation strain and constant, or weakly temperature dependent, stress hysteresis.
Abstract: A three-dimensional Landau theory of stress-induced martensitic phase transformations is presented. It describes transformations between austenite and martensitic variants and transformations between martensitic variants. The Landau free energy incorporates all temperature-dependent thermomechanical properties of both phases. The theory accounts for the principal features of martensitic transformations in shape memory alloys and steels, namely, stress-strain curves with constant transformation strain and constant, or weakly temperature dependent, stress hysteresis, as well as nonzero tangent elastic moduli at the phase transformation point. In part I, the austenite$\ensuremath{\leftrightarrow}$martensite phase transformation is treated, while transformations between martensitic variants are considered in part II.
221 citations
TL;DR: Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present, resulting in a list of 40 different structures, each with a unique space-group symmetry.
Abstract: Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolome [Phase Transit. (2001), 74, 255–335] and a number of differences are found. The group–subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.
193 citations
TL;DR: In this paper, the freezing/melting behavior of fluids of small molecules in pores of simple geometry can be understood in terms of two main parameters: the pore width H* and a parameter a that measures the ratio of the fluid-wall to the fluid's attractive interaction.
Abstract: Using molecular simulations and free energy calculations based on Landau theory, we show that freezing/melting behavior of fluids of small molecules in pores of simple geometry can be understood in terms of two main parameters: the pore width H* ~expressed as a multiple of the diameter of the fluid molecule ! and a parameter a that measures the ratio of the fluid-wall to the fluid‐fluid attractive interaction. The value of the a parameter determines the qualitative nature of the freezing behavior, for example, the direction of change in the freezing temperature and the presence or absence of new phases. For slit-shaped pores, larger a values lead to an increase in the freezing temperature of the confined fluid, and to the presence of a hexatic phase. For pores that accommodate three or more layers of adsorbate molecules several kinds of contact layer phase ~inhomogeneous phases in which the contact layer has a different structure than the inner layers! are observed. Smaller a values lead to a decrease in the freezing temperature. The parameter H* determines the magnitude of shift in the freezing temperature, and can also affect the presence of some of the new phases. Results are presented as plots of transition temperature vs a for a particular pore width. Experimental results are also presented for a variety of adsorbates in activated carbon fibers~ACF! covering a wide range of a values; the ACF have slit-shaped pores with average pore width 1.2 nm. The experimental and simulation results show qualitative agreement. © 2002 American Institute of Physics. @DOI: 10.1063/1.1426412#
158 citations
TL;DR: Landau theory is employed, extending an investigation begun by Yamashita and Ueda for the case of S = 1, and classical analyses are used to argue that magnetoelastic couplings generate bond order via a spin-Peierls transition.
Abstract: We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S = 1, and classical analyses to argue that such couplings generate bond order via a spin-Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Neel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Neel phase, a dispersionless stringlike magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.
154 citations
TL;DR: In this article, the three-dimensional Landau model of martensitic transformations was generalized to include transformations between an arbitrary number of Martensitic variants. And the model can incorporate all temperature-dependent thermomechanical properties of both phases for arbitrary crystal symmetries, including higher-order elastic constants, and it correctly describes the characteristic features of stress-strain curves for shape-memory alloys and steels.
Abstract: In this paper, the three-dimensional Landau model of austenite-martensite transformations constructed in Part I is generalized to include transformations between an arbitrary number of martensitic variants. The model can incorporate all temperature-dependent thermomechanical properties of both phases for arbitrary crystal symmetries, including higher-order elastic constants, and it correctly describes the characteristic features of stress-strain curves for shape-memory alloys and steels, namely, constant transformation strain tensors, constant or weakly temperature dependent stress hysteresis, and transformation at nonzero tangent moduli. Geometric representations of the conditions for phase equilibrium and phase transformations in six-dimensional stress space are developed. For the cubic-tetragonal phase transformation, equilibrium and transformation surfaces in three-dimensional stress space and the corresponding lines in the deviatoric-stress plane are found at various temperatures, and transformation processes are analyzed. All model parameters are obtained for the NiAl cubic-tetragonal phase transformation using the results of molecular dynamics simulations available in the literature.
153 citations
TL;DR: In this paper, it was shown that the tetrahedral molecule at the heart of the pyrochlore magnet undergoes a Jahn-Teller distortion when lattice motion is coupled to the antiferromagnetism.
Abstract: In the highly frustrated pyrochlore magnet spins form a lattice of corner-sharing tetrahedra. We show that the tetrahedral ``molecule'' at the heart of this structure undergoes a Jahn-Teller distortion when lattice motion is coupled to the antiferromagnetism. We extend this analysis to the full pyrochlore lattice by means of Landau theory and argue that it should exhibit ``spin-Peierls'' phases with bond order but no spin order. We find a range of N\'eel phases, with collinear, coplanar, and noncoplanar order. While collinear N\'eel phases are easiest to generate microscopically, we also exhibit an interaction that gives rise to a coplanar state instead.
93 citations
TL;DR: The first empirical example of a nucleus located at the isolated triple-point is suggested, which explains why it is associated with one special type of structure and requires the recently proposed first-order phase transition between prolate and oblate nuclear shapes.
Abstract: We show that the second-order phase transition between spherical and deformed shapes of atomic nuclei is an isolated point following from the Landau theory of phase transitions. This point can occur only at the junction of two or more first-order phase transitions which explains why it is associated with one special type of structure and requires the recently proposed first-order phase transition between prolate and oblate nuclear shapes. Finally, we suggest the first empirical example of a nucleus located at the isolated triple-point.
75 citations
TL;DR: This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.
Abstract: In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers cross-linked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.
71 citations
TL;DR: This work demonstrates the divergence in the behavior of the compressibility near the density driven Mott transition at finite temperatures using DMFT and quantum Monte Carlo simulations in the one-band and the two-band Hubbard model.
Abstract: In the context of the dynamical mean-field theory (DMFT) of the Hubbard model, we study the behavior of the compressibility near the density driven Mott transition at finite temperatures. We demonstrate this divergence using DMFT and quantum Monte Carlo simulations in the one-band and the two-band Hubbard model. We supplement this result with considerations based on the Landau theory framework, and discuss the relevance of our results to the alpha-gamma end point in cerium.
68 citations
TL;DR: The pressure-temperature phase diagram of BaTiO3 has been investigated using a modification of the standard Landau potential to take account of quantum saturation of the order parameter at low temperatures as mentioned in this paper.
Abstract: The pressure–temperature phase diagram of BaTiO3 has been investigated using a modification of the standard Landau potential to take account of quantum saturation of the order parameter at low temperatures. The calculated phase diagram agrees well with experiment for the cubic–tetragonal and tetragonal–orthorhombic transitions, but underestimates the orthorhombic–rhombohedral transition temperature somewhat. The saturation temperature (θS = 160 K) is sufficiently high that the expected critical point is not observed experimentally. Instead, each phase boundary bends sharply down, so each of the four crystalline structures of BaTiO3 has a stability field with increasing pressure at 0 K.
TL;DR: In this paper, a general Landau model for the coupled orientational and translational order parameters and including the tilt angle was proposed to describe the smectic C-isotropic phase transition.
Abstract: We propose a Landau model to describe the smectic C–isotropic phase transition. A general Landau theory for the coupled orientational and translational order parameters and including the tilt angle is developed. The conditions for the smectic C–isotropic phase transition and the stability conditions of the smectic C phase are calculated. On the basis of this model it is argued that the smectic C–isotropic phase transition is always first order. We present a detailed analysis of the question under which conditions a direct smectic C–isotropic phase transition prevails in comparison to smectic A–isotropic and nematic–isotropic transitions. The theoretical results are found to be in qualitative agreement with all published experimental results.
TL;DR: In this article, the authors show that the off-axis stripes compromise the elastic energy of the inplane and antiplane deformation, and that the transition between the along-axis and the offaxis stripes obeys the Landau theory of phase transition of the second kind.
TL;DR: In this article, the authors proved the existence of a weak function-solution of class C ∞ with bounded derivatives of the Landau equation for a generalization of Maxwellian molecules when the initial data is a probability measure.
TL;DR: A Landau-type free energy based on a primary order parameter coupled to finite strain with an elastic energy derived from an arbitrary equation of state V = V(P) is constructed.
Abstract: We show how to construct a Landau-type free energy based on a primary order parameter coupled to finite strain with an elastic energy derived from an arbitrary equation of state V = V(P). The resulting class of models provides an excellent and efficient framework for the systematic study of phase transformations for a wide range of materials up to ultrahigh pressures.
TL;DR: In this paper, a Ginzburg-Landau formulation of the bosonic resonating-valence-bond (RVB) theory of superconductivity is presented, where the superconducting order parameter is characterized by phase vortices that describe spinon excitations.
Abstract: We present a Ginzburg-Landau formulation of the bosonic resonating-valence-bond (RVB) theory of superconductivity. The superconducting order parameter is characterized by phase vortices that describe spinon excitations and the transition to the superconducting state occurs when such phase vortices (un)bind. We show that the boson RVB theory always leads to hc/2e flux quanta and that the presence of a trapped spin-½ moment inside a vortex core gives rise to observable consequences for the low-temperature field-dependent specific heat. We also show that the cores of magnetic fluxoids exhibit enhanced antiferromagnetic correlations with a midgap energy scale and discuss some experimental implications.
TL;DR: In this paper, the thermodynamics of superfluid 4He at negative pressures were calculated using the Landau theory, in which thermodynamic properties are expressed as sums over the thermal distribution of elementary excitations.
Abstract: We calculate the thermodynamics of superfluid 4He at negative pressures. We use the Landau theory in which thermodynamic properties are expressed as sums over the thermal distribution of elementary excitations. The excitation dispersion curve is taken from the density functional theory developed by Dalfovo et al. To give a good description of the liquid near to the lambda line, we include the interaction between the elementary excitations using a modification of the roton liquid theory of Bedell, Pines, and Fomin. The calculated quantities include the location of the lambda line, the liquid-vapor spinodal, and lines of constant entropy in the pressure-temperature (P-T) plane. We have also calculated the line of minimum density (zero expansion coefficient) in theP-T plane. This joins the lambda line tangentially at about −5.3 bars. Using the critical properties near the lambda line, we find that the line of maximum density in He I also joins the lambda line tangentially at this pressure. For use in cavitation experiments, we have calculated the states on the lambda line reached by isentropic expansion from He I.
TL;DR: It is pointed out that the ‘‘dissipation’’ is caused mainly by the dynamical instability induced by the optical lattice, not by Landau instability (fluid velocities being greater than the local speeds of sound) as claimed.
Abstract: Recently Burger et al. [1] reported an observation of ‘‘dissipative dynamics of a Bose-Einstein condensate (BEC) in a periodic optical lattice.’’ We here point out that the ‘‘dissipation’’ is caused mainly by the dynamical instability [2,3] induced by the optical lattice, not by Landau instability (fluid velocities being greater than the local speeds of sound) as claimed in Ref. [1]. By attributing this dissipative dynamics to Landau instability, Burger et al. presented a theory, which gives an excellent fit to the experimental data, as indicated in Fig. 4 of Ref. [1]. However, this theory was unable to explain their further experiments with decreased lattice strength V0 and lower BEC densities. If Landau instability were the true cause of the dissipative dynamics, the dissipation would become more severe with lower densities of BEC (smaller speeds of sound). To the contrary, they ‘‘observed indications that the dissipation onset occurs at higher velocities for decreasing V0 and that the BEC propagates without dissipation in a regime of very low atom number’’ [1]. As the density of BEC (interaction strength) and the lattice strength are two key parameters in this system, any complete theory should be able to predict what happens when these two parameters are changed. In the experiment [1], after the preparation of a cigarshaped BEC in a trap with the presence of an optical lattice, the trap was suddenly shifted by x along the longitudinal direction. The subsequent motion of the BEC is oscillatory when the displacement x is small, but becomes dissipative when x is big enough. The dynamical instability of BEC Bloch waves is the main cause of this dissipation, and our theory [2] provides a good explanation of the experimental observations, including the change of BEC density and lattice strength. The BEC prepared is largely a Bloch state; after the shift of the trap center, the BEC not only oscillates in the real space, but also in the k space around the center of the Brillouin zone. As the shift x is increased, a larger portion of the Brillouin zone is swept, thus the oscillation can turn dissipative as a result of being affected by the dynamical instability existing in the outer region of the zone (dark areas of Fig. 1 in Ref. [2]). As shown in Figs. 1 and 2 in Ref. [2], as the density of BEC is lowered, the dynamical instability is reduced both in terms of ‘‘dark area’’ and growth rates. This explains that ‘‘the BEC propagates without dissipation in a regime of very low atom number.’’ The dynamical instability also becomes less severe as V0 is decreased; it is consistent with ‘‘the dissipation onset occurring at higher velocities for decreasing V0’’. For the typical case reported in Ref. [1], the growth rate is about 1.6 per ms. Therefore, a few milliseconds spent in the dangerous zone of dynamical instability means that only 1% of the system will remain in the initial state. The oscillation is destroyed.
TL;DR: In this paper, a lattice model of spinless interacting electrons is used to formulate the Landau theory of the Fermi liquid to electron-glass quantum phase transition and it is shown that the presence of additional random site energies does not affect the character of the transition, once the replica symmetry breaking is considered self-consistently at the mean-field level.
Abstract: A lattice model of spinless interacting electrons is used to formulate the Landau theory of the Fermi liquid to electron-glass quantum phase transition. We demonstrate that the presence of additional random site energies does not affect the character of the transition, once the replica symmetry breaking is considered self-consistently at the mean-field level. Inside the glass phase, the low temperature conductivity assumes a non-Fermi liquid δσ∼T 3 / 2 form, in agreement with recent experiments.
TL;DR: In this article, the fatigue peculiarities of PZr,Ti,O3 (PZT) films prepared by sol-gel and rf sputtering were investigated using a Landau theory-based model based on formation of degraded regions in a ferroelectric lattice.
Abstract: Characterization of the fatigued state in Pb(Zr,Ti)O3 (PZT) films has been carried out by nanoscale piezoelectric displacements measured simultaneously with the macroscopic polarization hysteresis. For explaining the fatigue peculiarities of PZT films prepared by sol-gel and rf sputtering, a Landau theory-type model based on formation of degraded regions in a ferroelectric lattice has been used. The relevance of local piezoelectric loops for the macroscopic polarization hysteresis has been assessed and the possibility of recovering the latter as a weighted convolution of the former has been shown to depend on the film quality.
TL;DR: In this paper, the authors consider the Ginzburg-Landau equation in dimension two and introduce a key notion of the vortex (interaction) energy, defined by minimizing the renormalized GLEF functional over functions with a given set of zeros of given local indices.
Abstract: We consider the Ginzburg–Landau equation in dimension two. We introduce a key notion of the vortex (interaction) energy. It is defined by minimizing the renormalized Ginzburg–Landau (free) energy functional over functions with a given set of zeros of given local indices. We find the asymptotic behaviour of the vortex energy as the inter-vortex distances grow. The leading term of the asymptotic expansion is the vortex self-energy while the next term is the classical Kirchhoff–Onsager Hamiltonian. To derive this expansion we use several novel techniques.
TL;DR: It is shown that pulses in the complete quintic one-dimensional Ginzburg–Landau equation with complex coefficients appear through a saddle-node bifurcation which is determined analytically through a suitable approximation of the explicit form of the pulses.
Abstract: It is shown that pulses in the complete quintic one-dimensional Ginzburg–Landau equation with complex coefficients appear through a saddle-node bifurcation which is determined analytically through a suitable approximation of the explicit form of the pulses The results are in excellent agreement with direct numerical simulations
TL;DR: The roles of space charge induced in the ferroelectric thin film and the presence of Schottky barriers at the two electrode/film interfaces are studied by numerical simulation using Landau-Khalatnikov theory.
Abstract: The role of space charge induced in a ferroelectric thin film and the presence of Schottky barriers at the two electrode/film interfaces are studied by numerical simulation using Landau-Khalatnikov theory. In this work, the whole film is considered as the stacking of dipolar layers, each of which contains multilayers of perovskite cells. In the presence of a local electric field, the double-well thermodynamic potential of each layer is modified in an asymmetric manner. The local electric field distribution is determined both by the space charge and the boundary conditions imposed by the Schottky barrier heights. Asymmetric and skewed hysteresis loops are generated.
TL;DR: In this article, a superconducting cylinder placed in a magnetic field along the direction of the axis of the cylinder is computed based on the numerical solutions of the Ginzburg-Landau model by the finite element method.
TL;DR: In this article, an effective Ginzburg-Landau theory for ferromagnetic cubic Ni-Mn-Ga was presented, in which structural and magnetic phase transitions took place, and the general problem of a cubic ferromagnet was taken into account by fitting the parameters of the Ginzberg-landau functional to experimental data.
Abstract: We present an effective Ginzburg-Landau theory for ferromagnetic cubic Ni-Mn-Ga in which structural and magnetic phase transitions take place. The general problem of a cubic ferromagnet is taken into account by fitting the parameters of the Ginzburg-Landau functional to experimental data. This enables us to obtain a realistic phase diagram for Ni-Mn-Ga.
TL;DR: In this paper, an effective Hamiltonian in the lowest Landau level (LLLL) was derived and the effects of LL mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy.
Abstract: We derive an effective Hamiltonian in the lowest Landau level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy, $\ensuremath{\kappa}{=(e}^{2}/\ensuremath{\varepsilon}l)/{\ensuremath{\omega}}_{c}.$ We then transcribe the Hamiltonian to the composite fermion basis using our Hamiltonian approach, and compute the effect of LL mixing on transport gaps.
TL;DR: In this article, two-band Ginzburg-Landau (G-L) theory equations were solved analytically to determine the temperature dependence of the London penetration depth λ(T).
TL;DR: In this article, the authors present a heuristic way to develop a diagrammatic expansion that is connected to the Feynman diagram expansion, which is required to write the S matrix as S = 1 + R + and its Hermitian conjugate as S + = 1 - R -.
Abstract: The “diagrammatic” framework of S -matrix theory is provided by the unitarity equations. In its purest form, the S -matrix theory establishes those analyticity properties of the S matrix that can be based on physical principles clearly formulated separately from the field theory. The chapter presents a heuristic way to develop a diagrammatic expansion that is connected to the Feynman diagram expansion. It is required to write the S matrix as S = 1 + R + and its Hermitian conjugate as S + = 1 - R - . Scattering processes can be described by a Landau diagram. The Landau equations for a given Landau diagram are the set of conditions for all internal loops of the diagram. The set of external momenta that satisfies the complete set of equations provides the Landau singularity corresponding to the diagram. The set of all physical region (+α) Landau diagram thresholds is the minimal set of singularities that an analytic scattering amplitude must have.
TL;DR: In this article, a phenomenological description of the first-order magnetocrystalline transition that occurs in the Gd-5 (6Ge1-x)(4) (0.24 < x < 0.5) alloys is presented.
Abstract: With the help of the Landau-Devonshire theory, in this paper we produce a good phenomenological description of the first-order magnetocrystalline transition that occurs in the Gd-5(SixGe1-x)(4) (0.24 < x < 0.5) alloys, and derive the magnetic phase diagram in a magnetic field versus temperature presentation. The description reproduces not only the field-induced magnetic transition and the temperature-induced transition, but also the magnetic hysteresis and the thermal hysteresis. Also, it gives the critical external field and the critical temperature for the magnetic hysteresis and the thermal hysteresis.