Extension Of Mean-field Theory Research Articles

Electric field effects on N–Sm-A–Sm-C phase transitions

A liquid crystalline system formed by rod-shaped molecules that have a small transverse dipole moment is analyzed in the presence of an external electric field normal to the smectic layers. The approach focuses on the phase transition diagram displaying the N–Sm–A-Sm-C phases, when both negative and positive dielectric anisotropies are considered. The analysis is carried out within the framework of an extended mean field theory, which shows the emergence of a re-entrant Sm-C phase in the strong field regime, accompanied by a suppression of the translational ordering of the Sm-A phase, in the case of a negative anisotropy. A different scenario is observed in the case of positive anisotropy, as the electric field tends to suppress the Sm-C phase because the molecular alignment is driven by the field along its direction. In this case, the emergence of a residual nematic phase is also observed, which replaces the isotropic phase and is characterized by a low-value orientational order parameter.

Quantum Droplet States of a Binary Magnetic Gas.

Quantum droplets can emerge in bosonic binary magnetic gases (BMGs) from the interplay of short- and long-ranged interactions, and quantum fluctuations. We develop an extended mean field theory for this system and use it to predict equilibrium and dynamical properties of BMG droplets. We present a phase diagram and characterize miscible and immiscible droplet states. We also show that a single-component self-bound droplet can bind another magnetic component, which is not in the droplet regime, due to the interspecies dipole-dipole interactions. Our results should be realizable in experiments with mixtures of highly magnetic lanthanide atoms.

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated (cigar shaped) confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.

Origin of mean-field behavior in an elastic Ising model

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical fluctuations of such a model. A mean field theory applied to the resulting effective Hamiltonian quantitatively accounts for both thermodynamics and kinetics observed in computer simulations, including a barrier to magnetization reversal that grows extensively with system size. For nanocrystals, which break translational symmetry, a straightforward extension of mean field theory yields similarly accurate results.

On the inclusion of dissipation on top of mean-field approaches

We discuss extensions of time-dependent mean-field theories such as time-dependent local density approximation (TDLDA) in order to include incoherent dynamical correlations, which are known to play a key role in far-off equilibrium dynamics. We focus here on the case of irradiation dynamics in clusters and molecules. The field, still largely unexplored, requires quantum approaches which represents a major formal and computational effort. We present several approaches we have investigated to address such an issue. We start with time-dependent current-density functional theory (TDCDFT), known to provide damping in the linear regime and explore its capability far-off equilibrium. We observe difficulties with the scaling of relaxation times with deposited energy. We next briefly discuss semi-classical approaches which deliver kinetic equations applicable at sufficiently large excitation energies. We then consider a first quantum kinetic equation at the level of a simplified, though rather elaborate in its content, relaxation time approximation (RTA). Thanks to its sophistication, the method allows us to address numerous realistic irradiation scenarios beyond the usual domain of reliability of such theories. We demonstrate in particular the key role played by dense spectral regions in the impact of dissipation in the response of the irradiated system. RTA nevertheless remains a phenomenological approach which calls for more fundamental descriptions. This is achieved by a stochastic extension of mean field theory, coined stochastic time dependent Hartree–Fock (STDHF), which provides an ensemble description of far-off equilibrium dynamics. The method is equivalent to a quantum kinetic equation complemented by a stochastic collision term. STDHF clearly leads to proper thermalization behaviors in 1D test systems considered here. It remains limited by its ensemble nature which requires possibly huge ensembles to properly sample small transition rates. An alternative approach, coined average STDHF (ASTDHF), consists in overlooking mean field fluctuations of STDHF. ASTDHF provides a robust tool, properly matching STDHF when possible and allowing extension to realistic dynamical scenarios in full 3D. It can also be used in open systems to explore, as done in RTA, the competition between ionization and dissipation.

Hot and dense matter beyond relativistic mean field theory

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $\Gamma_{th}=1+(P_{th}/\epsilon_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $\Gamma_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.

Higgs-Yukawa model with higher dimension operators via extended mean field theory

Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $\phi^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $\phi^6$ interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e. the mass of the lightest mediator particle, is around $1.5$ TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.

Extended mean field study of complexφ4-theory at finite density and temperature

We review the extended mean field theory (EMFT) approximation and apply it to complex, scalar ${\ensuremath{\varphi}}^{4}$ theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $\ensuremath{\mu}$ at both zero and nonzero temperature and determine the $(T,\ensuremath{\mu})$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the ``Silver Blaze'' behavior at zero temperature and dimensional reduction at finite temperature.

Mean-field transfer-matrix analysis of the p-state chiral clock model.

The phase diagram of the mean-field transfer-matrix (MFTM) approximation for the three-dimensional p-state chiral clock model is determined numerically for p=3, 4, and 5 and compared to the simple mean-field and exact low-temperature phase diagrams. The MFTM approximation is a natural extension of mean-field theory in which the interactions are treated exactly in one direction with mean-field treatment of the other directions. For p=3, the MFTM low-temperature phase sequence near the multiphase point agrees with the exact low-temperature phase diagram, which is different from that of the simple mean-field theory. Thus, treating only the direction of anisotropy exactly in the three-state chiral clock model results in an improvement over simple mean-field theory in the qualitative (as well as the quantitative) features of the phase diagram. The case p=4 is similar, but for p=5 the MFTM approximation is inconclusive in a way that suggests a change in the nature of the model for p\ensuremath{\ge}5. The results indicate that with care the MFTM method is useful for analyzing the qualitative phase behavior of models with modulated phases.

Relativistic many-body theory of finite nuclei and the Schwinger-Dyson formalism.

A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green's functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as {ital c}-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka {ital et} {ital al}.$---- The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states inmore » a systematic way.« less

Attractive Forces between Charged Surfaces in the Presence of Polyelectrolyte

We have used Monte Carlo simulations and an extended mean field theory to study the interaction between two uniformly charged surfaces with an interstitial, neutralising solution of counterions, consisting of flexible polyelectrolytes. The latter are modelled as charged monomers bonded via harmonic potentials. The monotonic repulsion between surfaces, expected from traditional double layer theory, is not realised in this system. Indeed, the force can be attractive over a wide range of parameter values, with a magnitude significant compared to ordinary double layer or van der Waals forces. This attraction is attributed to both an entropically driven bridging, as well as electrostatic correlations, of polyelectrolyte chains across the mid-plane. The former effect is predicted by mean field theory. These results have relevance to numerous experimental systems of technical and biological importance.