A spin polaron in a two-dimensional antiferromagnet: From a local singlet to a complex quasiparticle

We set forth basic theoretical ideas concerning the spin-polaron scenario for charge excitations in a two-dimensional antiferromagnet. A distinctive feature of the approach being developed consists in considering a local polaron (rather than a bare hole) as a zero approximation for the quasiparticle. At the next step, this excitation is dressed in antiferromagnetic spin waves to form a polaron of intermediate (or infinite) radius. The method allows us to continuously describe the transition from zero to finite temperatures and to consider a wide doping range. Our approach accounts for the main results of ARPES experiments in a CuO₂ plane.     

Dynamics of the two-dimensional Heisenberg antiferromagnet in an external magnetic field

In this paper we study the dynamics of the two-dimensional Heisenberg antiferromagnet in an external magnetic field at zero temperature, using the memory function formalism. The imaginary part of the memory function, which is related to the damping, shows a one peak structure. The dynamical structure factor shows a smooth peak well defined separated from another very small peak.     

Relativistic fermion in a spherically symmetric potential well of finite depth in a two-dimensional space

The problem of existence of bounded relativistic fermion states in a spherically symmetric well of finite depth in a two-dimensional space is investigated. The well depth critical for the appearance of standard states with energies E = m, 0, and –m is determined; moreover, cases with zero and nonzero fermion momenta are considered. Approximate analytical expressions for the critical depths of narrow and wide wells are derived which are in good agreement with the results of numerical calculations. Approximate energies of levels located on the boundaries of the upper and lower continuums and determined analytically are in good agreement with the results of numerical calculations.     

Dynamics of a spherically symmetric inhomogeneous coupled dark energy model with coupling term proportional to non relatvistic matter

The quasi-local scalar variables approach is applied to a spherically symmetric inhomogeneous Lemaître–Tolman–Bondi metric containing a mixture of non-relativistic cold dark matter and coupled dark energy with constant equation of state. The quasi-local coupling term considered is proportional to the quasi-local cold dark matter energy density and a quasi-local Hubble factor-like scalar via a coupling constant \(\alpha \). The autonomous numerical system obtained from the evolution equations is classified for different choices of the free parameters: the adiabatic constant of the dark energy w and \(\alpha \). The presence of a past attractor in a non-physical region of the energy densities phase-space of the system makes the coupling term non physical when the energy flows from the matter to the dark energy in order to avoid negative values of the dark energy density in the past. On the other hand, if the energy flux goes from dark energy to dark matter, the past attractor lies in a physical region. The system is also numerically solved for some interesting initial profiles leading to different configurations: an ever expanding mixture, a scenario where the dark energy is completely consumed by the non-relativistic matter by means of the coupling term, a scenario where the dark energy disappears in the inner layers while the outer layers expand as a mixture of both sources, and, finally, a structure formation toy model scenario, where the inner shells containing the mixture collapse while the outer shells expand.     

Synergistic polaron formation in the Hubbard-Holstein model at small doping

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.     

Higher dimensional spherically symmetric inhomogeneous cosmological model with heat flow

We study spherically symmetric inhomogeneous cosmological model with heat flow in higher dimensional space-time and present a class of solutions in which the velocity field is shear-free. Some of these solutions are analogous to the known solutions in 4-dimension while some are totally new.     

Stability of the two-dimensional Fermi polaron

A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity and fermions is given in terms of two-body point interactions whose strength is determined by the two-body binding energy, which is a free parameter of the model. If the mass of the impurity is 1.225 times larger than the mass of a fermion, it is shown that the energy is bounded below uniformly in the number N of fermions. This result improves previous, N-dependent lower bounds, and it complements a recent, similar bound for the Fermi polaron in three space dimensions.     

Redistribution of the hole spectral weight due to longrange spin correlations in the three-band Hubbard model

The spectrum of the spin-polaron hole exitation is investigated in the framework of the three-band model for the CuO₂ plane in hightemperature superconductors. The problem is treated taking into account the coupling of a local polaron with the antiferromagnetic spin wave with Q=(≈,≈). This leads to fundamental changes in the lowest polaron band ε₁(k) and to a strong redistribution of the bare electron filling. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 173–177 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

A two-dimensional model associating fluid with spherically symmetric intracore square-well shell. Integral equations and Monte Carlo simulation study

The structure and thermodynamics of a monolayer of an associating fluid in the framework of the primitive model of Cummings and Stell is studied by using a two-dimensional approximation. The model permits formation of dimer species for small values of the bonding length parameter, the formation of chains, if the bonding length is slightly larger, and also the vulcanization of species for bonding length values close to the diameter of particles. The structure and thermodynamics of the model that are of interest for statistical mechanics of surface chemical reactions, are studied by computer simulations in the canonical, grand canonical and isobaric ensembles and from the two-dimensional Ornstein—Zernike-like or Wertheim's Ornstein—Zernike integral equation. We have shown that the theory is satisfactory for the case of dimerization if the fluid density is low. For higher densities one must apply a correction for the cavity distribution functions to describe the fraction of unbonded species more adequately. For the case of chain formation the theory just resembles trends following from the simulation data. For the model with vulcanization of species we have obtained the fractions of differently bonded particles and have shown that chemical ordering of species is manifested in the antiphase oscillations of the pair distribution functions of species.     

Geometric inequalities in spherically symmetric spacetimes

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.     

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

Communicated by S.-T. Yau     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.     

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

We show that global asymptotically flat singularity-free solutions of the spherically symmetric Vlasov-Einstein system exist for all initial data which are sufficiently small in an appropriate sense. At the same time detailed information is obtained concerning the asymptotic behaviour of these solutions. A key element of the proof which is also of intrinsic interest is a local existence theorem with a continuation criterion which says that a solution cannot cease to exist as long as the maximum momentum in the support of the distribution function remains bounded. These results are contrasted with known theorems on spherically symmetric dust solutions.