A simple model calculation of pion condensation in neutron matter

The charged pion condensed state in pure neutron matter is described analytically in an approximate calculation based on the chirally invariant σ-model. The calculation includes s- and p-wave condensed pion-nucleon interactions, pi-pi interactions, the effect of the N¹ (1236) resonance, and the (Ericson-Ericson Lorentz-Lorentz) effect of nuclear correlations.     

Density functional theory of fermion condensation

A density functional formulation of the fermion condensation is presented. It is demonstrated that the standard Kohn-Sham scheme is not valid beyond the fermion condensation phase transition since the functional starts to depend on the quasiparticle density matrix. Our consideration also furnishes an opportunity to calculate the real single particle excitation spectra of superconducting systems within the density functional theory.     

Toward the theory of fermionic condensation

The diagrammatic technique elaborated by Belyaev for the theory of a Fermi liquid has been implemented to analyze the behavior of Fermi systems beyond the topological phase transition point, where the fermionic condensate appears. It has been shown that the inclusion of the interaction between the condensate and above-condensate particles leads to the emergence of a gap in the single-particle excitation spectrum of these particles even in the absence of Cooper pairing. Hence, the emergence of this gap in homogeneous electron systems of silicon field-effect structures leads to a metal–insulator phase transition rather than to superconductivity. It has been shown that the same interaction explains the nature of the Fermi arc structure in twodimensional electron systems of cuprates.     

A simple quantum chemical theory of dissociative adsorption

Potential energy curves for the adsorption of a hydrogen atom on the (100), (110), (111) and the stepped (311) crystal faces of copper have been calculated in the pairwise additive model for gas atom-solid interactions. A Morse function is used to represent the lowest singlet pairwise H-Cu interaction potential and its parameters are adjusted so that the calculated maximum bond energies conform with the available experimental data. Bond strength on the low index faces is found to increase with the adatom's local coordination number. Except for the edge sites, the steps on the (311) surface strengthen the bonds to sites on the component low index facets. A systematic study of the convergence of the bond energy as a function of the number of solid atoms is reported. The H-Cu(s) potential is shown to be relatively insensitive to changes in the first layer separation distance of the size inferred from experiment. A new model for diatom-solid potentials is proposed in which the diatom-solid potential is expressed as a sum of the differences between diatom-solid atom London-Eyring-Polanyi-Sato three-body potentials and the diatom singlet potential. This model is used to calculate potential curves for various approaches of a hydrogen molecule towards the same copper faces. H₂ is predicted to be physisorbed on each face. The atom-solid and diatom—solid potentials are used in conjunction with a model formulated by Lennard-Jones to estimate activation energies for dissociative adsorption. The correct order is obtained for the activation energies on the low index faces. Substantially lower activation energies are obtained for approaches toward many of the sites on the two low index facets of the (311) surface as compared to the same approaches towards the individual component faces. Dissociative adsorption is predicted to proceed without activation near the steps on this surface. In general, higher activation energies are obtained when the admolecule is perpendicular to the surface or facet in question. The simple idea that the activation energies are determined by small shifts of the atomic potential relative to the less structure-sensitive molecular potential works well for the low index faces, but is not wholly satisfactory for the stepped (311) surface. All results reported in this paper are negligibly different from those that are fully converged with respect to cluster size in the present model.     

Quasiparticles in the theory of fermion condensation

It is shown that Landau’s quasiparticle formalism continues to work in systems with a fermion condensate. In the case of a finite system this formalism is suitable for describing the restructuring of states at the Fermi surface. It also works in an infinite system, and the idea of quasiparticles at low temperature as well-defined excitations at the Fermi surface remains valid. The quasiparticle lifetime is directly proportional to the temperature, and the density of states is inversely proportional to the temperature. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 719–723 (10 May 1996)     

Crossover from BCS superconductivity to Bose-Einstein condensation: A self-consistent theory

A dilute three-dimensional Fermi liquid is considered with an instantaneous attractive short-range interaction. Two sets of self-consistent equations for the temperature dependent fermion Greens functiong and the four-point vertex function are derived by field theoretic means. The interaction is taken into account using the results of low energys-wave scattering theory. The crossover region between BCS superconductivity and Bose-Einstein condensation of tightly bound pairs is located near the threshold where in the two-particle scattering problem a virtual or quasi-stationary state turns into a bound state. We show how from our self-consistent equations the BCS theory and the theory of a superfluid Bose gas can be recovered in the weak and strong coupling limit, respectively. In the strong coupling limit we find that there is a repulsive interaction between the composite bosons due to the Pauli exclusion principle. It is described by a positive scattering lengtha _B which is twice the scattering length of the fermions,a _B =2a _F . Furthermore we find that this interaction reduces the Bose-Einstein transition temperature to leading order by T _c /T _{c, BE} =–(k _F a _F )³/3. We show that most of the previous theories of the crossover scenario can be obtained from our theory in mean-field approximation neglecting self consistency.     

A simple molecular theory for photo-induced smectic phase

The response of liquid crystals to light is very important for applications of liquid crystals in display and memory devices. Recently experiments have been carried out on liquid crystals doped with photoactive azo compounds. It is seen that UV rays incident on such systems can lower the nematic isotropic transition temperature T _NI . Also, in some mixtures, a photo-induced smectic phase is observed. This is attributed to the change in the trans (longer) isomer to cis (shorter) isomer of the photoactive dopant. We have earlier developed a molecular mean-field model assuming the medium to consist of inter-converting anti-parallel and parallel pairs to explain the molecular origin of “two lengths”. The model was used to explain double re-entrance, the effect of electric field on T _NI , etc. This model is modified to include the change of trans to cis isomer which is equivalent to an increase of fraction of parallel (shorter) pairs. The calculated phase diagram with respect to incident UV radiation energy shows an induced smectic phase. This is in qualitative agreement with experimental trends.     

A simple theory of the laser-induced damage in semiconductors

A simple theory is presented for the laser-induced damage in semiconductors in the range of low irradiation intensities. This theory avoids the solution of coupled differential equations, and takes into account characteristic physical properties of semiconductors—i.e. energy gap, carrier lifetime, and surface recombination velocity. The deduced equations permit us to estimate the damage threshold, or the minimum irradiation time required for damage to occur. Comparison is made with some experimental results reported in the literature and a reasonable agreement is found.     

A simple theory of spin-wave relaxation in ferromagnetic metals

The anisotropic exchange interaction between localized spins and conduction electrons is described by an appropriate spin hamiltonian. This is used to calculate the lifetime of magnons for arbitrary values of Λ_eq, where Λ_e is the electron mean free path and q the magnon wavevector. At Λ_eq ? 1, this lifetime depends on the angle between q and the saturation magnetization. The antisymmetric part of anisotropic exchange (Dzialoshinsky-Moriya interaction) may dominate the relaxation of spin-waves of large q. The complicated band structure of transition metals gives rise to a magnon lifetime independent of Λ_e. The contribution of isotropic exchange is also considered.     

Tachyon condensation and open string field theory

We perform canonical quantization of open string on a unstable D-brane in the background of tachyon condensation. Evaluating the Polyakov path-integral on a strip, we obtain a field theoretical propagator in the open string theory. As condensation occurs the string field theory is continuously deformed. At the infrared fixed point of condensation, the open string field on the unstable D-brane transmutes to that on the lower-dimensional D-brane with the correct D-brane tension.     

More accurate theory for Bose-Einstein condensation fraction

Bose-Einstein statistics is derived in the thermodynamic limit when the ratio of system size to thermal de Broglie wavelength goes to infinity. However, according to the experimental setup of Bose-Einstein condensation of harmonically trapped Bose gas of alkali atoms, the ratio near the condensation temperature (To) is 30-50. And, at ultralow temperatures well below To, this ratio becomes comparable to 1. We argue that finite size as well as the ultralow temperature induces corrections to Bose-Einstein statistics. From the corrected statistics we plot condensation fraction versus temperature graph. This theoretical plot satisfies well with the experimental plot [A. Griesmaier et al., Phys. Rev. Lett. 94 (2005) 160401].     

Stochastic approach to the kinetic theory of condensation

The nonequilibrium statistical operator method in conjunction with the theory of physical FrenkelBand groups is used to derive a stochastic equation that describes the kinetics of nucleation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 139–142, June, 1977.     

Evolution of species from Darwin theory: A simple model

Evolution of species is a complex phenomenon. Some theoretical models take into account evolution of species, like the Bak–Sneppen model that obtain punctuated equilibrium from self-organized criticality and the Penna model for biological aging that consists in a bit-string model subjected to aging, reproduction and death. In this work we propose a simple model to study different scenarios used to simulate the evolution of species. This model is based on Darwin’s ideas of evolution. The present findings show that punctuated equilibria and stasis seem to be obtained directly from the mutation, selection of parents and the genetic crossover, and are very close to the fossil data analysis.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Interstitialcy theory of simple condensed matter

A simple, more physical and compelling version of the Interstitialcy Theory of Simple Condensed Matter than that given previously is provided here. Also, computer simulation and direct and indirect experimental evidence is updated and reviewed. The theory is based on the properties of an interstitial in the interstitialcy, sometimes known as the dumbbell configuration. A free energy is derived, taking account of the unusually large shear susceptibility and vibrational entropy of the dumbbell to find the thermodynamic and kinetic properties of simple liquids and glasses. The connection between theory and experiment for some of the more notable properties of simple condensed matter found later is also discussed. The direct visual observation of interstitial diffusion to the surface in platinum near 20 K in irradiated thin films by Morgenstern et al. [M. Morgenstern, T. Michely, G. Comsa, Phys. Rev. Lett. 79, 1305 (1997)] is found to be sufficient compelling evidence for the interstitialcy theory.     

Development of band patterns in surface films: A simple theory

Semiconductor technology often employs thin films deposited on crystal surfaces, and in some cases these films can self-organize into band, ring or spiral patterns during annealing. A simple theory is proposed which predicts the stability or instability of such films and, in the case of instability, the band spacing, which depends upon bulk, surface and interfacial free energies. This information could be of use in self-assembly techniques. In some cases, bands condense into particle arrays upon further annealing, and a theoretical model is developed to predict the subsequent evolution of circular band patterns by diffusion, which causes the regular disappearance of alternate bands.     

Field theory of collective excitations III condensation of four-particle clusters

For many fermions with arbitrary two-body forces we investigate the effective action Г[?, α] where ? is the density matrix including pair correlations and α is the four-particle vertex. The physical state including all radiative corrections is obtained by extremizing Г[?, α] with respect to ? and α. Just as ? ≠ 0 corresponds to non-zero density and condensation of pairs, α ≠ 0 signals the presence of a condensate of four-particle clusters. A simple loop expansion is given for Г[?, α]. To lowest order, the extremum amounts to the Hartree-Fock-Bogoliubov equations. The next two steps bring in the four-particle condensate.