ТЕОРИЯ БЕЗИЗЛУЧАТЕЛЬНОЙ РЕКОМБИНАЦИИ ЭЛЕКТРОНОВ НА ДЕФЕКТАХ РЕШЕТКИ В ПОЛЯРНЫХ КРИСТАЛЛАХ

Разработана однофононная теория безизлучательной рекомбинации электрона на дефектах решетки в полярных кристаллах. Гамильтониан системы электрон + дефект решетки + поле фононов, подходящим унитарным преобразованием переводится к гамильтониану, диагональные элементы которого отвечают двум независимым системам; одна из них совпадает с поляроном в неадиабатическом приближении, движущимся в поле дефекта решетки, и вторая отвечает ?свободным“ фононам, т. е. фононам, не участвующим при движении полярона. Недиагоналвные элементы отвечают взаимодействию этих систем вблизи от дефекта решетки. Этот последний член рассматривается как возмущение, вызывающее переход полярона из непрерывного спектра в дискретное возбужденное состояние в дефекте решетки. Рассматриваемый переход интерпретируется как безизлучательная рекомбинация. Вычислен коэффициент рекомбинации и температурная зависимость эффективного сечения рекомбинации на дефектах решетки кулоновского типа в кристалле.     

Singlet triplet-triplet-triexcitons in organic molecular crystals

A theory on the formation of triexcitons consisting of one singlet exciton and two triplet excitons is developed by considering exciton-exciton dynamical interactions. The conditions for the existence of the singlet-triplet-triplet-triexciton bound states are established and discussed.     

A simple and direct periodic solution of the Korteweg-de vries equations

The solutionq(x, t) of one of the KdV hierarchy is assumed to be a potential in the Schrödinger equation as usual. We differentiate this equation with respect to the time variable and solve it with the aid of the Green function. The obtained equation relatesw _t (x, t, λ)=φ _t (x + c, x, t, λ) withq _t (x, t). The functionφ(x, x ₀,t, λ) obeys the Schrödinger equation and the boundary conditionsφ(x ₀,x ₀,t, λ)=0,φ _x (x ₀,x ₀;t, λ)=1. The shiftingc is equal to the period. We differentiatew _t (x, t, λ) three times with respect to thex coordinate and obtain the time derivative of the Milne equation. The integration of this equation with respect tox allows to solve simply the inverse problem. The reconstructed periodic potential is given by means of the well known formula for the root functions ofw(x, t, λ). The time behaviour of this function, i.e. the solution of the KdV equation, is obtained when one replacesq _t (x, t) by an expression of the KdV hiearchy in the relation betweenq _t (x, t) andw _t (x, t, λ) and transforms it. We estimated also the limit, whenc → ∞, i.e. the possible relation of the periodic solutions with the soliton ones.     

New relations for the general oscillator brackets

Some new relations for the general oscillator brackets are derived on the basis of the explicit formulae, which have been given recently by the author. By means of these relations and the derived relation between two triads of the oscillator brackets a new explicit formula is also presented.     

The diffusion and non-radiative transfer of excitation energy in molecular crystals containing foreign molecules

A study is made of the non-radiative transfer and diffusion of excitation energy in molecular crystals containing foreign molecules and its influence on the luminescent properties of these crystals.

---

,

, .

     

Large tilting modules and representation type

We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (infinite dimensional) tilting module W that generates the divisible modules. Finally, we extend to the wild case some results on Baer modules and torsion-free modules proven in Angeleri Hügel, L., Herbera, D., Trlifaj, J.: Baer and Mittag-Leffler modules over tame hereditary algebras. Math. Z. 265, 1–19 (2010) for tame hereditary algebras.     

Brown Representability Test Problems in Locally Grothendieck Categories

Open questions concerning Brown representability have recently led Rosicky and Muro to formulate two test problems for Grothendieck categories. We prove that these test problems have a negative solution in the locally Grothendieck category C = è_{k 3 à0} Mod-K^k\mathcal C = \bigcup_{\kappa \geq \aleph_0} {\mbox{\rm{Mod}--}K^{\kappa}} where K is a field.