Phonon-Assisted Photoluminescence in a Spherical Nanocrystal

Using the matrix density in the representation of path integrals for an electron, the multiphoton nonlinear absorption light coefficient in the second order of interaction energy with polar optical phonons is derived. This coefficient describes any electron interaction mechanism with phonons. From the interaction mechanism, the main role is played by dimensional resonance when the electron continuously absorbs energy from the field as a result of synchronizing its oscillation with the field. This dimensional resonance is possible when the frequency characterizing the laser field is a multiple of the phonon frequency. Whether a photon is absorbed or emitted, the initial level from where the transition occurs defines the temperature dependence. The absorption spectrum has the form of stripes whose intensity depends on the resonance character. The most pronounced absorption is at the triple resonance, where values of radiation and oscillatory and optical phonon frequencies are equal

Polaron in a quasi 1D cylindrical quantum wire

Polaron states in a quasi 1D cylindrical quantum wire with a parabolic confinement potential are investigated applying the Feynman variational principle. The effect of the wire radius on the polaron ground state energy level, the mass and the Frohlich electron-phonon-coupling constant are obtained for the case of a quasi 1D cylindrical quantum wire. The effect of anisotropy of the structure on the polaron ground state energy level and the mass are also investigated. It is observed that as the wire radius tends to zero, the polaron mass and energy diverge logarithmically. The polaron mass and energy differ from the canonical strong-coupling behavior by the Frohlich electron-phonon coupling constant and the radius of the quasi 1D cylindrical quantum wire that are expressed through a logarithmic function. Moreover, it is observed that the polaron energy and mass for strong coupling for the case of the quasi 1D cylindrical quantum wire are greater than those for bulk crystals. It is also observed that the anisotropy of the structure considerably affects both the polaron ground state energy level and the mass. It is found that as the radius of the cylindrical wire reduces, the regimes of the weak and intermediate coupling polaron shorten while the region of the strong coupling polaron broadens and extends into those of the weak and intermediate ones.За допомогою варіаційного принципу Фейнмана вивчаються стани полярона в квазіодновимірному циліндричному квантовому дроті з параболічним обмеженим потенціалом. Досліджується вплив радіуса дроту на енергетичний рівень основного стану полярона, масу і електрон-фонон постійну зв’язку Фрьоліха. Також вивчається ефект анізотропії структури на енергетичний рівень основного стану полярона і його масу. Виявлено, що якщо радіус дроту прямує до нуля, маса і енергія полярона розбігаються логарифмічно. Маса і енергія полярона відрізняються від канонічної поведінки сильного зв’язку на електрон-фонон постійну зв’язку Фрьоліха і на радіус квазіодновимірного циліндричного квантового дроту, які виражаються через логарифмічну функцію. Більше того, спостережено, що енергія та маса полярона для випадку квазіодновимірного циліндричного квантового дроту є більшими, ніж для випадку об’ємних кристалів. Також виявлено, що анізотропія структури сильно впливає на енергетичний рівень основного стану полярона та його масу. Знайдено, що якщо радіус циліндричного дроту зменшується, режими слабкого та середнього зв’язку полярона скорочуються, тоді як область сильного зв’язку полярона розширюється. Отримано аналітичні вирази для енергетичного рівня основного стану полярона і для його маси для випадку сильного зв’язку поляронів

Polaron in a quasi 1D cylindrical quantum wire

Polaron states in a quasi 1D cylindrical quantum wire with a parabolic con-finement potential are investigated applying the Feynman variational prin-ciple. The effect of the wire radius on the polaron ground state energy level, the mass and the Fröhlich electron-phonon-coupling constant are obtained for the case of a quasi 1D cylindrical quantum wire. The effect of anisotropy of the structure on the polaron ground state energy level and the mass are also investigated. It is observed that as the wire radius tends to zero, the polaron mass and energy diverge logarithmically. The polaron mass and energy differ from the canonical strong-coupling behavior by the Fröhlich electron-phonon cou-pling constant and the radius of the quasi 1D cylindrical quantum wire that are expressed through a logarithmic function. Moreover, it is observed that the polaron energy and mass for strong coupling for the case of the quasi 1D cylindrical quantum wire are greater than those for bulk crystals. It is also observed that the anisotropy of the structure considerably affects both the polaron ground state energy level and the mass. It is found that as the radius of the cylindrical wire reduces, the regimes of the weak and inter-mediate coupling polaron shorten while the region of the strong coupling polaron broadens and extends into those of the weak and intermediate ones. Analytic expressions for the polaron ground state energy level and mass are derived for the case of strong coupling polarons. Key words: polaron, polaron energy, polaron mass, parabolic confinement, Fröhlich electron-phonon coupling constant, quantum wir

An investigation of string-like cooperative motion in a strong network glass-former

The presence of string-like cooperative motion in silica, a strong network glass former, is investigated using large scale molecular dynamics simulations based on a realistic potential. We observe that dynamical heterogeneities and string-like motion in this strong glass-former show similarities with the results obtained by Donati et al. on a fragile model system. We observe that silicon and oxygen atoms are heterogeneously moving in a string-like fashion on different time scales corresponding to the maximum of their respective non-Gaussian parameter. We observe that the average string length increases when the temperature decreases. This result suggests that the length of the strings is not the determinant parameter for discriminating strong from fragile glass formers. We also observe that in silica the excess of cooperativity of mobile atoms is entirely due to the string-like motion of some of them. Copyright Springer-Verlag Berlin/Heidelberg 2004

A molecular dynamics investigation of dynamical heterogeneity in supercooled water

We investigate the presence of dynamical heterogeneity in supercooled water with molecular dynamics simulations using the new water model proposed by Mahoney and Jorgensen [M.W. Mahoney, W.L. Jorgensen J. Chem. Phys. 112, 8910 (2000)]. Prompted by recent theoretical results [J.P. Garrahan, D. Chandler, Phys. Rev. Lett. 89, 35704 (2002)] we study the dynamical aggregation of the least and the most mobile molecules. We find dynamical heterogeneity in supercooled water and string-like dynamics for the most mobile molecules. We also find the dynamical aggregation of the least mobile molecules. The two kinds of dynamical aggregation appear however to be very different. Characteristic times are different and evolve differently. String-like motions appear only for the most mobile molecules, a result predicted by the facilitation theory. The aggregation of the least mobile molecules is more organized than the bulk while the opposite is observed for the most mobile molecules. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005