Infinitely improvable upper bounds in the theory of polarons

An infinite convergent sequence of improving non-increasing upper bounds to the low-lying branch of the slow-moving "physical" Fröhlich polaron ground-state energy spectral curve, adjacent to the ground state energy of the polaron at rest, was obtained by means of generalized variational method. The proposed approach is especially well-suited for massive analytical and numerical computations of experimentally measurable properties of realistic polarons, such as inverse effective mass tensor and excitation gap, and can be elaborated even further, without major alterations, to allow for treatment of multitudinous polaron-like models, those describing polarons of various sorts placed in external magnetic and electric fields among them

Method of intermediate problems in the Fröhlich polaron model

Method of intermediate problems in the theory of linear semi-bounded self-adjoint operators on rigged Hilbert space was applied to the investigation of the ground state energy of the Fröhlich polaron model. It was shown that various infinite sequences of non-decreasing improvable lower bound estimates for the polaron ground state energy can be derived for arbitrary values of the electron-phonon interaction constant. The proposed approach allows for explicit numerical evaluation of the thus obtained lower bound estimates at all orders and can be straightforwardly generalized for investigation of the low-lying branch of the slow-moving polaron excitation energy spectral curve adjacent to the ground state energy of the polaron at rest. In conjunction with numerous, already derived by multitudinous methods, well-known upper bound estimates for the energy spectral curve of the Fröhlich polaron as a function of the electron-phonon interaction constant and the polaron total momentum, the aforesaid improvable lower bound estimates might provide one with virtually precise magnitude for the energy of the slow-moving polaron

Method of intermediate problems in the Fröhlich polaron model

Method of intermediate problems in the theory of linear semi-bounded self-adjoint operators on rigged Hilbert space was applied to the investigation of the ground state energy of the Frohlich polaron model. It was shown that various infinite sequences of non-decreasing improvable lower bound estimates for the polaron ground state energy can be derived for arbitrary values of the electron-phonon interaction constant. The proposed approach allows for explicit numerical evaluation of the thus obtained lower bound estimates at all orders and can be straightforwardly generalized for investigation of the low-lying branch of the slow-moving polaron excitation energy spectral curve adjacent to the ground state energy of the polaron at rest. In conjunction with numerous, already derived by multitudinous methods, well-known upper bound estimates for the energy spectral curve of the Frohlich polaron as a function of the electron-phonon interaction constant and the polaron total momentum, the aforesaid improvable lower bound estimates might provide one with virtually precise magnitude for the energy of the slow-moving polaron.Метод промiжних задач в теорiї лiнiйних напiвобмежених самоспряжених операторiв у пристосованому просторi Гiльберта використовується для дослiдження енергiї основного стану в моделi полярона Фрьолiха. Показано, що для довiльних значень константи електрон-фононної взаємодiї можуть бути отриманi рiзнi безмежнi неспаднi послiдовностi оцiнок знизу для енергiї основного стану полярона. Запропонований пiдхiд дозволяє отримати точнi числовi оцiнки знизу у всiх порядках i може бути узагальнений для вивчення нижньої гiлки енергетичного спектру збуджених станiв повiльного полярона, що межує з енергiєю основного стану нерухомого полярона. В комбiнацiї з iншими добре вiдомими пiдходами до оцiнки зверху залежностей енергетичного спектру полярона Фрьолiха вiд константи електрон-фононної взаємодiї i повного iмпульсу полярона вищезгаданi оцiнки з уточненням знизу можуть забезпечити знаходження практично точних значень для енергiї полярона, що повiльно рухається

Infinitely improvable upper bounds in the theory of polarons

An infinite convergent sequence of improving non-increasing upper bounds to the low-lying branch of the slowmoving “physical” Frohlich polaron ground-state energy spectral curve, adjacent to the ground state energy of the polaron at rest, was obtained by means of generalized variational method. The proposed approach is especially well-suited for massive analytical and numerical computations of experimentally measurable properties of realistic polarons, such as inverse effective mass tensor and excitation gap, and can be elaborated even further, without major alterations, to allow for treatment of multitudinous polaron-like models, those describing polarons of various sorts placed in external magnetic and electric fields among them.За допомогою узагальненого варіаційного методу одержано нескінченнозбіжну послідовність покращених незростаючих верхніх меж до низьколежачої гілки спектральної кривої "фізичного" полярона Фроліха в основному енергетичному стані, що повільно рухається, і яка є прилеглою до основного енергетичного стану полярона в спокої. Запропонований підхід особливо підходить для громіздких аналітичних і числових обчислень експериментально вимірюваних властивостей реалістичних поляронів, таких як тензор оберненої ефективної маси та щілина збуджень, та його можна розвинути навіть далі, без значних змін, для опису численних поляроноподібних моделей, зокрема таких, які описують полярони різних сортів, розміщених у зовнішніх магнітних та електричних полях

On the Widder inversion method in problems of statistical mechanics

An alternative way of reconstructing a function from its Laplace transform using the Widder inversion method was shown to be useful in treating some problems of nonequilibrium statistical mechanics. As an example of a successful application of the method, a decay was investigated of the excited atomic state in a simple, but nonetheless physically relevant, model featuring a two-level atom interacting with a continuum of field modes.Показано, що альтернативний спосіб відновлення функції за її образом Лапласа, відомий як метод оберненого перетворення Уіддера, може бути корисним при розв’язуванні деяких проблем нерівноважної статистичної механіки. Як приклад успішного застосування цього підходу розглянуто процес релаксації збудженого стану атома у простій, але фізично змістовній моделі, яка описує взаємодію дворівневого атома з полями в континуальній границі

Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field

Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can only confine a finite number of excess electrons thus forming a realistic model of a QD with smooth interface between the QD and its embedding environment. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus resulting in an efficient tool for analytical and numerical studies of the energy spectrum and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons, with controllable or prescribed precision

Performance of a fine-sampling electromagnetic calorimeter prototype in the energy range from 1 to 19 GeV

The fine-sampling electromagnetic calorimeter prototype has been experimentally tested using the 1-19 GeV/c tagged beams of negatively charged particles at the U70 accelerator at IHEP, Protvino. The energy resolution measured by electrons is Delta{E}/E=2.8%/\sqrt{E} + 1.3%. The position resolution for electrons is Delta{x}=3.1 + 15.4/sqrt{E} mm in the center of the cell. The lateral non-uniformity of the prototype energy response to electrons and MIPs has turned out to be negligible. Obtained experimental results are in a good agreement with Monte-Carlo simulations.Comment: Article is prepared for pdflatex using the class elsart. 13 pages, 9 figures in 11 PDF file

RESEARCH OF ORAL MUCOSA REGENERATION AFTER FRACTIONAL TREATMENT BY DIODE LASER WITH 980 NM WAVELENGTH

Subject of Research. The paper presents the study of the oral mucosa reaction of experimental animals to fractional laser treatment by diode laser radiation with a wavelength of 980 nm.Methods. A single fractional laser treatment of oral mucosa was carried out in the experiment on Wistar laboratory rats at different exposure regimes: combinations of laser power from the range Р = 5-15 W, pulsewidth tp = 100-120 ms and the filling factor. The animals were taken out of the experiment immediately after exposure, on the 5th, 7th and 28th day after the treatment. For histological evaluation mucosal preparations were stained with hematoxylin and eosin, as well as aniline blue according to Masson. Thickness of mucosa layers and concentration of collagen fibers were defined as a result of computer processing of images of histological samples. Main Results. It was established that the mucous condition depends significantly on the laser treatment regime and the time elapsed since the fractional treatment. When exposed to pulsed laser radiation with P = 5 W, tp = 100 msor P = 7 W, tp = 120 ms,at the filling factor F = 200±50 microdamages/cm2 the mucous regeneration has been completed on the 28th day after treatment, and for the other studied regimes it continues. After regeneration the thickness of the epithelial layer of the oral mucosa is less, and the thickness of the submucosal layer with lamina propria of mucosaand concentration of collagen fibers in the mucosa correspond to control. Practical Relevance. The obtained results are promising for further research on the reconstruction of thinning oral mucosa

Nonequilibrium phase transitions induced by multiplicative noise: effects of self-correlation

A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise leading to the transition is colored. Within an effective Markovian approximation and a mean-field scheme it is found that when the self-correlation time of the noise is different from zero, the transition is also reentrant with respect to the spatial coupling D. In other words, at variance with what one expects for equilibrium phase transitions, a large enough value of D favors disorder. Moreover, except for a small region in the parameter subspace determined by the noise intensity and D, an increase in the self-correlation time usually preventsthe formation of an ordered state. These effects are supported by numerical simulations.Comment: 15 pages. 9 figures. To appear in Phys.Rev.

From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors

The Ettore Majorana paper - Theory of incomplete P triplets- published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism to be publishe