Simulation of the coherent excitation of molecules by laser radiation is carried out. It is based on simple models, i.e., quantum systems with N + 1 energy level. The exact solution of differential equations describing the process in terms of the simplest semi-classical Rabi model is obtained without integration of differential equations but using discrete mathematics with Fourier transform and discrete orthogonal polynomials. The Fourier transform realizes the transition from continuum t-space with time-dependent probability amplitudes an(t) of a quantum system to discrete Fourier space where Fourier spectra Fn(ω) are spectral images of an(t). The spectra are shown to be described by some discrete orthogonal polynomial sequence corresponding to the quantum system. The example shows how using specially constructed polynomials one can calculate the Fourier spectra and find the probability amplitudes an(t) describing the excitation of a quantum system. The established one-to-one correspondence between the polynomial characteristics and the coefficients of differential equations allows us to calculate all the characteristics of quantum systems whose excitation is described by the solution. Thus, the transition from functions an(t) to their spectral space allows one to solve some dynamic equations without integration reducing the problem to calculating the finite sum from 0 to N.

A method to build various integrable models for description of coherent excitation of multilevel media by laser pulses is suggested. Distribution functions over the energy levels of quantum systems depending on the time and frequency detuning are obtained. The distributions follow from Schrödinger equation exact solutions and give the complete dynamical description of laser-excited quantum multilevel systems. Interpretation based on the Fourier spectra of the probability amplitudes of a quantum system is presented. The spectra are expressed in terms of orthonormal polynomials and their weight functions. Matrix elements of the dipole transitions between levels are equal to coefficients of the recurrence formula for the orthonormal polynomial system. Some examples are presented. The Kravchuk oscillator family as an integrable model is constructed to describe the coherent excitation dynamics of multilevel resonance media. It is based on the use of the Kravchuk orthogonal polynomials. The Kravchuk oscillator excitation dynamics is described by the binomial distribution of energy level populations and the distribution parameter depends on excitation conditions. Two known basic models in quantum physics – the harmonic oscillator and two-level system are the special representatives of the Kravchuk oscillator family.

Protonation of a free-base meso-pyrimidinyl-substituted AB(2)-corrole (H(3)AB(2)) in ethanol solution by stepwise addition of sulfuric acid has been studied in the temperature range from 293 to 333 K. The formation rate of protonated species was found to depend profoundly on the temperature at which the titration was undertaken. Two steps in the titration curve were identified at temperatures around 293-298 K, whereas one-step formation of protonated species was found to occur at temperatures above 308 K. The protonation product was the same in both cases, i.e., H(4)AB(2)(+) corrole, protonated at the macrocycle core nitrogen atoms. The two steps in the protonation kinetics at lower temperatures were attributed to protonation of individual tautomers of the free-base H(3)AB(2) corrole. To the best of our knowledge, this is the first well-illustrated (spectrophotometric) observation of individual properties of corrole NH tautomers in fluid solution. Concomitant increase in the NH tautomerization rate with increasing temperature is proposed to account for the one-step protonation. Evidences for the role of individual corrole NH tautomers in the protonation process as well as their optical features are discussed based on spectroscopic results and simulation data.

The absorption spectra of 10-(4,6-dichloropyrimidin-5-yl)-5,15-dimesitylcorrole have been studied in 15 solvents. The formation of deprotonated corrole species was found to account for the dramatic changes in the absorption spectra in several solvents. Careful analysis of the relationship between the formation of deprotonated species and solvent properties results in the conclusion that there is no single solvent parameter correlation, and either multiparameter correlations or specific solute-solvent interactions (preferential solvation of the most acidic NH tautomer or perturbation of intramolecular hydrogen bonding in the macrocycle core) should be considered. The fluorescence properties of the deprotonated pyrimidinylcorrole are also reported for the first time and compared to those of free-base and protonated species.

In the method with the use of integral transform with orthogonal polynomials to construct exact analytical solutions for dynamics of quantum multilevel systems in laser field algorithm is presented to solve dynamical equations describing excitation by laser pulse with an arbitrary prescribed form. Examples of solutions are given. It is justified that orthogonal polynomials are adequate and natural instruments for analytical investigation of the dynamics of multilevel quantum systems since orthogonal polynomials and probabilities amplitudes of dynamical equations are connected to one another with Fourier transform. A brief survey of the theory of q-calculus, the theory of special q-functions and orthogonal q-polynomials as special cases of basic hypergeometric functions is given. Certain orthogonal q-polynomials being q-deformed analogues of classical orthogonal polynomials are presented. Orthogonal q-polynomials are promising mathematical structures for constructing new multilevel quantum systems and for obtaining exact analytical solutions describing their coherent dynamics in laser fields and for other physical problems as well.

An effective method to obtain exact analytical solutions of dynamical equations for multilevel quantum systems in high-power laser fields is presented. The method is based on the use of integral transforms with orthogonal polynomials. Exact solutions are obtained that describe excitation dynamics of various multilevel models with different position of energy levels, with various dependence of dipole moment functions on energy. These models describe laser coherent control of molecular populations. It is necessary for the development the methods of laser controlling chemical reactions

Background: Elevated serum levels of the cell adhesion molecule E-cadherin have been associated with the presence of tissue injury and inflammation. We compared soluble E-cadherin response during laparoscopic and open cholecystectomy. Methods: The E-cadherin response to surgery was studied in 16 patients undergoing laparoscopic cholecystectomy and 12 patients undergoing open cholecystectomy. Serum E-cadherin levels were measured by an enzyme immunoassay (ELISA) preoperatively, 10 and 30 min after the commencement of surgery, and at 6 and 24 h following the operation. Results: Serum E-cadherin levels decreased progressively during laparoscopic cholecystectomy; their concentrations at 24 h after surgery were significantly lower when compared with preoperative values. In the open cholecystectomy group, serum E-cadherin levels did not differ from preoperative values at any time point. Serum E-cadherin concentrations at 24 h after surgery and the cumulative E-cadherin response were significantly higher in the open cholecystectomy group than in the laparoscopic group. Conclusion: Compared with open cholecystectomy, the cumulative E-cadherin response is significantly reduced following laparoscopic cholecystectomy.

An excitation dynamics of new quantum systems of N equidistant energy levels in a monochromatic field has been investigated. To obtain exact analytical solutions of dynamic equations an analytical method based on orthogonal functions of a real argument has been proposed. Using the orthogonal Legendre functions we have found an exact analytical expression for a population probability amplitude of the level n. Various initial conditions for the excitation of N-level quantum systems have been considered.

Analytical solutions of the equations describing coherent dynamics of various multilevel systems excited by radiation are given. The peculiarities of dynamics related with detuning from resonance, with arrangement and amount of levels, with dipole moment dependence on level number, along with excitation in a pulse laser field are studied.

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete analogues. All the obtained solutions are expressed by way of special or elementary functions.

The coherent mechanism of ultrafast state-selective excitation of atoms and molecules is presented by a theoretical simulation. To excite a molecule into a target vibrational level high-power picosecond pulses are necessary in the infrared area. This mechanism can be used to excite an atom in the target state by subpicosecond laser pulses in the visible region. Some pulses with different frequencies and powers can be used to reach a target.

Theoretical calculations of atom excitation dynamics by powerful (about 10 MW/cm 2 ) pico- and femtosecond laser pulses demonstrate that efficient and selective population of the desired atomic level is achieved. The conditions and the value for the maximum population degree of a desired level have been found. The mechanism of the ultrafast coherent excitation under study is able to shift 90% of lithium atoms to the 3d-level and 50% of rubidium atoms to the 7s-level. This mechanism is a convenient tool for preparing notable quantities of atoms in the required state.

The paper presents the results of investigations on excitation of multilevel molecular systems in the laser radiation field. For a number of systems consisting of a finite number of equidistant levels, total population inversion is achieved at some time instants under resonant excitation: all the particles assemble in the upper level. Under nonresonant action, self-confinement of the system excitation is achieved: the upper region of levels remains always empty, the dimensions of this region depend on the frequency detuning. If the dipole moment function grows faster than the corresponding harmonic oscillator function (∼√n), then under nonresonant excitation there exists a finite region of frequency detunings where the nonresonant self-confinement of excitation is absent. The excitation confinement associated with nonresonant conditions is compensated by a rapid growth of the function of transition dipole moments of the system. If the dipole moment of one of consecutive transitions is considerably less than that of the remaining ones, then the system, naturally, is locked, the particles stay in the lower region of the energy spectrum. If the dipole moment of one of the transitions is considerably higher than that of the rest, locking also occurs: the particles cannot transfer through the allowed transition. Frequent use of an N-level system as a molecular model with a complicated energy spectrum is justified by the presence of this effect. Multilevel molecular models demonstrate a variety of features of coherent excitation dynamics in powerful laser fields.

In principle, a possibility has been shown to excite an atom on the target level selectively and very fast with the use of high-power laser pulses. For this aim the effect of ultrafast selective excitation which was revealed earlier for vibrational levels of a molecule can be used. The example Li atom is considered. Some pulses with different frequencies should be used to excite an atom on high energy levels.

A method based on the use of integral transform and orthogonal polynomials is presented to obtain the analytic solutions of the equations for coherent dynamics of multilevel quantum systems as simple molecular models describing molecule-radiation interactions in the high-power laser field and many other processes. As an example the Jacobi polynomials have been used and exact analytic solution has been obtained for dynamics of the family of multilevel Jacobi systems with both equidistant and nonequidistant energy levels, with various dependencies of dipole transition moments on energy, with both resonant and non-resonant laser excitation. Some special cases of the solution for definite systems from the family are given.

A problem of multiphoton excitation by IR laser radiation was solved for systems with the dipole moment increasing with the level number as mu(n-1,n) = mu(0,1){5n (n + 2) chi1 (b) chi(n-1) (b)/(2n + 1) (2n + 3) chi0 (b) chin(n) (b)}1/2, where b greater-than-or-equal-to 1 and chi(n) (b)=P(n)(b)/P(n+2) (b) is Legendre polynomial ratio. The solution for any system with parameter 1 less-than-or-equal-to b < infinity was found to be the sum of solutions for systems with parameter value b=1 and infinity.