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The high-resolution infrared spectra of the H2 32S molecule were recorded with a Bruker IFS 125 HR Fourier transform interferometer in the region of the first hexad. In the present study, high resolution analysis was carried out for the 4ν2 band. Around 400 transitions were assigned in the experimental spectra with the maximum values of quantum numbers Jmax. /Kmax. A=17/8 and 132 upper energy levels were obtained. The weighted fit of experimentally obtained energy levels was made with the Hamiltonian model, which takes into account the resonance interactions between the studied vibrational states. As the result, a set of 28 fitted parameters was obtained which reproduces the original experimental data with the drm=3.5×10−4 cm −1.

The Fourier Transform IR spectra of the v3 band of ClO2 (OClO) have been recorded at 0.0015 cm-1 resolution with essentially Doppler limited resolution at an instrumental linewidth of 0.001 cm−1 using the Zürich prototype ZP2001 Bruker IFS 125 HR Fourier transform infrared spectrometer. Band has been analyzed with an improved effective Hamiltonian and a newly developed computer code for ro-vibrational spectra of open-shell free radical molecules including spin-rotation interactions. More than 4200 transitions belonging to these band have been assigned with Nmax = 21 and Ka max = 68 provide a set of 30 accurate effective Hamiltonian parameters for the ν3 fundamental band.

The problem of constructing alternative Hamiltonian formulations in the extended Chern–Simons theory with higher derivatives is considered. It is shown that the fourth-order extended theory admits a four-parameter series of alternative Hamiltonians which can be bounded from below, even if the canonical energy of the model is unbounded from below.

Most general third-order $3d$ linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the zero-zero components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations., 19 pages

In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field and one-point transition energy field. The former of them, namely the transition energy function, is a generalization of the notion of relative Hamiltonian introduced by Pirogov and Sinai. However, unlike the (relative) Hamiltonian, our objects are defined axiomatically by their natural and physically well-founded intrinsic properties. The developed approach allowed us to give a proper mathematical definition of the Hamiltonian without involving the notion of potential, to propose a justification of the Gibbs formula for infinite systems and to answer the problem stated by D. Ruelle of how wide the class of specifications, which can be represented in Gibbsian form, is. Furthermore, this approach establishes a straightforward relationship between the probabilistic notion of (Gibbs) random field and the physical notion of (transition) energy, and so opens the possibility to directly apply probabilistic methods to the mathematical problems of statistical physics.

This work continues our investigation on the high resolution infrared 13C-enriched spectrum of methane recorded on a Bruker IFS-125HR Fourier transform spectrometer at 80 K in the 4970–6200 cm−1 range. In this paper we report the results of assignment and modelling of the line positions and intensities of 13CH4 in the range between 5471 and 5852 cm−1, corresponding to the middle part of Tetradecad. The analysis was performed using a non-empirical effective Hamiltonian (EH) derived from the ab initio potential energy surface (PES) by high-order Contact Transformations (CT). The EH parameters were empirically optimized during the treatment of experimental data. In total, 3297 lines belonging to nine cold bands of the Tetradecad of 13CH4 were assigned in the 5471–5852 cm−1 range up to Jmax = 11. The 3297 lines included correspond to 91% of the total line number in the region. Among them, 3251 line positions were fitted with an rms deviation of 1.33×10−3 cm−1. Measured line intensities for 1624 transitions were modeled using the effective dipole transition moments approach with an rms deviation of about 9%. Finally, the observed transitions were incorporated to fit simultaneously the 13CH4 Hamiltonian parameters for the {Ground state/Dyad/Pentad/Octad/Tetradecad} system and the dipole moment parameters for the {Ground state - Tetradecad} system.

Eight spectra of normal samples of CH4 in the 3760–4100 cm−1 region were recorded by using a Fourier transform spectrometer in Reims, France at long paths (202 m, 602 m, 1604 m and 1804 m) and different pressures. Additional spectra of 12CH4 covering the same region were obtained at 100 K and very low sample pressures, which was used for low-J line position identification. Line positions and intensities were retrieved by least squares curve-fitting procedures and analyzed using the effective Hamiltonian and the effective dipole. A new measured line list contains positions and intensities for 9000 features. Quantum assignments were made for more than 3500 new transitions, which represent ∼95% of the integrated line intensity observed in this region. The resulting list of lines is much more accurate than the list of lines HITRAN 2016. All assigned 5703 line positions were fitted to RMS standard deviations of 0.0018 cm−1. The sum of observed intensities between 3760 and 4100 cm−1 fell within 2% of the predicted value from ab initio variational calculations reported in the TheoReTS database ( http://theorets.univ-reims.fr ; http://theorets.tsu.ru ).

This paper considers an assignment of the high-resolution Fourier spectra of 15NHD2 molecule in the region of ν6 band. The analysis is based on the combination differences method. As a result of the analysis, the energy structure of inversion-vibrational states (v6=1, s) and (v6=1, a) was obtained. More than 550 vibration-rotation transitions were found and values of about 140 upper vibrational energy levels were determined in total.

The Fourier transform spectrum of CF4 in the 1600–1800 cm−1 was recorded in Reims by using a White-type multi-pass cell to provide a path length of 8.262 m. In the present work, all spectrum analyses and fits were realized using the MIRS software based on tetrahedral tensorial formalism. By combining non-empirical contact transformation Hamiltonians for line positions and ab initio ro-vibrational normal-mode predictions for line intensities, we are able to achieve a simultaneous fit of effective Hamiltonian and dipole moment parameters of several cold and hot bands of CF4. Hamiltonian operator was expanded up to the sixth order for the ground state and for the {ν2+2ν4,ν2+ν3,4ν2,ν1+2ν2,2ν1} pentad. 1831 line positions were fitted to RMS of 1.5X10−3 cm−1. The standard deviation for line intensities for the cold bands {ν2+2ν4,ν2+ν3,4ν2,ν1+2ν2,2ν1} is of 1.1% and of 8% and 5% for the hot band transitions {2ν2+2ν4−ν2,2ν2+ν3−ν2} and {ν2+3ν4−ν4,ν2+ν3+ν4−ν4}, respectively.

The positivity conditions of the relative entropy between two thermal equilibrium states ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{1}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{2}$ are used to obtain upper and lower bounds for the subtraction of their entropies, the Helmholtz potential and the Gibbs potential of the two systems. These limits are expressed in terms of the mean values of the Hamiltonians, number operator, and temperature of the different systems. In particular, we discuss these limits for molecules that can be represented in terms of the Franck--Condon coefficients. We emphasize the case where the Hamiltonians belong to the same system at two different times $t$ and ${t}^{\ensuremath{'}}$. Finally, these bounds are obtained for a general qubit system and for the harmonic oscillator with a time-dependent frequency at two different times.

In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013) 405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015) 031701], representation theory of the centrally extended l-conformal Galilei algebra with half-integer l has been applied so as to construct second order differential equations exhibiting the corresponding group as kinematical symmetry. It was suggested to treat them as the Schrodinger equations which involve Hamiltonians describing dynamical systems without higher derivatives. The Hamiltonians possess two unusual features, however. First, they involve the standard kinetic term only for one degree of freedom, while the remaining variables provide contributions linear in momenta. This is typical for Ostrogradsky's canonical approach to the description of higher derivative systems. Second, the Hamiltonian in the second paper is not Hermitian in the conventional sense. In this work, we study the classical limit of the quantum Hamiltonians and demonstrate that the first of them is equivalent to the Hamiltonian describing free higher derivative nonrelativistic particles, while the second can be linked to the Pais-Uhlenbeck oscillator whose frequencies form the arithmetic sequence omega_k=(2k-1), k=1,...,n. We also confront the higher derivative models with a genuine second order system constructed in our recent work [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212] which is discussed in detail for l=3/2., V2:12 pages,clarifying remarks included into the Introduction and Conclusion, the version to appear in NPB

The absorption spectrum of the 18 O 3 isotopologue of ozone is recorded by CW-Cavity Ring Down Spectroscopy between 7400 and 7920 cm −1 . The typical noise equivalent absorption of the recordings is α min ≈1×10 −10 cm −1 allowing for the detection of extremely weak vibrational bands located only a few % below the dissociation limit. The absorption spectrum also includes the weak 3 A 2 (000)–X(110) hot vibronic band at 7877.53 cm −1 affected by predissociation broadening. Overall, about 1000 lines were rovibrationnally assigned to six vibrational bands. Their line positions were modelled using effective Hamiltonian models covering three vibrational interacting systems and involving several “dark” states perturbing observed transitions. Line positions could be reproduced with rms deviations on the order of 0.01 cm −1 . The dipole transition moment parameters of the six bands were determined from the retrieved line intensities. The obtained set of effective parameters and the experimentally determined energy levels were used to generate a list of 1461 transitions provided as Supplementary materials .

Different families of generalized CS for one-dimensional systems with general time dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schr\"odinger and Glauber CS of a harmonic oscillator, we call them simply CS. However, even among these CS there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency., Comment: 11 pages, 1 figures, Submitted to Brazilian Journal of Physics

The main goal of the present study was to improve the already published rotational structure analysis of the ground vibrational state of the 13CH3D molecule. To realise that, we recorded high-resolution spectra of a set of the strongly interacting vibrational bands, 2ν3(A 1), 2ν6(A 1), 2ν6(E), ν2(A 1), ν5 + ν6(A 1), ν5 + ν6(A 2), ν5 + ν6(E) and ν3 + ν6(E). From the analysis of the experimental data, more than 1900 ground state combination differences (GSCD) were determined with , and . The a 1/a 2 splittings of the states with quantum number K = 3 were taken into account. The presence of numerous forbidden transitions allowed us to determine with high accuracy GSCD not only with ΔK = 0, but with ΔK = ±1, ±2 and ±3, as well. Spectroscopic parameters of the ground vibrational state were determined from the joint fit of the obtained GSCD (they are reproduced with cm−1). The 21 highly accurate THz-region transitions which were also used as input data, are reproduced with kHz.

Статья посвящена исследованию подвижных особых точек решений автономной системы Гамильтона шестого порядка в случае, когда промежуточные аргументы гамильтониана – дробно-линейные функции. Найдены коэффициентные условия, при выполнении которых решения указанной системы в плоскости независимой переменной имеют подвижные точки ветвления второго порядка. Отдельно изучен случай, когда решения исходной системы Гамильтона в плоскости независимой переменной не имеют никаких подвижных особенностей.

Представлена теоретическая модель, впервые использующая преобразование Паде-Бореля для улучшения сходимости рядов теории возмущений в методе эффективных гамильтонианов. Модель применена для расчетов полуширины и сдвига центров линий водяного пара давлением азота и аргона в диапазоне 13550...13950 см{-1}. Проведено сравнение рассчитанных релаксационных параметров линий Н[2]О с измеренными.

Рассмотрен подход к решению задачи подгонки гамильтониана молекулы типа асимметричного волчка, основанный на применении метода регуляризации. В отличие от ранее известных подходов, применены специальные методы для обеспечения устойчивости процесса решения и для ограничения области решений. Ограничение области решений обеспечивает получение решения, имеющего физический смысл.

Выполнен анализ впервые зарегистрированного с высоким разрешением (0,0027 см-1) спектра молекулы AsD3 в районе поглощения однократно возбужденных валентных колебаний. В исследуемых полосах идентифицировано свыше 3300 переходов с максимальным значение квантового числа J=28. При анализе спектра использовалась модель гамильтониана, учитывающая резонансные взаимодействия между состояниями (1000) и (0010). Полученные 50 спектроскопических параметров (26 параметров диагональных и 24 - резонансных блоков), воспроизводят экспериментальные данные со средней точностью ~0,00024 см-1.

Предложена модель взаимодействия атома, движущегося вблизи поверхности, с поверхностными плазмонами. Поверхность твердого тела рассматривается в приближении свободных электронов (модель "желе"), атом - в двухуровневом приближении. С использованием гамильтонианов в представлении вторичного квантования и выводов теории возмущений рассчитана вероятность возбуждения атома, пересекающего поле поверхностных плазмонов, в зависимости от параметров атома и поля плазмонов. Приведены экспериментальные данные, подтверждающие существование рассматриваемого процесса.

Построен гамильтониан кристалла, испытывающего структурный переход мартенситного типа, в котором система конфигурационных возбуждений описывается как двухуровневая квантовая система (квантовая система псевдоспинов).

Работа посвящена исследованию проблемы введения переменной времени для различных космологических моделей Вселенной. Известно, что в силу масштабной инвариантности данные космологические модели являются системами со связями первого рода, что приводит к проблеме введения времени и к проблеме квантования. В данной работе показано, что учет уравнений связи Логунова обуславливает отличие от нуля гамильтониана, что позволяет решить проблему времени квантовой космологии вне рамок традиционных подходов решения этой проблемы.