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The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2...), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C2v, C3v and Td molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Spin-torsion dominated hyperfine splittings in vt = 1 torsional state of methanol. • Proton-spin magnetic hyperfine interactions in E torsional states of methanol. • Least-squares fit to effective spin-rotation, spin-torsion, & spin–spin Hamiltonian. • Lamb-dip sub-mm-wave measurements for methanol from three laboratories. Abstract Doublet, triplet and quartet hyperfine splitting patterns have been observed in the E-species component of the first excited (v t = 1) torsional state of CH 3 OH. Four series of lines dominate the available data: (i) a K = 6 ← 7, Q branch series of quartets, with 7 ≤ J ≤ 15; (ii) a K = 3 ← 2, Q branch series, with 3 ≤ J ≤ 18, which starts as quartets, changes to doublets at J = 7, and then finally to singlets at J = 17; (iii) a K = −2 ← −3, P branch series of doublets, with 8 ≤ J ≤ 13; and (iv) a K = 8 ← 7, Q branch series, with 8 ≤ J ≤ 24, which starts as triplets and becomes doublets at J = 12. There are also a few isolated doublets and quartets, which do not form long spectroscopic branches. We have modeled the hyperfine quartet and doublet splittings with empirically chosen symmetry-allowed spin-torsion, spin-rotation, and spin–spin interaction terms appropriate for the two I = ½ spin systems arising from the OH proton and from the CH 3 protons, respectively, and have achieved a least-squares fit of 144 hyperfine components (88 hyperfine intervals) to six hyperfine parameters with a standard deviation (0.75 kHz) near experimental measurement accuracy. The three spin-rotation parameters associated with one I = ½ spin system in the fit agree well with ab initio predictions for I OH parameters in the literature. The two spin-torsion parameters agree to some extent with other fitted values in the literature. The physical effects included in the present Hamiltonian differ from those included in the Hamiltonian for our earlier work on hyperfine splittings in v t = 0 E states, because the experimentally observed v t = 1 splittings are found to decrease approximately as 1/ J , whereas the v t = 0 splittings increase approximately as J. The position and relative intensities of the weak central features of the triplets are explained as three-level Λ-type crossover resonances. [ABSTRACT FROM AUTHOR]

Highlights • 9015 line positions and intensities were retrieved in the 3760–4100 cm−1 region. • More than 3500 new assignments were made in the region. • 5703 experimental line positions were modeled to 0.00179 cm−1. • 2659 experimental line intensities at 296 K were modeled to 7.46% rms. Abstract Eight spectra of normal samples of CH 4 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 12CH 4 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). [ABSTRACT FROM AUTHOR]

A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that a low-scaling step may be used to cast the electronic Hamiltonians of real systems into the form required. Two proof-of-principle demonstrations are presented here for non-covalent interactions. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems (Be atoms) to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. Since the cost of the global calculation does not depend directly on the correlation models used for the fragments, this should provide a way to incorporate difficult electronic structure problems into large systems. This framework opens a promising path for building tunable, systematically improvable methods to capture properties of systems interacting with a large number of other systems. The extension to excited states is also straightforward. [ABSTRACT FROM AUTHOR]

Highlights • 5819 line positions and intensities were retrieved from measured spectra in the 5550- 5825 cm−1 region. • More than 2800 new assignments were made in the region. • More than 3445 experimental line positions were modeled to 0.0024 cm−1. Abstract A new study of 12CH 4 line positions and intensities was performed for the Tetradecad regions 5550,000–5695.250, 5718.8–5724.250 and 5792.36–5814.290 cm−1 using long path (202 m, 602 m, 1604 m and 1804 m) spectra of normal samples of CH 4 at different pressures recorded with a Fourier transform spectrometer in Reims, France. Line positions and intensities were retrieved by least squares curve-fitting procedures and analyzed using the effective Hamiltonian and the effective dipole moment expressed in terms of irreducible tensor operators adapted to spherical top molecules. An 80 K spectrum recorded in Jet Propulsion Laboratory (JPL), Pasadena, of enriched 12CH 4 was used for low-J line positions. Another 80 K spectrum of enriched 13CH 4 from JPL was used to discern the isotopic lines. A new measured linelist contains positions and intensities for 5819 features. Quantum assignments were made for more than 3400 transitions, which represent ∼95% of the integrated line intensity observed in this region. All assigned 3445 line positions were fitted with RMS standard deviations of 0.0024 cm−1. The sum of observed intensities between 5550 and 5695 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). [ABSTRACT FROM AUTHOR]

Highlights • First detection of the ν 1 + 4ν 3 B-type band of 14N16O 2 near 1.34 µm. • More than 800 lines corresponding to 1117 transitions are assigned. • Line positions are reproduced by an effective Hamiltonian model. • The (1,0,4) upper level is found unperturbed. • Effective dipole moment and Herman-Wallis type parameters are determined. Abstract The very weak ν 1 +4ν 3 Β -type absorption band of nitrogen dioxide (14N16O 2) is newly detected by high sensitivity continuous wave-cavity ring down spectroscopy between 7376 and 7550 cm−1. The noise equivalent absorption of the recordings is α min ≈ 1 × 10−10 cm−1. The ν 1 +4ν 3 band is the highest energy B -type absorption band of NO 2 detected so far by absorption within the ground electronic state. More than 800 lines are assigned with rotational quantum numbers N and K a up to 50 and 7, respectively, what corresponds to 1117 spin-rotation-vibration transitions. No resonance perturbation of the spectrum was observed. The fitted set of the effective Hamiltonian parameters reproduces the observed line positions with an rms of 3.7 × 10−3 cm−1. A selected set of measured line intensities are used to determine the effective dipole moment parameters including two Herman-Wallis type parameters. The rms deviation of the intensity fit is 15.2%. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Improved analysis of positions and intensities of phosphine spectral lines in the Octad region 2733–3660 cm −1 is reported. Some 5768 positions and 1752 intensities were modelled with RMS deviations of 0.00185 cm −1 and 10.9%, respectively. Based on an ab initio potential energy surface, the full Hamiltonian of phosphine nuclear motion was reduced to an effective Hamiltonian using high-order Contact Transformations method adapted to polyads of symmetric top AB 3 -type molecules with a subsequent empirical optimization of parameters. More than 2000 new ro-vibrational lines were assigned that include transitions for all 13 vibrational Octad sublevels. This new fitting of measured positions and intensities considerably improved the accuracy of line parameters in the calculated database. A comparison of our results with experimental spectra of PNNL showed that the new set of line parameters from this work permits better simulation of observed cross-sections than the HITRAN2012 linelist. In the 2733–3660 cm −1 range, our integrated intensities show a good consistency with recent ab initio variational calculations. [ABSTRACT FROM AUTHOR]

The weak 2ν 1 + 3ν 2 + ν 3 absorption band of the nitrogen dioxide main isotopologue ( 14 N 16 O 2 ) is investigated near 6350 cm −1 . The absorption spectrum was recorded by high sensitivity Cavity Ring Down Spectroscopy with a noise equivalent absorption of α min ≈ 1 × 10 −10 cm −1 . In total, 1069 lines of the 2ν 1  + 3ν 2  + ν 3 band were assigned with rotational quantum numbers N and K a up to 48 and 8, respectively, that corresponds to 1276 vibration-rotation transitions. The derived set of line positions is reproduced with an effective Hamiltonian with an rms of 2.35 × 10 −3 cm −1 for the (obs.-calc.) deviations. The effective Hamiltonian takes explicitly into account the Coriolis interactions between the spin rotational levels of the (2,3,1) upper vibrational state and those of two nearby dark states - (2,5,0) and (2,1,2) - together with the electron spin-rotation interactions. Using the corresponding eigenfunctions the principal effective dipole moment parameter responsible for the line intensities of the 2ν 1  + 3ν 2  + ν 3 band is fitted to selected measured line intensities which are reproduced with an rms deviation of 6.2%. [ABSTRACT FROM AUTHOR]

This paper records for the Hamiltonian H = 1/2 | p| + W( x) some old and new identities relevant for the PDE/variational approach to weak KAM theory. [ABSTRACT FROM AUTHOR]

We study approximation schemes for effective Hamiltonians arising in the homogenization of first order Hamilton-Jacobi equations in stationary ergodic settings. In particular, we prove error estimates concerning the rate of convergence of the approximated solution to the effective Hamiltonian. Our main motivations are front propagation problems, but our results can be generalized to other types of Hamiltonians. [ABSTRACT FROM AUTHOR]

Abstract: Understanding the dynamics of electron or nuclear spins during a magnetic resonance experiment requires to solve the Schrödinger equation for the spin system considering all contributions to the Hamiltonian from interactions of the spins with each other and their surroundings. In general, this is a difficult task as these interaction terms can be both time‐dependent and might not commute with each other. A powerful tool to analytically approximate the time evolution is average Hamiltonian theory, in which a time‐independent effective Hamiltonian is taking the place of the time‐dependent Hamiltonian. The effective Hamiltonian is subjected to the Magnus expansion, allowing to calculate the effective Hamiltonian to a certain order. The goal of this paper is to introduce average Hamiltonian theory in a rigorous but educational manner. The application to two composite pulses in NMR spectroscopy is used to demonstrate important aspects of average Hamiltonian theory. [ABSTRACT FROM AUTHOR]

The absorption spectrum of acetylene has been recorded at room temperature (296 K) using high sensitivity Cavity Ring Down Spectroscopy in the 7914 and 8252 cm −1 interval. The noise equivalent absorption of the spectra is α min ∼ 5×10 −11 cm −1 . A list of about 5600 absorption features was constructed. The smallest intensities are on the order of 10 −29 cm/molecule. A total of 1325 rovibrational lines of 12 C 2 H 2 were assigned by comparison with accurate predictions provided by a global effective operator model. In addition, 132 rovibrational lines of 12 C 13 CH 2 present in natural isotopic abundance were assigned on the basis of their published positions. The assigned 12 C 2 H 2 lines belong to 12 new and 6 already known bands, for which additional J -lines were assigned. The line intensities of the three cold bands of 12 C 13 CH 2 are reported for the first time. The new data will be valuable to refine the parameters of the global effective Hamiltonian and dipole moments of 12 C 2 H 2 in the region. Spectroscopic parameters of the 12 C 2 H 2 and 12 C 13 CH 2 upper vibrational levels were derived from a band-by-band fit of the line positions (typical rms values are on the order of 0.001 cm −1 ). A few of the analyzed bands were found to be affected by rovibrational perturbations, which are discussed. In particular, the rotational structure of the 2 ν 1 + ( ν 4 + ν 5 ) 0 Σ u + –Σ g + band near 7994 cm −1 exhibits a particularly surprising intensity distribution: while the P (19) and R (17) transitions share the same J = 18 upper level, the R (17) line has an intensity about 4 orders of magnitude smaller than the P (19) line. This unusual situation is quantitatively interpreted as resulting from a Coriolis interaction between the ν 1 + 2 ν 2 + ν 5 1 and 2 ν 1 + ( ν 4 + ν 5 ) 0 bands with a energy crossing at J = 18. The accidental nearly perfect cancelation of the two terms contributing to the line strength of the R (17) line leads to the near disappearance of this line. [ABSTRACT FROM AUTHOR]

The global modeling of both line positions and intensities of the acetylene molecule in the 50–9900 cm −1 region has been performed using the effective operators approach. The parameters of the polyad model of effective Hamiltonian have been fitted to the line positions collected from the literature. The used polyad model of effective Hamiltonian takes into account the centrifugal distortion, rotational and vibrational ℓ -doubling terms and both anharmonic and Coriolis resonance interaction operators arising due to the approximate relations between the harmonic frequencies: ω 1 ≈ ω 3 ≈5 ω 4 ≈5 ω 5 and ω 2 ≈3 ω 4 ≈3 ω 5 . The dimensionless weighted standard deviation of the fit is 2.8. The fitted set of 237 effective Hamiltonian parameters allowed reproducing 24,991 measured line positions of 494 bands with a root mean squares deviation 0.0037 cm −1 . The eigenfunctions of the effective Hamiltonian corresponding to the fitted set of parameters were used to fit the observed line intensities collected from the literature for 15 series of transitions: Δ P = 0-13,15, where P =5 V 1 +5 V 3 +3 V 2 + V 4 + V 5 is the polyad number ( V i are the principal vibrational quantum numbers). The fitted sets of the effective dipole moment parameters reproduce the observed line intensities within their experimental uncertainties 2–20%. [ABSTRACT FROM AUTHOR]

The goal of this paper is to obtain a numerical approximation of the effective Hamiltonian for a system of PDEs deriving from a second order discrete model for traffic flow. We will propose an explicit and an implicit discretization for this effective Hamiltonian and we will provide the corresponding error estimates of Crandall–Lions type. Finally, we will also present some numerical simulations. [ABSTRACT FROM AUTHOR]

Bloch's transformation [ABSTRACT FROM AUTHOR]

In this paper, we present a protocol to engineer upper bounded and sliced Jaynes–Cummings and anti-Jaynes–Cummings Hamiltonians in cavity quantum electrodynamics. In the upper bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging fromup to, while in the sliced interaction the Fock subspace ranges fromup to. We also show how to build upper bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper bounded and sliced Hamiltonians and Liouvillians can be used, among other applications, to generate steady Fock states of a cavity mode and for the implementation of a quantum-scissors device for optical state truncation. [ABSTRACT FROM AUTHOR]

We consider two interacting quantum dots coupled by standard s-wave superconductors. We derive an effective Hamiltonian, and show that over a wide parameter range a degenerate ground state can be obtained. An exotic form of Majorana bound states is supported at these degeneracies, and the system can be adiabatically tuned to a limit in which it is equivalent to the one-dimensional wire model of Kitaev. We give the form of a Majorana bound state in this system in the strong interaction limit in the many-particle picture. We also study the Josephson current in this system, and demonstrate that a double slit-like pattern emerges in the presence of an extra magnetic field. This pattern is shown to disappear with increasing interaction strength, which is due to the current being carried by chargeless Majorana bound states. [ABSTRACT FROM AUTHOR]

Gas-liquid criticality in the ultrasoft restricted primitive model (URPM) of polyelectrolytes is studied using the collective variables-based theory. For the model, an effective Hamiltonian is derived and explicit expressions for all the coefficients are found in a one-loop approximation. Based on this Hamiltonian, the phase and critical behaviour is analysed. Our results provide evidence that the nature of the gas-liquid criticality in the URPM is the same as in the restricted primitive model that includes a hard core. [ABSTRACT FROM AUTHOR]

In this paper we study the behavior of solutions of a nonlinear Schrödinger equation in presence of an external potential, which is allowed to be singular at one point. We show that the solution behaves like a solitary wave for long time even if we start from an unstable solitary wave, and its dynamics coincides with that of a classical particle evolving according to a natural effective Hamiltonian. [ABSTRACT FROM AUTHOR]

Based on the relation between quantum mechanical concepts such as effective Hamiltonians (EHs), perturbation theory (PT), and unitary transformations, and phenomenological aspects of spin Hamiltonians (SHs), the present tutorial tries to address the basics of the SH formalism. Using simple physical models and historical important examples, we have reviewed the derivation methods and applications of the SHs for a brief and in-depth description of various sources of anisotropies and interactions such as electronic (EZ), and nuclear Zeeman (NZ), terms, electron-exchange interaction (EE), zero-field splitting (ZFS), spin-spin (SS), spin-orbit (SO), nuclear quadrupole (NQ), and hyperfine couplings (HFCs), in a step-wise manner. In this way, this tutorial is tailored for the graduate students and young researchers who intend to begin their studies in the field of magnetism, electron magnetic resonance (EMR), spectroscopy, and related areas. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Many models of condensed-matter systems have interactions with unexpected features: for example, exclusively distant-neighbor spin-orbit interactions. On first inspection these interactions seem physically questionable in view of the basis states used. However, such interactions can be physically reasonable if the model is an effective one, in which the basis states are not exactly as described, but instead include components of states removed from the problem. Mathematically, an effective model results from partitioning the Hamiltonian matrix, which can be accomplished by energy-dependent or energy-independent methods. We examine effective models of both types, with a special emphasis on energy-independent approaches. We show that an appropriate choice of basis makes the partitioning simpler and more accurate. We illustrate the method by calculating the spin-orbit splitting in graphene. [ABSTRACT FROM AUTHOR]

Abstract: The spectrum of tetraquark states with hidden charm is studied within an effective Coulomb gauge Hamiltonian approach. Of the four independent color schemes, two are investigated, the singlet–singlet (molecule) and the triplet–triplet (diquark), for selected states using a variational method. The predicted masses of triplet–triplet tetraquarks are roughly a GeV heavier than the singlet–singlet states. There is also an interesting flavor dependence with states about half a GeV lighter than . The lightest and predictions are in agreement with the observed and masses suggesting they are molecules with and , rather than and , type structure, respectively. Similarly, the lightest isovector molecule, having a flavor composition, has mass near the recently observed charged value. These flavor configurations are consistent with observed X, Y and decays to . [Copyright &y& Elsevier]

Highlights: [•] Reduced rovibrational Hamiltonian for combination levels of C3v molecules. [•] Explicit form of the H 41 term for such states is given for the first time. [•] Some useful reduction schemes are discussed. [Copyright &y& Elsevier]

We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $$k=0,+1,-1$$ are considered. To construct the path integrals in the timeless framework, a multiple group-averaging approach is proposed. Meanwhile, since the transition amplitude in the deparameterized framework can be expressed in terms of group-averaging, the path integrals can be formulated for both deparameterized and timeless frameworks. Their relation is clarified. It turns out that the effective Hamiltonian derived from the path integral in deparameterized framework is equivalent to the effective Hamiltonian constraint derived from the path integral in timeless framework, since they lead to same equations of motion. Moreover, the effective Hamiltonian constraints of above models derived in canonical theory are confirmed by the path integral formulation. [ABSTRACT FROM AUTHOR]

Based on the first-principles electronic-structure calculations, we construct the effective magnetic Hamiltonians that can be used to search for the ground state of solids and nanostructures. Moreover, using the methods of statistical mechanics, one can study the magnetic properties at T>0 such as the magnetic structure as a function of temperature, magnon spectra, the Curie/Néel temperature, etc. The present approach is highly flexible and it makes possible to study magnetic structure of complex systems with the accuracy of ab initio methods. As an illustration, we show how the magnetic structure of a magnetic monolayer (Fe) on a non-magnetic substrate (Ir(001)) can be determined. [ABSTRACT FROM AUTHOR]

The transport properties of Pd-rich PdFe alloys are investigated as a function of the atomic and magnetic orders on the L2 (CuAu) lattice. The residual resistivity, anisotropic magnetoresistance (AMR), and anomalous Hall effect are calculated from first-principles as a function of the atomic order. The calculations are based on the relativistic generalization of the transport Kubo-Greenwood approach as formulated in the framework of the first principles TB-LMTO method and Coherent Potential Approximation (CPA). The effect of the thermal magnetic disorder on the resistivity and AMR has been also studied using the disordered local moment approach based on the CPA. Our results are in an overall good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

The magnetic interactions in the V2Cl [ABSTRACT FROM AUTHOR]

The article presents a solution in addressing the problem of phase transition in the presence of fluctuations and the effect of exchange interaction in magnetic systems. It highlights the use of the Hamiltonian system in the phase transition line by considering the long-wave thermodynamic fluctuations of the system. It also examines the solution with regards to stability to determine their stationary points and stability of the behavior of the phase trajectories of the system.

In this paper, the hadronic decay has been analyzed in naive and QCD factorization methods. The simplest approach to obtain the amplitude of the hadronic B decays is naive factorization, where the matrix elements have been parametrized into products of decay constant and form factors. We have calculated the factorizable amplitudes and nonfactorizable contributions corresponding to the vertex corrections and the hard spectator interactions in QCD factorization. We treat the charm quark as light, compared to the large scale provided by the mass of the decaying b quark (mc ≪mb and mc fixed as mb→∞). Our obtained branching ratio of is (1.36±0.02)×10-5 using naive factorization, which is smaller than the experimental data: (1.2±0.4)×10-4. On the other hand, by considering QCD corrections in QCDF and by treating D-meson as a light, we have obtained the value (2.57±0.01)×10-5, which has been used to decrease the discrepancy between the theoretical and experimental data. [ABSTRACT FROM AUTHOR]

The vibration–rotation dynamics of acetylene are computed from a spectroscopic Hamiltonian with 468 parameters fit to 19,582 vibration–rotation transitions up to 13,000 cm−1 of vibrational energy. In this energy range, both the bending and the CH stretching vibrations can reach large amplitudes, but the maximum energy remains below the threshold for isomerization to vinylidene. In contrast to the behavior at energies below 5000 cm−1 [Mol. Phys. 108, 1115 (2010)], excitation of single bright states leads, in almost all cases, to computed intramolecular vibrational redistribution (IVR) that is irreversible on the timescales investigated. Hierarchies of IVR processes on timescales ranging from 20 fs to 20 ps result when different bright states are excited. Different parts of the vibrational quantum number space are explored as a result of the four different classes of coupling terms: vibrational l-type resonance, anharmonic resonances, the rotational l-type resonance, and Coriolis couplings. The initial IVR rates are very different depending on whether the bright states are bending states or stretching states, normal modes or local modes, edge states or interior states. However, the rates of the rotationally mediated couplings do not depend substantially on these distinctions. [ABSTRACT FROM AUTHOR]

The electrical conductivities and plausible charge-ordering states in the room temperature (r.t.) phase for MMX chains [Ni2(dta)4I]∞ and [Pt2(dta)4I]∞ (dta = CH3CS [ABSTRACT FROM AUTHOR]

Abstract: The effective rotational Hamiltonian for molecules with one or two periodic large-amplitude motions has had considerable success in modeling rotational spectra over the past 15years. This article spells out the basic premises and summarizes the theory of this Hamiltonian which is implemented in the program code called ERHAM. The essential features of the code are described. The modular approach to define tunneling parameters (and implicitly the Hamiltonian) makes the code very flexible. Published applications of ERHAM (including comparisons of results between ERHAM and other program codes) are reviewed and the limitations of ERHAM are discussed. [Copyright &y& Elsevier]

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrodinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a con-stant measuring the asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curva-ture. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a paral-lel transport along the curve and a refined smoothing of the curvature via the Steklov approximation. [ABSTRACT FROM AUTHOR]

Abstract: The absorption spectrum of nitrous oxide, N2O, has been recorded by CW-Cavity Ring Down Spectroscopy between 6950 and 7653cm−1. The spectra were obtained at Doppler limited resolution using a CW-CRDS spectrometer based on a series of fibered DFB laser diodes. The typical noise equivalent absorption, in the order of α min ≈1×10−10 cm−1, allowed for the detection of lines with intensity as small as 1×10–29 cm/molecule. The positions of 7203 lines of four isotopologues (14N2 16O, 14N15N16O, 15N14N16O and 14N2 18O) were measured with a typical accuracy of 1.0×10−3 cm−1. The transitions were rovibrationally assigned on the basis of the global effective Hamiltonian models developed for each isotopologue. The band by band analysis allowed for the determination of the rovibrational parameters of more than 95 bands, most of them being newly reported while new rotational transitions are measured for the others. The measured line positions of the main isotopologue are found to be in good agreement with the predictions of the effective Hamiltonian model but a few deviations up to 0.20cm−1 are observed. Local rovibrational perturbations were evidenced for several bands. The interaction mechanisms and the perturbers were univocally assigned on the basis of the effective Hamiltonian models. [Copyright &y& Elsevier]

Two independent methods to obtain ab initio effective rotational Hamiltonians have been implemented recently. The first one is based on a generalization of perturbation theory to noncommutative rings, the other one on contact transformation (CT) techniques. In principle, both methods are able to give rotational Hamiltonians including centrifugal distortion effects of arbitrary high orders. These methods are compared, for the first time, in this article with regard to calculations of the rotational levels of methane vibrational ground state. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012 [ABSTRACT FROM AUTHOR]

Abstract: The extended Krenciglowa–Kuo (EKK) method allows us to calculate the effective Hamiltonian in a non-degenerate model space. We show that the EKK method can be implemented numerically in two iterative schemes, which are explained in detail with emphasis on convergence conditions. Using test calculations in a simple model, we clarify how and on what conditions we can calculate the effective Hamiltonian. [Copyright &y& Elsevier]

Abstract: The absorption spectrum of nitrous oxide, N2O, in normal isotopic abundance has been recorded by CW-Cavity Ring Down Spectroscopy between 7647 and 7918cm−1. The spectra were obtained at Doppler limited resolution by using a CW-CRDS spectrometer based on a series of fibered DFB lasers. The typical noise equivalent absorption on the order of αmin ≈1×10−10 cm−1, allowed for the detection of lines with intensity as weak as 2×10−29 cm/molecule. The positions of 2272 lines of five isotopologues (14N2 16O, 15N14N16O, 14N15N16O, 14N2 18O and 14N2 17O), were measured with a typical accuracy of 1.0×10−3 cm−1. The transitions were rovibrationally assigned on the basis of the global effective Hamiltonian models respective to each isotopologue. The band by band analysis allowed for the determination of the rovibrational parameters of a total of 30 bands, 19 of them being newly reported while new rotational transitions are measured for the others. The maximum deviation of the predictions of the effective Hamiltonian models is 0.18cm−1 for the line positions of the main isotopologue and up to 1.3cm−1 for the 14N2 18O species. Local rovibrational perturbations were evidenced for three bands of 14N2 16O and the ν 1 +3ν 3 band of 14N2 17O. The interaction mechanisms and the perturbers were univocally assigned on the basis of the effective Hamiltonian models. [Copyright &y& Elsevier]

We study the influence of wetting films on (density-density) correlations for a fluid in a slit-like geometry near capillary condensation. We show that, for systems with short-ranged forces, the interaction between the wetting films strongly enhances the amplitude of the exponential decay of correlations and, unlike the interfacial roughness, is independent of a high-momentum cut-off. The correlation function shows scaling behaviour near condensation arising from the equality of two characteristic length scales: the parallel correlation length (associated with the complete wetting films) and a length scale related to the non-local interaction between the wetting films on either side of the slit. We introduce a dimensionless amplitude ratio associated with the decay of correlations which allows us to distinguish between local and non-local effective Hamiltonian theories. Only the latter is fully consistent with microscopic density functional descriptions of correlation functions. The influence of long-ranged intermolecular forces and fluctuation effects in two dimensions is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: The effective interaction in a model space has been calculated by the Krenciglowa–Kuo (KK) and the Lee–Suzuki (LS) iterative methods, both of which assume that the unperturbed energies in the model space are degenerate. We generalize these two methods in a natural and simple manner so that they apply also to non-degenerate model spaces. The key to the generalization is to use the effective hamiltonian instead of the effective interaction in the formulation of iterative schemes. Using test calculations in a simple model, we demonstrate that the new methods work excellently. [Copyright &y& Elsevier]

Abstract: The and bands of 15N substituted nitrous oxide isotopologues have been recorded by a continuous-wave cavity ring-down spectrometer (CW-CRDS) operated near . The sensitivity limit was at the level of . In total, 213, 86 and 191 transitions were observed for the 14N15N16O, 15N14N16O and 15N2 16O isotopologues, respectively. The ro-vibrational spectroscopic parameters of the upper states are determined from least square fitting of the transitions. The absolute line intensities of the cold bands have been retrieved by a multi-line fitting procedure from the spectra with an estimated accuracy of 4% for majority of the unblended lines. The vibrational transition dipole moment squared values and the empirical Herman–Wallis coefficients are also presented. [ABSTRACT FROM AUTHOR]

Abstract: The absorption spectrum of highly enriched 13C carbon dioxide has been investigated by CW-Cavity Ring Down Spectroscopy with a setup based on fibered distributed feedback (DFB) laser diodes. By using a series of 30 DFB lasers, the CO2 spectrum was recorded in the 7029–7917cm−1 region with a typical sensitivity of 3×10−10 cm−1. The uncertainty on the determined line positions is on the order of 8×10−4 cm−1. More than 3800 transitions with intensities as low as 1×10−29 cm/molecule were detected and assigned to the 13C16O2, 16O13C17O, 16O13C18O, 17O13C18O and 13C18O2 isotopologues. For comparison, only 104 line positions of 13C16O2 were previously reported in the literature in the considered region. The band-by-band analysis has led to the determination of the rovibrational parameters of a total of 83 bands including 56 bands of the 13C16O2 species. The measured line positions of 13C16O2 and 16O13C18O were found in good agreement with the predictions of the respective effective Hamiltonian (EH) models but the agreement degrades for the minor isotopologues. Several cases of resonance interactions were found and discussed. In the 20033-10002 band of 13C16O2, an anharmonic resonance interaction leads to deviations on the order of 0.05cm−1 compared to the EH predictions. The existence of interpolyad interactions affecting the non-symmetric isotopologues of carbon dioxide is confirmed by the observation of two occurrences in 16O13C17O and 16O13C18O. The obtained results improve significantly the knowledge of the spectroscopy of the 13C isotopologues of carbon dioxide. They will be valuable to refine the sets of effective Hamiltonian parameters used to generate the CDSD database. [Copyright &y& Elsevier]

Abstract: We have derived a system of equations that describes the evolution of the density matrix of a centrosymmetric molecule interacting with a single nonresonant femtosecond laser pulse. The dynamics of the ground electronic state is expressed in terms of the effective Hamiltonian and the coherences between the ground an excited electronic states are functionals of the ground state density matrix. Using the time-dependent perturbation theory, we have calculated the energy deposited in the molecule as a result of rotational stimulated Raman scattering. The effective absorption coefficient is found to be proportional to the fourth power of the pulse amplitude and has a resonance-like dependence with respect to the pulse duration. [Copyright &y& Elsevier]

We show that the Krylov-Bogoliubov-Mitropolsky averaging in the canonical formulation can be used as a method for constructing effective Hamiltonians in the theory of strongly correlated electron systems. As an example, we consider the transition from the Hamiltonians of the Hubbard and Anderson models to the respective Hamiltonians of the t-J and Kondo models. This is a very general method, has several advantages over other methods, and can be used to solve a wide range of problems in the physics of correlated systems. [ABSTRACT FROM AUTHOR]

Abstract: The Hougen’s formalism of group-theoretical effective Hamiltonian has been extended to include the resonances between the wagging, ν 9, and third or fourth excited torsional, 3ν 15 and 4ν 15, states in methylamine. The presented Hamiltonian treats explicitly these couplings. For each of these bands the rovibrational sublevels belong to all symmetry species of the G 12 group of methylamine. On the other hand the vibrational states for ν 9 and 4ν 15 are symmetric with respect to reflection in the symmetry plane of the NH2 group, and antisymmetric for 3ν 15. We have shown that the coupling terms between the ν 9 and 3ν 15 states are limited to Coriolis-like coupling, and no Fermi-type interactions are allowed. For the coupling between the ν 9 and 4ν 15 states all kind of interaction terms are possible. [Copyright &y& Elsevier]

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of the exchange interaction. The quantum model is associated with a classical model (the continuous classical analogue) based on a Landau-Lifshitz-like equation, which describes large-scale fluctuations of the mean field. On the other hand, the classical model in the case of spin s is a Hamiltonian system on a coadjoint orbit of the unitary group SU( 2s+ 1). We construct a class of mean-field configurations that can be interpreted as topological excitations because they have fixed topological charges. Such excitations change their shapes and grow, conserving energy. [ABSTRACT FROM AUTHOR]

Abstract: We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy. [Copyright &y& Elsevier]

For the periodic Anderson model in the strong correlation regime, we construct the effective Hamiltonian H eff up to terms of the fourth order in the parameter V/U, where V is the hybridization interaction intensity and U is the intra-atom Coulomb repulsion strength. This Hamiltonian contains interactions inducing both magnetic ordering and Cooper instability under conditions of a mixed valency of rare-earth ions. Based on numerical calculations, we obtain information about the dependences of the effective interaction parameters on the distance between crystal lattice sites. We demonstrate that realizing exchange interactions corresponds to a strongly frustrated system of localized spin moments and facilitates the suppression of the antiferromagnetic order parameter with a possible transition to the state of a quantum spin liquid. It is essential that among the terms in H eff inducing the transition to the superconductivity phase, there are terms resulting in the d-type symmetry of the superconductivity order parameter; such a symmetry is realized in many heavy-fermion compounds. [ABSTRACT FROM AUTHOR]

This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a 'Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields. [ABSTRACT FROM AUTHOR]

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting. [ABSTRACT FROM AUTHOR]