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We calculate the tipping time of a quantum rod that has a height several times that of the edge length of its square base. We use an expression for the tipping time that has heuristic value, and gives the average time at which, upon measurement, the initially balanced rod is found to tip. We use two methods to calculate the tipping time. One method is to examine the "late time" behaviour of the quantum state of the center of mass of the rod by using an equation that has the form of the time-independent Schrödinger equation except that it involves a "complex energy." The other method uses energy resonances in the eigenstates of the Hamiltonian to determine the tipping time. We use the well-known Wentzel–Kramers–Brillouin approximation to calculate the energy eigenstates. With these methods, we obtain expressions for the tipping time that are valid for very long tipping times. PACS Nos.: 03.65.–w, 03.65.Xp

A new construction of quantum mechanical Gamow states is presented. The physical nature of these states is revealed without introducing the notion of complex energy. In the presented aproach the time reversal is a linear transformation instead of the customary antilinear one. Also the Fourier integral solution of the free nonrelativistic wave equation contains both positive and negative frequencies.

The method of complex dilation is used to define the partial wave S-matrix in the sector of the fourth quadrant of the complex energy plane. Two ways of obtaining the expansion coefficients—the partial wave S-matrix residues—are studied. The Mittag-Leffler decomposition of the partial wave S-matrix as a sum of residue terms and an integral contribution is used to define the contributions of a number of the partial wave S-matrix poles, related to a 1-D potential, to the corresponding S-wave cross-section. The obtained expansion demonstrates a way of describing the contribution from a single pole to the partial wave S-matrix and thereby to various types of cross-sections. Our model study shows how peaks in a cross-section not only can be attributed to so-called isolated resonances but also to a set of overlapping barrier-type resonances. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two-particle states are calculated by using a single-particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long-lived resonances are mostly determined by either bound states or by narrow Gamow resonances. However, they are significantly affected by wide resonances and the continuum background itself.

The folding trajectories of a 16-residue β-hairpin are studied using the activation–relaxation technique with a generic energy model. From more than 70 trajectories, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bonding interactions. The first two follow closely those observed by previous theoretical studies, while the third can be described as a reptation move of one strand of the β-sheet with respect to the other. This reptation move indicates that non-native interactions can play a dominant role in the folding of secondary structures.

The delocalization phenomenon was discovered by Hatano et al. and Miller et al. for a class of non-Hermitian quantum-mechanical problems. We show that the delocalization is only one example of many possible critical phenomena which are associated with the self-orthogonality of an eigenstate of the non-Hermitian Hamiltonian. It is shown that in this class of problems the self-orthogonality occurs at the series of branch points in the complex energy plane that serve as gates for the particle to hop from one Bloch energy band to another one.

A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples document that the method works well for two-nucleon scattering and three-nucleon scattering, if the set of complex energies is properly chosen., Comment: 6 pages, no figures, resubmitted to Prog. Theor. Phys

Coated thermoelectric refrigeration is a means of infrared stealth for target. The study on the infrared characteristic of target that coated with thermoelectric refrigeration is the foundation for infrared stealth technology coated with thermoelectric refrigeration. The infrared characteristic model of target coated with thermoelectric refrigeration was established considering of complex energy exchange of target on the sea and the structure and transfer character of thermoelectric refrigeration. Analyze the effect of current and hot-side transfer coefficient on the surface temperature of target by making corresponding program. Depending on the target and background temperature consistent standard, ideal current in a day was designed.

In this work, we find systematic transitions of electron transport regimes by controlling the number of strongly-interacting P donors in SOI-FET nano-channels. We found that, as a function of the location and number of dopants, doped using a selective-doping technique, electron transport occurs via individual P donors (in samples with low N D ), via “clusters” of a few P donors (for higher N D ) and via many-donor QDs, which form complex energy bands (for highly-doped samples).

Strictly finite-range (SFR) potentials are exactly zero beyond their finite range. Single-particle energies and densities as well as S-matrix pole trajectories are studied in a few SFR potentials suited for the description of neutrons interacting with light and heavy nuclei. The SFR potentials considered are the standard cut-off Woods--Saxon (CWS) potentials and two potentials approaching zero smoothly: the SV potential introduced by Salamon and Vertse and the SS potential of Sahu and Sahu. The parameters of these latter were set so that the potentials may be similar to the CWS shape. The range of the SV and SS potentials scales with the cube root of the mass number of the core like the nuclear radius itself. For light nuclei a single term of the SV potential (with a single parameter) is enough for a good description of the neutron-nucleus interaction. The trajectories are compared with a bench-mark for which the starting points (belonging to potential depth zero) can be determined independently. Even the CWS potential is found to conform to this bench-mark if the range is identified with the cutoff radius. For the CWS potentials some trajectories show irregular shapes, while for the SV and SS potentials all trajectories behave regularly., 14 figs

Ruthenium nitrosyl complexes have received considerable attention due to the fact that they are able to store, transfer and release NO in a controlled manner. It is well-known that the NO reactivity of ruthenium nitrosyl complexes can be modulated with the judicious choice of equatorial and axial ligands. In this piece of research we elucidate the nature of the Ru-NO and Ru-NO2 bonding in a cis-[Ru(NO)(NO2)(bpy)2](2+) complex energy decomposition (Su-Li EDA) and topological (e.g., QTAIM) and natural bond orbital analysis. It was observed that the strength of these bonds is directly correlated with the relative stability of isomers involved in nitro-nitrito and nitrosyl-isonitrosyl isomerism, as described previously by Coppens and Ooyama.

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) of proteins are very common and instrumental for cellular signaling. Recently, a number of studies have investigated the kinetic binding mechanisms of IDPs and IDRs. These results allow us to draw conclusions about the energy landscape for the coupled binding and folding of disordered proteins. The association rate constants of IDPs cover a wide range (10(5)-10(9) M-1 s(-1)) and are largely governed by long-range charge-charge interactions, similarly to interactions between well-folded proteins. Off-rate constants also differ significantly among IDPs (with half-lives of up to several minutes) but are usually around 0.1-1000 s(-1), allowing for rapid dissociation of complexes. Likewise, affinities span from pM to mu M suggesting that the low-affinity high-specificity concept for IDPs is not straightforward. Overall, it appears that binding precedes global folding although secondary structure elements such as helices may form before the protein-protein interaction. Short IDPs bind in apparent two-state reactions whereas larger IDPs often display complex multi-step binding reactions. While the two extreme cases of two-step binding (conformational selection and induced fit) or their combination into a square mechanism is an attractive model in theory, it is too simplistic in practice. Experiment and simulation suggest a more complex energy landscape in which IDPs bind targets through a combination of conformational selection before binding (e. g., secondary structure formation) and induced fit after binding (global folding and formation of short-range intermolecular interactions).

Some aspects of resonances in nuclear physics are discussed. Their properties are studied and it is shown how to obtain them numerically in realistic situations for experimental detection. Particular attention is given to resonances in non-spherical potentials that represent deformed exotic nuclei, and their trajectories in the complex energy plane are followed.

We study a wide class of solvable [Formula: see text] symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results are new. We demonstrate that the occurrence of conjugate energy pairs is a natural phenomenon for these potentials and that the present method can readily be extended to further potential classes.

We study virtual states in 5 He and 10 Li by using the Jost function method (JFM). In 5 He, we obtained an s -wave pole with the complex energy E=7.50−44.7 i MeV using a 4 He–n potential called KKNN. In 10 Li, we investigated s -wave virtual poles with the 9 Li–n interaction microscopically constructed by taking into account the Pauli-blocking effect. We obtained a virtual state at E=−0.135 MeV ( k=−0.077 i fm −1 ). The attractive property of the s -wave 9 Li–n potential for 10 Li is discussed in comparison with the 5 He ( 4 He + n) system and also calculational results for the 9 Li–n potential of Thompson and Zhukov.

We investigate electron tunneling through ultrathin gate oxides using scattering theory within a tight-binding framework. We employ Si[100]/SiO 2 /Si[100] model junctions with oxide thicknesses between 7 and 18 A. This approach accounts for the three-dimensional microscopic structure of the model junctions and for the three-dimensional nature of the corresponding complex energy bands. The equilibrium positions of the atoms in the heterostructure are derived from first-principles density-functional calculations. We show that the present method yields qualitative and quantitative differences from conventional effective-mass theory.

The photochemistry and photophysics of papaverine N-oxide in polar aprotic and protic solvents has been studied in detail. Complex energy and charge-transfer phenomena between chromophores occur in papaverine. New photochemistry for the papaverine N-oxide system is reported. Irradiation in protic media results in the formation of an emissive charge-transfer state with ensuing intramolecular hydroxylation in high isolated yields (75–80%).

The first ever NATO Advanced Study Institute devoted to `Thermodynamics and the Optimization of Complex Energy Systems' was held in July 1998 in Neptun, Romania. The ASI unified the field by bringing together leading researchers from engineering and physics, and from West and East. This note outlines the objectives and proceedings of the Institute, which reviewed the most recent advances in exergy analysis, entropy-generation minimization and thermoeconomics. Directions for future developments (e.g. constructal theory) are also outlined.

Properties of scalar-isoscalar mesons are analysed using separable interactions in three decay channels: pion-pion, kaon-antikaon and an effective 2pion-2pion. We obtain different solutions by fitting various data on the pion-pion and kaon-antikaon phase shifts and inelasticities including the CERN-Cracow-Munich measurements of the pion- p --> pion+ pion- n reaction on a polarized target. Analytical structure of the meson-meson multichannel amplitudes is studied with a special emphasis on the role played by the S-matrix zeroes. S-matrix poles are found in the complex energy plane and interpreted as scalar resonances. We see a wide f0(500), a narrow f0(980) and a relatively narrow f0(1400). In one solution a resonance at about 1700 MeV is also found. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with data. We construct approximation to our model and show that the Breit-Wigner approach has a limited phenomenological applicability., 36 pages with 6 figures, slightly modified version, accepted for publication in Eur. Phys. J. C

Maps are not reserved for geography. Chemical reactions, atomic diffusion and protein folding all involve atomic displacements determined by the topography of a complex energy landscape. These landscapes are largely unexplored, and our first priority is to identify their key features: the energy minima and the connecting paths between them. Such a study represents a formidable task. The effort needed to map a space increases exponentially with its dimensionality and becomes rapidly out of reach for the high-dimensional problems of interest in physics, chemistry and biology. Therefore, we have to satisfy ourselves with only a very crude knowledge of these energy landscapes. Recently, many researchers have been developing algorithms for exploring and mapping the potential energy landscapes of systems as diverse as polypeptides, chemical reactions, Lennard-Jones clusters and silica glass. In this article, we address some of the general issues and present an algorithm, called the activation-relaxation technique (ART), which we developed for mapping high-dimensional landscapes.

In this recent article, both figures 1 and 2 were misprinted. The correct figures appear below: Figure 1. Real and imaginary parts of the complex energy of ls2 as functions of parameter b. For each value of Z the curves corresponding to the following values of the parameter a have been presented 1/Z = 1.11: a = -0.1 , 0.0 (×), 0.1 , 0.2 , 0.3 , 0.4 , 0.5 (). 1/Z = 1.12: a = 0.0 (), 0.1 (×), 0.2 , 0.3 , 0.4 , 0.5 . 1/Z = 1.13: a = -0.2 (), -0.1 (×), 0.0 , 0.1 , 0.2 . 1/Z = 1.14: a = -0.3 (), -0.2 (×), -0.1 , 0.0 , 0.1 . Figure 2. Trajectories for constant a and increasing b values in the complex energy plan.

The materials of which thin-film transistors (TFTs) are fabricated are characterized by a large amount of defects, giving rise to localized states with a complex energy distribution within the gap. As a consequence, the electrical characteristics of TFTs are difficult to model analytically, and a numerical approach may be preferred to predict their performance. A new efficient method is presented to solve the time-dependent semiconductor equations accounting for energy-distributed gap states. Applications are provided to the analysis of realistic devices and inverters.

Open-channel effects on charmonium (\(\)- and \(\)-waves) and bottomonium (\(\)-wave) \(\) spectra are investigated within a one-open-channel approximation. Mass shifts and decay widths of these states just above the threshold are obtained by taking into account a coupling between confined quarkonium states and decaying states of the open channel. The final-state interaction (FSI) between the decaying meson and antimeson plays a very important role in producing a reasonable magnitude of coupling; the FSI provides the open-channel poles (R\(\), R\(\)) at the appropriate positions on the complex energy plane. The result is found to be independent of the detailed form of the transition potential and the final-state interaction.

The effect of the glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwire has been studied by the switching field distribution technique. The thermoactivated mechanism model is used to describe the thermally activated switching through the complex energy barrier in amorphous FeSiB microwires. Glass removal leads to the increase of the probability of the thermally activated switching pointing to the decrease of the energy barrier.

Proteins possess a complex energy landscape with a large number of local minima called conformational substates that are arranged in a hierarchical fashion. Here we discuss experiments aimed at the elucidation of the energy landscape in carbonmonoxy myoglobin (MbCO). In the highest tier of the hierarchy, a few taxonomic substates exist. Because of their small number, these substates are accessible to detailed structural investigations. Spectroscopic experiments are discussed that elucidate the role of protonations of amino acid side chains in creating the substates. The lower tiers of the hierarchy contain a large number of statistical substates. Substate interconversions are observed in the entire temperature range from below 1 K up to the denaturation temperature, indicating a wide spectrum of energy barriers that separate the substates.

Temperature dependent shell corrections are calculated taking into account the continuum spectrum of a finite depth mean field potential. The effect of the continuum is split up into a discret term which includes Gamow resonances and an integral along a contour in the complex energy plane. The resonances appear in the formalism in the same manner as bound states and at low temperatures they give the main part of the contribution due to the continuum. The method is applied to the particular case of {sup 208}Pb. The temperature for which the shell corrections are washed out completly is estimated at T{approx}2.5 MeV. {copyright} {ital 1997} {ital The American Physical Society}

Perovskite manganites have attracted considerable attention recently due to inhomogeneities in multi-functional properties, observed by various high resolution probes. We present an analysis of the essential role played by complex energy landscapes in the nanometer to micron-scale inhomogeneities observed in perovskite manganites using a model expressed in terms of symmetrized atomic-scale lattice distortion modes. We also discuss the origin for the stability of large metal and insulator domains in the absence of defects. We demonstrate that an intrinsic mechanism, which specifically involves longrange interactions between strain fields, the Peierls-Nabarro energy barrier, and complex energy landscapes with multiple metastable states is responsible for the inhomogeneities in perovskite manganites. This is in contrast to an extrinsic mechanism such as chemical randomness. We highlight experimental results which support our intrinsic, rather than extrinsic, mechanism.

We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $g\to0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy $\Delta E(\KK)$ of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses $m_\parallel^*(\KK)$, $m_\perp^*(\KK)$, as functions of the impurity wave vector $\KK$. Depending on the modulus of $\KK$ and on the impurity-to-fermion mass ratio $M/m$ we identify four regions separated by singularities in derivatives with respect to $\KK$ of the second-order term of $\Delta E(\KK)$, and we discuss the physical origin of these regions. Remarkably, the second-order term of $m_\parallel^*(\KK)$ presents points of non-differentiability, replaced by a logarithmic divergence for $M=m$, when $\KK$ is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold atom experiments., Comment: 6 pages, 4 figures; final version, including a finite temperature calculation

Colloidal particles spontaneously attach to the interface between two immiscible fluids to minimize the interfacial area between the two phases. The shape and wettability of particles have a strong influence on their configuration and interactions at fluid-fluid interfaces. In this study, we investigate the behavior of asymmetrically hydrophilic Janus cylinders (or double hydrophilic Janus cylinders with two different hydrophilic regions) trapped at an air-water interface. We find that these double hydrophilic Janus cylinders with aspect ratios of 0.9, 1.2, and 2.4 adopt both end-on and tilted configurations with respect to the interface. Our numerical calculations show that the coexistence of these configurations is a result of multiple energy minima present in the attachment energy profile that can be represented as a complex energy landscape. Double hydrophilic Janus cylinders with tilted orientations induce hexapolar interface deformation, which accounts for the pair interactions between the particles as well as the nondeterministic assembly behaviors of these particles at the interface.

A new approach to time-frequency analysis of fetal heart rate (FHR) variability is the matching pursuit (MP) method. MP analysis is proposed as away to capture complex energy structures ranging from burst-type to continuous activity in the time-frequency plane that other methods such as power-spectrum analysis and wavelet transforms may not detect. This article summarizes previous FHR analysis techniques, presents the MP algorithm, and shows the advantages of the MP method over other methods of FHR analysis.

The four-body equations of Alt, Grassberger and Sandhas are solved for the neutron-${}^3$H scattering at energies above the four-nucleon breakup threshold. The accuracy and practical applicability of the employed complex energy method is significantly improved by the use of integration with the special weights. This allows to obtain fully converged results with realistic nuclear interactions. A satisfactory description of the existing neutron-${}^3$H elastic scattering data is obtained., 5 pages, 2 tables, 3 figures, submitted to PRC

Rapid physical modelling of complex energy systems is a requirement for coping with rapid changing technologies demanded by this field. The variety of model domains and component types required for describing such complex systems makes the modelling task very challenging. Moreover, while a wide set of advanced tools for modelling highly-specialized tasks and perspectives already exists, a tool that covers all perspectives and components of a complex energy system does not exist. For this purpose, a rather primary but comprehensive evaluation of employing the universal modelling language Modelica in modelling applications of complex energy systems is presented. The advantages of utilizing such an approach is emphasized on an abstract model that is composed of several typical components within a complex energy system.

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of $K\pi $ form factors up to an energy $\tin=1 {\rm GeV}^2$. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros., Comment: 6 pages, 5 figures; Seminar given at DAE-BRNS Workshop on Hadron Physics Bhabha Atomic Research Centre, Mumbai, India October 31-November 4, 2011, submitted to Proceedings

Using the complex energy method, the problem of nucleon-deuteron scattering is solved with a simple three-body force having a separable form. Our results are compared with the results of modern direct two-variable calculations and a good agreement is found. This forms a firm base for other applications of the complex energy method., Comment: 6pages, 3figures

We have adopted the multistep shell model in the complex energy plane to study nuclear excitations occurring in the continuum part of the spectrum. In this method one proceeds by solving the shell model equations in a successive manner. That is, in each step one constructs the building blocks to be used in future steps. We applied this formalism to analyze the unbound nuclei $^{12,13}$Li starting from the one-particle states in $^{10}$Li and two-particle states in $^{11}$Li. In the former case the excitations correspond to the motion of three particles partitioned as the product of a one-particle and two-particle systems. The ground state of $^{12}$Li is thus calculated to be an antibound (virtual) state. In the four-particle system $^{13}$Li the states can be constructed as the coupling of two correlated pairs. We found that there is no bound or antibound state in $^{13}$Li., Comment: 10 pages, 2 table, 3 figures, Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Series

By means of a numerical analysis of the 2 + doublet in 8 Be, we show that accidental degeneracies of two resonant states mixed by a Hermitian interaction are associated with the occurrence of a simple and a double pole of the S -matrix in the complex energy plane. A true crossing may be brought about by the variation of just two parameters.

A simple cogeneration system consisting of a regenerative gasturbine system and a heat-recovery steam generator serves as an example to illustrate the application of exergoeconomic methods for evaluating and optimizing complex energy systems. We discuss various exergycosting approaches, the exergoeconomic variables, and the procedures used in evaluating and optimizing energy systems.

We present a general formalism for doing the perturbation theory in the complex energy plane, where the notion of the generalized quantum mechanical systems is used. This formalism is applied to the Friedrichs-Lee model. It reproduces the results of the exact solution, where the spectrum of the generalized quantum mechanical system consists of a discrete complex energy pole and a continuum spectrum (which passes below this discrete pole) in the complex energy plane. We also investigate the role of the “complex delta” function in the description of a resonance state. The unboundedness of the spectrum appears to be the very ingredient needed to give rise to a pure exponential decay.

We have adopted the multistep shell model in the complex energy plane to study excitations occurring in the continuum part of the nuclear spectrum. In this method of solving the shell model equatio ...

A workshop, 'Theory Meets Industry', was held on 12?14 June 2007 in Vienna, Austria, attended by a well balanced number of academic and industrial scientists from America, Europe, and Japan. The focus was on advances in ab?initio solid state calculations and their practical use in industry. The theoretical papers addressed three dominant themes, namely (i)?more accurate total energies and electronic excitations, (ii)?more complex systems, and (iii)?more diverse and accurate materials properties. Hybrid functionals give some improvements in energies, but encounter difficulties for metallic systems. Quantum Monte Carlo methods are progressing, but no clear breakthrough is on the horizon. Progress in order-N methods is steady, as is the case for efficient methods for exploring complex energy hypersurfaces and large numbers of structural configurations. The industrial applications were dominated by materials issues in energy conversion systems, the quest for hydrogen storage materials, improvements of electronic and optical properties of microelectronic and display materials, and the simulation of reactions on heterogeneous catalysts. The workshop is a clear testimony that ab?initio computations have become an industrial practice with increasingly recognized impact.

[1] A compilation of various spacecraft measurements made over the last 30 years suggests that the pitch angle distribution (PAD) width of a solar electron burst may have a complex energy signature. To date, no study has considered the PAD width over a broad energy range during a single solar electron burst. Here we use Wind 3DP data to examine the energy dependence of the PAD width between 100 eV to 100 keV during the solar electron burst of 22 March 2002. We find that the PAD width during this event varied nonmonotonically with energy, with a minimum in the width-energy profiles often being observed between 10 and 20 keV. In addition, we find time periods during and after the burst when the PAD width-energy profile had a distinct maximum or protuberance below 10 keV. The times at which the protuberance appeared were coincident with Type III radio events. This suggests that the protuberance in the width-energy profiles may be a manifestation of electron scattering by the electron/electron instability, as previously predicted by simulations.

In this paper we show how to compute the shear relaxation time from an underlying microscopic theory. We prove that the shear relaxation time in Israel-Stewart-type theories is given by the inverse of the pole of the corresponding retarded Green's function, which is nearest to the origin in the complex energy plane. Consequently, the relaxation time in such theories is a microscopic, and not a macroscopic, i.e., fluid-dynamical time scale., 10 pages, to appear in the proceedings of Advances in Nuclear Physics in Our Time (2010)

This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the energy is complex, the classical trajectories are open. Here it is shown that there is a discrete set of eigencurves in the complex-energy plane for which the particle trajectories are closed and periodic., Comment: 12 pages, 9 figures

The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the $\tau$-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications., Comment: Invited talk at the XII Mexican Workshop on Particles & Fields, Mazatlan, November 2009. To be published in American Institute of Physics Conference Proceedings Series

We consider a nonlinear evolution problem with an asymptotic parameter and construct examples in which the linearized operator has spectrum uniformly bounded away from Re z >= 0 (that is, the problem is spectrally stable), yet the nonlinear evolution blows up in short times for arbitrarily small initial data. We interpret the results in terms of semiclassical pseudospectrum of the linearized operator: despite having the spectrum in Re z < -c < 0, the resolvent of the linearized operator grows very quickly in parts of the region Re z > 0. We also illustrate the results numerically.

Within the framework of the J-matrix method of scattering, a given multichannel potential is modelled by its restriction on a subspace spanned by a certain set of L2 functions. The scattering S-matrix is found exactly for this model potential at the Harris eigenvalues which result from the diagonalization of the scattering Hamiltonian in the same subspace. These values are then analytically continued in the complex energy plane. The poles of the S-matrix are then identified with the complex resonance energies. The associated widths for each resonance are then extracted from the residues of the S-matrix elements at the designated energy.

Based on the generalized WKB and complex energy method, the authors study the atomic shape resonance in the IPA model, where the photoionization cross section shows maximum structure at resonance energies near the top of the barrier. Only f states of atoms around Xe and Rn have observable shape resonance structures.