Trajectories in the complex phase space and quantization by numerical contour integration

Semiclassical quantization of complex Henon–Heiles systems

We derive a semiclassical nonequilibrium work identity by applying the Wigner–Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us to extend the concept of work to the leading order in ℏ. We propose a geometric interpretation of this semiclassical Jarzynski relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable case of the quantum harmonic oscillator.

This paper presents the analysis and determination of microwave filter order using numerical contour integration method. Based on argument principle, the numerical contour integration is evaluated using central finite-differencing for the $S$ parameter derivative and applied to various microwave bandpass filters involving transmission line structures. It is useful to ascertain the filter order that is often not obvious especially for transmission line structures and enables one to know the targeted number of poles to solve for within certain passband. Using several examples, we show that the order or number of poles for bandpass filters may not be determined simply from the filter structures, their number of sections or reflection zeros. The correct order or number of poles can be determined using our numerical contour integration method.

On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions

In the present work, using the generalized Boltzmann equation of the first author [Phys. Rev. E 94, 023316 (2016)], a quantum kinetic model in the complex phase space is proposed. Employing the Chapman-Enskog analysis and applying the Wick rotation (using complex-valued relaxation time), it is shown that the present model recovers the time-dependent Schr\oedinger equation, while preserving the main features of the conventional lattice Boltzmann models, e.g., simplicity of implementation, second-order accuracy (in space), and convenience in parallel programming. The present results are numerically verified by simulating three benchmark problems.

With a view to increasing the scope of applications of supersymmetric quantum mechanics (SUSY QM), we formulate the same in a complex phase space. Within this framework, the concept of shape invariance is reinvestigated and an insight into the eigenvalue spectra of non-Hermitian Hamiltonians is sought. The results are applied to a variety of potentials. We claim that the shape invariance for these potentials in the complex phase space can be retrieved in terms of the prescriptions already proposed in the conventional SUSY QM, in that the transformation of potential parameters takes the form of a reflection in the parameter space. Interestingly, some of these features turn out to be the generalization of the concept of quasi-parity used recently in the context of SUSY QM of PT-symmetric potentials. Further, a correspondence of the present approach with other complex formulations of SUSY QM and also in two real dimensions is demonstrated.

Introduction: The availability of prescription drugs as OTC medications is also becoming more common. However, self-medication carries risks such as misdiagnosis, use of excessive drug doses, prolonged use, and drug interactions. This review aimed to collect evidence about the impact of self-medications on health outcomes. Methods: The systematic review in this study involved several steps to identify and assess relevant research. The search phase involved finding potentially relevant studies in various databases such as PubMed, PsychInfo, EBSCO Medline, BioMed central, and Science Direct. The screening phase involved applying predetermined inclusion and exclusion criteria to determine which studies were appropriate for the review. To conclude the selection process, the full text of the articles was reviewed to determine whether they met the inclusion criteria. Additionally, the full text of review articles was reviewed to identify any additional articles that might be relevant and included in the review. Results: A total of 17 studies were found that met the inclusion criteria. The majority (11/17) of these studies were cross-sectional and relied on self-report. The combined sample size of the 17 studies was 28,628 (ranging from 5 to 5,426), and the average response rate was 66%. In 76% of the studies, reported self-treatment was 50% (ranging from 12% to 99%). Overall, only one or two respondents were registered with a general practitioner (GP) or primary care physician (mean of 56%, ranging from 21% to 96%). In the 13 studies that provided information on self-prescription, the mean percentage of physicians reporting self-prescription was 61% with a standard deviation of 25% and a range of 9% to 99%. Conclusions: Although many patients view over-the-counter (OTC) medications as completely safe, their use always carries some degree of risk for the consumer. This is especially true for patients who do not follow the instructions on the label or package insert.

Full-text articles, manuscript tracking, and automated literature search lead new array of AJKD online features.

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (xγ, Πγ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

BackgroundWith the growing availability of full-text articles online, scientists and other consumers of the life sciences literature now have the ability to go beyond searching bibliographic records (title, abstract, metadata) to directly access full-text content. Motivated by this emerging trend, I posed the following question: is searching full text more effective than searching abstracts? This question is answered by comparing text retrieval algorithms on MEDLINE® abstracts, full-text articles, and spans (paragraphs) within full-text articles using data from the TREC 2007 genomics track evaluation. Two retrieval models are examined: bm25 and the ranking algorithm implemented in the open-source Lucene search engine.ResultsExperiments show that treating an entire article as an indexing unit does not consistently yield higher effectiveness compared to abstract-only search. However, retrieval based on spans, or paragraphs-sized segments of full-text articles, consistently outperforms abstract-only search. Results suggest that highest overall effectiveness may be achieved by combining evidence from spans and full articles.ConclusionUsers searching full text are more likely to find relevant articles than searching only abstracts. This finding affirms the value of full text collections for text retrieval and provides a starting point for future work in exploring algorithms that take advantage of rapidly-growing digital archives. Experimental results also highlight the need to develop distributed text retrieval algorithms, since full-text articles are significantly longer than abstracts and may require the computational resources of multiple machines in a cluster. The MapReduce programming model provides a convenient framework for organizing such computations.

We have recently published a new semiclassical method, generalized Gaussian wave packet dynamics, which extends Gaussian wave packet dynamics into complex phase space. Although we were able to give an accurate formulation of the method, we had at the time of writing that paper only an intuitive, heuristic understanding of the deeper causes which make the method work. A more mathematical understanding was needed. To close this gap we show in this paper the equivalence of the new method with a first order expansion of ℏ of the Schrödinger equation. We further prove that the new method is equivalent to the stationary phase approximation, using the usual WKB formula for the propagator. The latter equivalence enables us to show that all the symmetry properties of time-dependent quantum mechanics also hold in the new semiclassical theory. Finally, we provide some elaboration of the method, and clarify several issues that were not discussed before. With this new insight we are able to formulate a simple rule for the calculation of semiclassical wave functions that contain contributions from more than one branch. This corrects for the divergence of semiclassical wave functions near caustics, a problem that we encountered in the preceding paper.

Abstract. In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general, and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare events algorithms like TAMS (trajectory-adaptive multilevel sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called the committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (analog Markov chains, neural networks, reservoir computing, dynamical Galerkin approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analog Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

The method of parametric decomposition is focused on exact methods of the perturbed nonlinear systems' study. The method allows research into the behavior of many-dimensional nonlinear systems through the study of the behavior of the basic subsystems, no higher than the 2nd order, performing rigorous analysis. Investigation of the basic subsystems is proposed using the point transformation method in two-sided phase plane and into complex phase space.

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the monster flip, an almost impossible skateboard trick.

Highly excited atoms in external fields arc fundamental quantum systems which possess in many cases a classically chaotic analogue. The analysis of their quantum spectra is of fundamental importance for a deeper understanding of phenomena related to the so-called quantum chaos. The development and application of closed-orbit theory was the decisive step for a semiclassical calculation and interpretation of photoabsorption spectra. In its original version formulated by Du and Delos (1988) and Bogomolny (1989) closed-orbit theory was able to reproduce most structures in hydrogenie and even nonhydrogenic atoms but suffered from singularities at energies where orbits undergo bifurcations. Unphysical singularities at bifurcation energies of closed orbits are now removed in uniform semiclassical approximations and the analysis of these uniform solutions also reveals the role and physical importance of "ghost" orbits in complex phase space.