Multi-Valued Logic, Neutrosophy, and Schrödinger Equation

The uncertainty relation is considered to be one of key features of quantum mechanics which distinguishes quantum and classical systems. Recently, we developed a new formulation of the uncertainty relation based on the generalized scheme of variational principle, the stochastic variational method (SVM). In this method, the uncertainty relation is related to the nondifferentiability of observables and thus can be obtained even in classical stochastic systems. This new formulation resolves the famous paradox in quantum mechanics, the angular uncertainty relation without introducing artificial assumptions. In this paper, we show that the fluctuations of position and momentum for a nonrelativistic viscous fluid element satisfies the uncertainty relation analogous to the corresponding quantum mechanical one. Such a fluctuation is sensitive to the temperature gradient at the freezeout surface and can affect the collective flow anisotropy in relativistic heavy‐ion collisions.

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalize their argument, Schrödinger subsequently introduced the notion of quantum steering. Still, the question of which quantum states can be used for EPR steering and which cannot remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-1/2 particles, this approach completely characterizes the set of states leading to EPR steering. In addition, we discuss the generalization to higher-dimensional systems as well as generalized measurements. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question of which observables in quantum mechanics are jointly measurable.

We have already mentioned on many occasions that the probabilistic interpretation of quantum mechanics, the so called Gottingen (Born) – Copenhagen (Bohr) interpretation, was not accepted by the entire community of physi- cists and scientists as outstanding as Einstein, Schrodinger and de Broglie were among its opponents.

Paradox in quantum mechanics for an accelerating frame of reference

Nonlinear friction forces are a problem in classical Brownian motion for a long time [1]. They are described either by Langevin or by Fokker-Planck equations [2-4]. However, the rigorous generalized Langevin equation is linear, which points out that nonlinear friction forces possess a macroscopic hydrodynamic origin [1]. For this reason, they are not present in the modern quantum theory of open systems [5]. The scope of the present paper is to investigate the nonlinear friction effect on quantum mechanics. The analysis is based on a dissipative Madelung quantum hydrodynamics. Thus, the nonlinear friction is a result of nonlinear non-equilibrium thermodynamics in contrast to the traditional mechanical nonlinear friction forces. A quantum particle in vacuum is described by the Schrodinger equation

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces.

Quantum mechanics is generally an abstract theory that challenges intuition since it cannot be understood using ordinary experiences. Quantum tunneling is one of the topics which is more counterintuitive and challenges students' conceptual understanding. The study was aimed at investigating if final year undergraduate quantum mechanics students have alternative conceptions regarding quantum tunneling phenomena after a full course of instruction. In this study, students’ alternative conceptions are referred to as any student ideas related to the incorrect belief of scientific principles. Using the deep structured interviews involving 36 students who were registered in a quantum physics course from the University of Malawi, we found that some students hold on to the idea that the energy of a quantum tunneling electron is lost, the wave function graph depicts the physical wave, and the “potential step,” and “barrier” means a physical object/barrier. The study further established that the possible sources of these alternative conceptions emanated from students’ experience with classical tunneling / classical mechanics, quantum mechanics lecturer notes, and previous quantum mechanics lessons. The findings of this study further portray that traditional pedagogy has its limitation in facilitating students' comprehension of quantum tunneling. We recommend that further research into the design of instructional technology for quantum physics should consider these students' alternative conceptions when designing visual, interactive, and mental models, which may help establish students' conceptual understanding of quantum mechanics.

The aim of this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators, occurring in quantum mechanics. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms, in terms of the Fox’s H-function. Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented. The results given earlier by Saxena et al. [Fract. Calc. Appl. Anal., 13(2) (2010), pp. 177–190] and Purohit and Kalla [J. Phys. A Math. Theor., 44 (4) (2011), 045202] follow as special cases of our findings.

We propose an exact, testable relation between quantum mechanics and topological strings. The physical intuition behind this construction has its origin in the Fermi gas approach to ABJ(M) theory, in particular in its maximal supersymmetric version. By studying the relation between this model and topological strings on local P1xP1, we propose a more general Fermi gas formulation for topological strings on generic, toric Calabi-Yau manifolds. This formulation is fully non-perturbative, background independent and leads to a new and testable duality between quantum mechanics and topological strings. Our proposal has also a surprising mathematical counterpart, it exploits mirror symmetry to relate two well known mathematical fields: spectral theory and enumerative geometry.

Matter-wave dualism is a fundamental concept in quantum physics. The observation of wave properties of heavy organic molecules can be used to approach the borderline between classical and quantum physics. Up to which mass and size do particles or molecules still have wave properties? This question is subject to be answered within this thesis and as part of the international nanoquestfit-project where many researchers of different disciplines are involved.
\nThis thesis is a summary of the work done within a research collaboration between the group of Prof. Dr. Marcel Mayor (University of Basel) and the group of Prof. Dr. Markus Arndt (University of Vienna). The work is mainly focused on the development of novel quantum interference experiments that imply the development of new synthetic strategies towards tailor-made molecules. Novel interferometers have been developed by the Arndt group and therefore the molecular requirements changed strongly within the past years. The syntheses of these tailor-made molecules were performed by the author in the laboratories of Prof. Mayor in Basel. Quantum interference experiments and the preliminary investigations described within this work, namely the thermal stability test, the desorption studies and the laser-induced acoustic desorption have been performed by the Arndt group in Vienna.
\nInvestigations at the interface of quantum and classical physics are a fascinating part of the research. The final goal is to approach the quantum-to-classical transition by the observation of quantum properties of large and complex molecules. In order to study the wave nature of such particles—a purely quantum mechanical phenomenon—synthetic procedures towards tailor-made compounds are developed to improve the observation of this phenomenon through matter-wave experiments. 
\nAt the starting point of this work, a series of highly fluorinated porphyrin-monomers set a new benchmark in high-mass quantum interference experiments. The highest masses of particles used in quantum interference experiments were around 10’000 g/mol. Thus, our objective was to reach masses up to 25’000 g/mol with the suitable features for the quantum interferometry experiments.
\nIn the first chapter of this thesis, the principle of interferometry, the development and evolution of this technology are presented. In the subsequent chapters, the different synthetic approaches of the tailor-made molecules designed to improve the measurements and achieve the goal of this thesis are described.
\nThe main part of this thesis is focused on the synthesis of tailor-made molecules for quantum interference experiments. In a first part, the synthesis of a novel, more massive fluorinated phthalocyanine is presented. That phthalocyanine was used in far-field quantum interference experiments. Unfortunately, the molecular requirements could not been tuned to observe wave-particle duality in these experiments. The second part focuses on the synthesis of three different molecular libraries. Molecular libraries are mixtures of molecules having the same core but a to some extent random number of long perfluorinated chains. The individual members within the library were observable in MALDI-TOF mass spectrometry. We attached the chains to three different cores to obtain three different molecular libraries. To produce a first generation of libraries we used diacetylene bond porphyrin-dimer. The rather limited reaction scope of diacetylene bond porphyrins was enhanced by the second generation of tetramers and pentamers. To compare the modularity of the synthesis of oligo-porphyrin systems two additional cores, a porphyrin-dimer and a porphyrin-trimer, have also been synthesized. The possibility to produce a molecular beam with the three molecular-libraries has been investigated by thermal studies, desorption experiments and laser-induced acoustic desorption.
\nThe last part of the thesis is focused on the synthesis of photocleavable tags that can be attached to model compounds. These tags are synthesized since novel quantum interference experiments are based on light gratings where a mass difference is supposed to be observed at the detector level upon cleavage. The final idea is, in the near future, to attach these molecules to large particles, such as metal-nanoparticles, clusters or proteins. It is expected to enable the detection of mass differences of the intact clusters and the clusters with the cleaved tags. Three different model compounds have been synthesized. The cleavage of the tags was proven in solution upon irradiation of UV-light in solution, where a constant and reproducible decay was observed. In future quantum interference experiments, the cleavage should be performed in gas-phase as a final prove of concept. The molecules are currently under investigations in the Arndt group.

Quantum mechanics give significant cause to doubt conventional reality. This exegesis answers the question of how visual art, in engaging with quantum concepts, can enable a viewer to doubt conventional reality. I argue that visual art can do this by an artwork’s capacity to provoke unconventional thinking in the viewer and by the artist’s prudent considerations of materials and metaphor. I discuss my own artworks and those of others to assess the capacity of such works to cause ruptures of expected reality and so enable a viewer to doubt conventional reality. In particular, I argue that my three ‘mind works’ projects (the Metaphase Typewriter revival project, the Mind Lamp project and the Mind dispenser) are successful (even just on a metaphoric level) in enabling a viewer to doubt conventional reality. Specifically, this is because they provide the viewer opportunities to interact with events of quantum superposition, using only consciousness, to arguably affect or even create material reality.

This thesis develops a new way of modelling atoms that behave quantum mechanically on the inside, but classically on the outside. Doing so makes modelling the salient physics tractable. Prior to this technique, treating the outside of an atom classically failed to reproduce a bedrock experiment of quantum mechanics—the Stern–Gerlach experiment. I also report on the conception and flourishing of a control and analysis software suite for experiments in quantum science. This open-source project empowers experimenters to compose human-readable narratives upon their apparatus and has been adopted by a dozen groups worldwide.

It is demonstrated how quantum mechanics is generated by stochastic momentum kicks from the force carriers, transmitting the fundamental interactions between the point particles. The picture is consistent with quantum field theory and points out that the force carriers are the only quantum particles. Since the latter are waves in the coordinate space, they are responsible for the wavy character of quantum mechanics.

Ionic liquids (ILs) hold great promise in many fields including energy storage and generation, mechanical, pharmaceutical, synthetic and separation applications to name just a few. For any given application, the desired physical properties of the ideal IL may differ substantially from others and no widely applicable patterns or trends to facilitate intuitive design. The origins of physical properties lie in the characteristics of the intermolecular energetics, which consist of a complex interplay between electrostatic and dispersion forces. This thesis investigates and develops computational methodologies for calculating a reliable description of the intermolecular interactions for this challenging class of solvents and electrolytes of the future. The electrostatic approximation used in classical molecular dynamics (MD) where atomic partial charges are assigned was investigated in terms of methods based on density matrix partitioning, and the restrained electrostatic potentials (RESP) approaches. It was found that the “geodesic” atomic partial charge scheme, part of the RESP family, produced the most accurate charges. This was measured in terms of (a) charge convergence with increasing basis set size; (b) charge invariance with changes to the coordinate system; (c) insensitivity to minor structural changes on the resulting charges; (d) adequate capture of charge transfer effects; and (e) the preservation of symmetric of charges in symmetric molecules. Although charges can vary dramatically depending on the scheme used, the careful use of atomic partial charge schemes may still produce reliable forcefields, or at least serve as a rapid diagnostic tool to quantify electrostatic interactions and charge transfer. In moving towards unbiased a priori descriptions of IL intermolecular interactions, second-order Moller-Plesset perturbation theory (MP2) was used with the linear-scaling fragment molecular orbital (FMO) framework to assess the extent to which dispersion forces play a role in the intermolecular energetics. ILs of increasing size were examined such that the many-body effects may be captured. The dispersion energy contribution formed up to 20% of the total interaction energy. Furthermore, the interaction energy as produced by FMO was within 1 kJ mol−1 of the full-wavefunction MP2 interaction energy when three-body effects were included. As the dispersion interaction is purely a quantum mechanical phenomenon, correlated quantum mechanical methods, such as MP2 or coupled-cluster approaches, are required to provide an unbiased account of these effects. Ab initio methods such as MP2 and CCSD(T) scale formally as N⁵ an N⁷, respectively, with chemical system size. While the FMO approach provides a marked improvement in efficiency, the counterpoise (CP) approach to correcting the basis set superposition error (BSSE) is not amenable to fragmented approaches and requires each ion in the cluster to be calculated in the basis set of the entire system. In order to remove this bottleneck, the spin-component scaled second-order Moller Plesset perturbation theory (SCS-MP2) methodology was refined by fitting 174 non-CP corrected interaction energies at the MP2/cc-pVTZ level of theory to CP corrected CCSD(T)/CBS benchmark energies. This has resulted in an implicit BSSE correction that may be used within the highly efficient FMO framework, and is shown to yield results on par with or exceeding the accuracy of MP2/cc-pVQZ for clusters of two and four ion pairs (IPs). This new approach as been termed SCS-IL-MP2. An alternative dispersion corrected density functional theory (DFT) approach, DFT- D3, was assessed and refined in view of producing accurate interaction energies at the same CCSD(T)/CBS quality. The same test set of 174 ILs was used to fit the SCS-IL-MP2 approach was used to refit the DFT-D3 approach for both the Hartree-Fock (HF) wavefunction and the PBE and BLYP density functionals (DFs). In most cases, the selection of the DF and associated DFT-D version 3 (DFT-D3) parameters differed negligibly with all reaching within 1 to 2 kJ mol−1 per IP. HF-D3 parameters, on the other hand, showed a substantial improvement, particularly when used with the Becke-Johnson (BJ) damping function. Refitted HF-D3 and the BJ damping function was able to consistently provide interaction energy errors below 5 kJ mol−1 per IP. It would be worthwhile further investigating the application of the refined HF-D3 in its ability to produce reliable energies and geometries over a more diverse set of ILs. Both the SCS-IL-MP2 and new DFT-D3 approaches may be applied to the highly scal- able FMO framework. These form the core elements of the quantum chemistry toolbox for the study and understanding of the physicochemical properties of ILs that have so far been only superficially characterised by electronic structure theory. From this starting point, a rigorous and unbiased a priori understanding of the intermolecular interactions and resulting physicochemical properties may be predicted by means of efficient ab initio molecular dynamics (AIMD) techniques.

(1978). Orthomodular Lattices and Quantum Physics. Mathematics Magazine: Vol. 51, No. 5, pp. 299-303.