Classical Quantum Mechanics Research Articles

A transfer operator approach to relativistic quantum wavefunction * *Contribution to the Special Collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’.

The original intent of the Koopman–von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine what transfer operators can say about quantum mechanical evolution. To that end, we introduce a physically motivated scalar wavefunction formalism for a velocity field on a 4-dimensional pseudo-Riemannian manifold, and obtain an evolution equation for the associated wavefunction, a generator for an associated weighted transfer operator. The generator of the scalar evolution is of first order in space and time. The probability interpretation of the formalism leads to recovery of the Schrödinger equation in the non-relativistic limit. In the special relativity limit, we show that the scalar wavefunction of Dirac spinors satisfies the new equation. A connection with string theoretic considerations for mass is provided.

Machine learning in computational NMR-aided structural elucidation

Structure elucidation is a stage of paramount importance in the discovery of novel compounds because molecular structure determines their physical, chemical and biological properties. Computational prediction of spectroscopic data, mainly NMR, has become a widely used tool to help in such tasks due to its increasing easiness and reliability. However, despite the continuous increment in CPU calculation power, classical quantum mechanics simulations still require a lot of effort. Accordingly, simulations of large or conformationally complex molecules are impractical. In this context, a growing number of research groups have explored the capabilities of machine learning (ML) algorithms in computational NMR prediction. In parallel, important advances have been made in the development of machine learning-inspired methods to correlate the experimental and calculated NMR data to facilitate the structural elucidation process. Here, we have selected some essential papers to review this research area and propose conclusions and future perspectives for the field.

Histopathological effects of laser fiber diameter in different laser modulations: an experimental exvivo study

We aimed to compare the histopathological effects of different laser fiber diameters on kidney tissue using different modulations of holmium laser. An ex vivo trial was performed employing veal kidneys. A 100 W HoYAG laser device (Cyber Ho, Quanta System, Samarate, Italy) was employed, accompanied by 550 μm and 272 μm laser fibers for all experimental procedures. Incision depth (ID), vaporization area (VA), coagulation area (CA), surface section (SS), lateral effect (LE) and total laser area (TLA, calculated as VA+CA) were assessed. Histopathological measurement results of different laser fiber diameters were compared in Standard mode (SM) and Virtual BasketTM (VB) mode. In SM and VB, a statistically significant difference was found in the mean CA values between 272 (μm) and 550 (μm) laser diameters (p: 0.02 and p<0.001, respectively). In SM, the lowest and highest mean CAs were observed with the 272 (μm) lasers at 0.5 J-40 Hz and 1.5 J-40 Hz laser configurations (0.263±0.003 mm2 and 1.353±0.015 mm2, respectively). In VB, the lowest and highest mean CAs were observed with the 550 (μm) at 0.5 J-20 Hz and 1 J-20 Hz laser settings (0.987±0.014 mm2 and 1.969±0.029 mm2, respectively). We found that both SM and VB modulations have higher CA values, a measure of hemostasis, in 550 μm fibers compared to 272 μm fibers.

Low-temperature vibronic spectroscopy of condensed chromophore exhibiting inhomogeneous distribution of vibrational frequencies in a mixed quantum-classical environment.

This work has been motivated by the recent paper by the author [M. Toutounji, Phys. Chem. Chem. Phys., 2021, 23, 21981] whereby a mixed quantum-classical Liouville equation was used to probe the spectroscopy and dynamics of a spin-boson system. A mixed quantum-classical Liouville equation treats the system of interest quantum mechanically, the bath classically, and the coupling term mixed quantum-classical mechanically. This paper offers a two-fold advantage: correcting the treatment of the electronic transition decay (width in frequency domain) and assessing the local heterogeneous vibrational structure. The homogeneous linear absorption spectrum of a chromophore embedded in a mixed quantum-classical environment at low temperature is composed of a sharp peak called a zero-phonon line (ZPL) and a broad phonon sideband (PSB), whereby the ZPL and the PSB are assimilated by a Lorentzian function and Voigt profiles, respectively. The PSB, in this case, is characterized by a local heterogeneous structure due to a dispersive medium of vibrations, modeled by vibrational Gaussian distributions to represent the arising inhomogeneous broadening and Lorentzians to model the homogeneous vibrations. This description seems to model proteins and amorphous solids exhibiting a local heterogeneous structure as both electronic and vibrational inhomogeneous broadening seems to be large in these media. This work provides a derivation of linear absorption lineshape and vibronic transition dipole moment time correlation functions, both of which account for pure electronic dephasing (ZPL width) the Voigt profile description of the phonon profiles (PSB) in dispersive media.

The Historical Logic on the Basic Theory of Physics—A Summary on the Cosmic Continuum Theory

Any scientific system has a unified basic theory. But physics has no unified basic theory in the modern sense. Classical mechanics, relativity and quantum mechanics have their own basic concepts, categories and principles, so none of them can be regarded as true basic theories of physics. Cosmic Continuum Theory holds that the continuity and discreteness of the universe are fundamental issues related to the unification of physics. Because the contradiction between quantum non-locality and local reality is the fundamental obstacle to the unification of physics, while locality and non-locality correspond to the continuity and discreteness of physical reality respectively. The cosmic continuum theory introduces mathematical continuum and axiomatic ideas to reconstruct the basic theory of physics, and by the correspondence of existence and its dimensions to achieve the unification of the essence of physical reality, by introducing the cosmic continuum hypothesis to achieve the unification of the continuity and discreteness of physical reality, by introducing axiomatic methods to achieve formal unification of the foundations on physics. From the perspective of Cosmic Continuum, classical mechanics, relativity and quantum mechanics are no longer the basic theories of physics, but three branch theories of physics that are respectively applicable to macroscopic, cosmoscopic and microcosmic systems.

Finitely Repeated Adversarial Quantum Hypothesis Testing

Quantum technologies have been considered as a method to enhance cyber-security due to the unique properties of quantum systems. However, quantum systems themselves could also suffer from strategic attacks. In this paper, we formulate the relationship between the strategic attacker and a passive quantum detector into a Stackelberg game. By deriving the optimal detection rule at equilibrium, we study the detection performance of the detector under the setting of finite sample size of corrupted observations. Under mild assumptions, we show that the miss. We illustrate the general decaying results of the miss rate numerically, depicting that the passive detector manages to achieve a miss rate and a false alarm rate both exponentially decaying to zero given infinitely many quantum states, although at a much slower rate than a quantum non-adversarial counterpart. Finally, we adopt our formulations upon a case study of detection with quantum radars.

THE THEORY OF COMMUNICATION DYNAMICS: Application to Modelling the Valence Shell Orbitals of Periodic Table Elements

Atoms are considered basic building blocks of the material world. Computational modelling is a useful technique for studying and predicting natural events. Due to the complexity and wide scale range of particle systems, current computational modelling approaches, including Classical Mechanics, General Relativity, and Quantum Mechanics are separately designed to describe systems at different sizes and precisions. While these disparate models have practical value for discrete, domain-specific problems, lack of consistency between models results in challenges when multi-scale integration and computational scalability is required. In this paper, we proposed a novel theoretical framework, inspired by the communication theory of Shannon, to describe physical reality from a new perspective. We call this approach Communication Dynamics. As an initial demonstration of the relevancy of this model, we represent electron orbital structures of atoms. Our model aims to use a uniformly applicable mathematical formula to describe natural structures at different scales. We believe this information theoretical approach represents a new way to investigate particle-wave duality and opens a pathway to multi-scale model integration between physics and other fields of science. The appendix containing actual calculations is 141-page Wolfram Mathematica file, which can be obtained from SDPS web page.

On the cosmological constant as a quantum operator

We regard the cosmological fluid within an exponentially expanding FLRW spacetime as the probability fluid of a nonrelativistic Schroedinger field. The scalar Schroedinger particle so described has a mass equal to the total (baryonic plus dark) matter content of the Universe. This procedure allows a description of the cosmological fluid by means of the operator formalism of nonrelativistic quantum theory. Under the assumption of radial symmetry, a quantum operator proportional to [Formula: see text] represents the cosmological constant [Formula: see text]. The experimentally measured value of [Formula: see text] is one of the eigenvalues of [Formula: see text]. Next we solve the Poisson equation [Formula: see text] for the gravitational potential [Formula: see text], with the cosmological constant [Formula: see text] playing the role of a source term. It turns out that [Formula: see text] includes, besides the standard Newtonian potential [Formula: see text], a correction term proportional to [Formula: see text] identical to that appearing in theories of modified Newtonian dynamics.

Modeling the Cognitive Activity of an Individual Based on the Mathematical Apparatus of Self-Oscillatory Quantum Mechanics

The goal of this research is to design a model of cognitive activity in the human brain. The fundamental component of such a model is the mathematical apparatus of self-oscillating quantum mechanics considered through the theory of information images/representations. Methods. This article provides a brief description of the proposed theory and highlights remarkable similarities between information images/representations and certain elementary particles, in particular—virtual Feynman particles. Following this principle, the human mind is considered as a one-dimensional potential hole with finite walls of different sizes. The internal potential barrier in this model represents the border between consciousness and subconsciousness. The authors carried out parametrization, taking into account the proposed theory. This allowed authors to lay down the foundations of the mathematical apparatus, viewing the proposed model both from the standpoint of classical quantum mechanics and through the mathematical apparatus of self-oscillatory quantum mechanics. The findings could open a way to the prediction of certain cognitive functions of the human brain. Additionally, the authors formulated the equation, which describes the state function of the information image during the cognitive activity of an individual. Conclusions. The key outcome of this research are the primary calculations of the state functions of information images/representations on the computer model, as well as the patterns of movement of the information image into and out of the human consciousness.

Free to harmonic unitary transformations in quantum and Koopman dynamics* *Contribution to the Special Collection `Koopman Methods in Classical and Quantum–Classical Mechanics.

In the context of quantum dynamics there exists a coordinate transformation which maps the free particle to the harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time coordinate transformation. We demonstrate that an equivalent transformation can be performed for classical systems in the context of Koopman–von Neumann dynamics. We further extend this mapping both to dissipative evolutions as well as for a quantum–classical hybrid, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics. The derived classical procedure presents a number of opportunities to import squeezing dependent quantum procedures (such as Hamiltonian amplification) into the classical regime.

On generalizing trace minimization principles

Various trace minimization principles have interplayed with numerical computations for the standard eigenvalue and generalized eigenvalue problems in general, as well as important applied eigenvalue problems including the linear response eigenvalue problem from electronic structure calculation and the symplectic eigenvalue problem of positive definite matrices that play important roles in classical Hamiltonian dynamics, quantum mechanics, and quantum information, among others. In this paper, Ky Fan's trace minimization principle is extended along the line of the Brockett cost function tr(DXHAX) in X on the Stiefel manifold, where D of an apt size is positive definite. Specifically, we investigate infX⁡tr(DXHAX) subject to XHBX=Ik (the k×k identity matrix) or XHBX=Jk, where Jk=diag(±1). We establish conditions under which the infimum is finite and when it is finite, analytic solutions are obtained in terms of the eigenvalues and eigenvectors of the matrix pencil A−λB, where B is possibly indefinite and possibly singular, and D is also possibly indefinite.

(Invited) Spin and Optical Properties of the Silicon Vacancy in 4H-SiC for Quantum Science and Technology

Silicon vacancies in SiC are of significant interest for quantum information and sensing due to their unusual combination of long spin coherence time, optical addressability, and room-temperature operation in an industrially-relevant semiconductor. We characterize the spin and optical properties of the V2 silicon vacancy in 4H-SiC for both single defects and ensembles. We also show that they can be deterministically placed with sub-micron precision using focused Li ion implantation. Low-temperature photoluminescence excitation spectroscopy of the spin-dependent optical transitions of single silicon vacancies reveals two sharp lines with linewidths near the radiative lifetime limit. These lines correspond to the ms=±1/2 and ms=±3/2 states of an S=3/2 spin system that can be optically initialized, coherently manipulated with RF pulses, and read out via spin-dependent photoluminescence. We measure the different properties of spins in the two bases, and compare them to theoretical models. To suppress the limiting effects of the nuclear spin bath, we grow isotopically purified SiC with a very low abundance of 29Si and 13C. Our room temperature spin coherence measurements show orders-of-magnitude improvement of the coherence times in these materials. In particular, the inhomogeneous dephasing time T2 * in the ms=±1/2 basis shows a ~100x improvement, reaching 20 μs. We consider the prospects of this system for quantum sensing and as an efficient spin-photon interface for use in quantum networks.This work was supported by the U.S. Office of Naval Research, the OSD Quantum Sciences and Engineering Program, the Defense Threat Reduction Agency, and the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Endoscopic Enucleation of the Prostate – A Retrospective Single-center Study: Early Outcomes

Abstract Purpose: This clinical study was designed to present our initial experience of holmium laser enucleation of the prostate (HoLEP) with the use of the Quanta Litho Cyber Ho 150 W™ (Quanta System, Samarate, Italy). Materials and Methods: The data of the current study including all the patients who underwent HoLEP from April 2022 to December 2022 were retrospectively collected. All the operations were performed by the same experienced surgeon and the surgical technique was similar in all the cases. The successful completion of the operations, the operative time, and the major complications were the primary endpoints of this study. Results: Fifteen patients underwent HoLEP from April 2022 to December 2022 in our department. The completion of all the surgeries was successful. The average enucleation time was calculated to be 47.13 (±8.44) min, while the morcellation phase was completed in a mean time of 29.8 (±5.35) min. No major complications were noticed. The average hemoglobin drop was 1.4 (±0.69) g/dL. Conclusion: Our initial experience and early outcomes of the use of Quanta Litho Cyber Ho 150 W™ (Quanta System, Samarate, Italy) in HoLEP were presented. All the cases were completed successfully, without major complications or significant blood loss.

Measurement of a quantum system with a classical apparatus using ensembles on configuration space* *Contribution to the Special Collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’

Finding a physically consistent approach to modeling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical–quantum interactions which made use of the Koopman–von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.

Factors Affecting the Irrigation Fluid Temperature During Laser Lithotripsy: In Vitro Experimental Study

To investigate the effect of the diameter of laser fiber, pelvis volume, presenceand type of the stone on irrigation fluid temperature rise. A 20ml syringe, 12/14 ureteral access sheath(UAS), a dual-lumen catheter and a thermocouple were used. The 12/14Fr UAS(Cook Ireland Ltd., Limerick, Ireland) and the Thermocouple(SE001, Pico Technologies, Cambridgeshire, UK) were inserted in the syringe. The syringe was closed allowing outflow from the UAS with rate at 10ml/min. The Quanta Ho 150W(Quanta System, Samarate, Italy) laser was used and fired with 10W(2Jx5Hz), 20W(2 × 10 Hz), 40W(2 × 20 Hz), 60W(2 × 30 Hz). These power settings were tested in different conditions: fibers(200µm, 365µm and 550µm), volumes(5ml, 10ml and 20ml) and artificial stones(soft, hard). The laser was activated for 30 seconds and reactivation was performed when the temperature reached below 26°C. For all trials 60W of energy resulted in higher temperature rise. No differences were observed when different fibers were used. The highest temperatures (up to 80°C) for 60W were reported in 5ml syringe and the lowest (<45°C) with 20ml. The maximal temperature of >59°C was recorded for the power of 60W(1Jx60Hz). The temperature exceeded 43°C when power settings >40W were applied. Increasing the overall power, increases the irrigation fluid temperature significantly. The smaller the volume of the pelvis, the greater the temperature elevation. The fiber size did not affect the temperature increase pattern. The presence ofartificial stones was associated with the absorption of energy emitted by the laser.

Non-Papillary Access for the Percutaneous Antegrade Treatment of Renal and Ureteral Stones

ObjectiveTo evaluate the feasibility and success of medial non-papillary percutaneous access for the antegrade treatment of different locations of ureteral stones, with and without concomitant renal stones. MethodsWe performed an analysis of prospectively collected data of 72 patients, being subjected to percutaneous antegrade ureterolithotripsy. Stones located anywhere in the ureter with or without concomitant renal stones were included. A 12Fr, 22Fr, or 30Fr percutaneous tract dilation was performed based on the size of the stone pelvicalyceal system. Perioperative and demographic parameters were gathered and evaluated. The Lithoclast Trilogy (EMS Medical, Nyon, Switzerland) High-power holmium laser devices Cyber Ho 150 (Quanta System, Samarate, Italy) or MOSES Pulse 120H (Lumenis Ltd, Yokneam, Israel) were used for lithotripsy. ResultsThe average age and cumulative stone size of the patients were 57.9 ± 27.1 years and 24.2 ± 5.4 mm, respectively. The mean manipulation time was 36.9 ± 14.8 minutes. The mean hospitalization time was 2.5 ± 0.5 days and the average hemoglobin loss was 1.02 ± 0.18 gr/dL. The stone-free rate after percutaneous antegrade ureterolithotripsy was 95.8 % (69 patients), while the overall complications rate was 5.6 %, with 3 cases of fever and one case of prolonged hematuria that were treated conservatively. ConclusionNon-papillary percutaneous antegrade ureterolithotripsy is a safe and reliable technique for the treatment of patients with ureteral stones, with or without the co-existence of renal stones. A high stone-free rate of 95.8% was reported at 1-month after the surgery carrying a weighted risk of developing postoperative complications.

Optical quantum super-resolution imaging and hypothesis testing

Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our set-up is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can super-resolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 μm apart at a distance of 1.0 m with a 1.7% accuracy - an almost 3-orders-of-magnitude improvement over shot-noise limited direct imaging.

A real-time quantum-conscious multimodal option mining framework using deep learning

Option mining is an arising yet testing artificial intelligence function. It aims at finding the emotional states and enthusiastic substitutes of expounders associated with a discussion based on their suppositions, which are conveyed by various techniques of data. But there exist an abundance of intra and inter expression collaboration data that influences the feelings ofexpounders in a perplexing and dynamic manner. Step by step instructions to precisely and completely model convoluted associations is the critical issue of the field. To pervade this break, an innovative and extensive system for multimodal option mining framework called a “quantum-conscious multimodal option mining framework (QMF)”, is introduced. This uses numerical ceremoniousness of quantum hypothesis and a long transientmemory organization. QMF system comprise of a multiple-modal choice combination method roused by quantum obstruction hypothesis to catch the co- operations inside every expression and a solid feeble impact model motivated by quantum multimodal (QM) hypothesis to demonstrate the communications between nearby expressions. Broad examinations are led on two generally utilized conversational assessment datasets: the multimodal emotional lines dataset (MELD) and interactive emotional dyadic motion capture (IEMOCAP) datasets. The exploratory outcomes manifest that our methodology fundamentally outflanks a broadscope of guidelines and best in class models.

Revisiting quantum relativistic effects from phase transition by the catastrophe theory

In this paper we start from the Schrödinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase transition process when the velocity variable increases. Considering that the catastrophe theory could describe qualitatively any phase transition process, we adopt the simplest folding catastrophe type as the potential function in the Schrödinger equation to obtain a revised Schrödinger relativistic equation through the dimensionless analysis first, and then further to derive out the steady-state Klein-Gordon equation and Dirac relativistic equation gradually. These results reveal that the quantum relativistic effect could be considered as the phase transition process, which could be described by adopting the catastrophe models as the potential function in the classical Schrödinger equation.

New nonrelativistic quantum theory of cold dark matter

Cold dark matter (DM) is conceived as a gas of massive particles that undergo collisions, interact gravitationally and exchange quanta of energy. A new nonrelativistic quantum theory is presented for this model of DM, based on a recently discovered equation for a spinless, no charge and free particle. This theory describes the quantum processes undergoing by the particles, specifies the required characteristic wavelength of the quanta of energy, gives constraints on the mass of DM particles, and predicts a detectable gravitational wave background associated with DM halos.