Quantum Manifestations Research Articles

Exploring Quantized Massless Photonic Wave-Particle Duality, Inertial Mass Resistance to Motion, and the Speed of Light as Representations of a Higher Dimensional Hyperspace Axis within Subspace Field Unification

This paper explores the potentially interlinked, multidimensional nature of three fundamental qualities of reality. First, wave-particle duality is examined as an intrinsic extension of the fundamental two-dimensional electromagnetic wavelength, which permeates into a three-dimensional quantum manifestation of photonic particles. Second, the speed of light is considered as a limiting factor imposed by a multidimensional hyperspatial subspace ether grid, where the tensile locality restricts light's travel. Third, the movement of mass-carrying particles through this subspace ether grid is analyzed as being responsible for inertial resistance—specifically, resistance to changes in motion, including acceleration, deceleration, and changes in relative velocity.This paper then postulates that the massless motion of photonic energy packets at the speed of light, and the inertial resistance of mass-carrying hadronic particles to changes in relative motion, are opposite dimensional aspects of a unified subspace field theory. These aspects, though seemingly distinct, are proposed to occupy opposing sides of the same intersecting hyperspatial axis, within a higher-dimensional etheric reality.

Mapping Ishigurian Temporality: The Timeless Universe and His Prodigal Offspring

Time's elusive and enigmatic nature becomes evident when examining its diverse conceptualizations across fields, from cyclical rhythms to linear progression and quantum manifestation. While in Einsteinian physics time intertwines with space to form spacetime, revolutionizing the view of the Universe, the human perception of time involves a complex interplay of psychological factors, influencing memories, decision-making, and well-being. Literature has also embraced time as a central theme, transcending reality and exploring temporal distortion. This study takes a comprehensive journey through the intricate and multi-dimensional nature of a concept so deeply embedded in the human experience. Drawing insights from temporal science, psychology, spirituality, and literary studies, the research paper delves into the profound implications of temporal manipulation in the works of renowned writer Kazuo Ishiguro. The protagonists' distorted timelines highlight the fluidity and subjectivity of time, reflecting the intricate relationship between psychological states and time perception. Ishiguro's use of temporal dislocation reflects feelings of alienation and disconnection, illuminating the characters' struggles with memory, identity, mortality, and the search for meaning. Ultimately, the study seeks to demonstrate that Kazuo Ishiguro's novels provide profound insight into the human condition and the timeless quest for understanding. By embracing the primordial nature of existence, individuals may transcend the limitations of their time perception and connect with cosmic greatness. Ishiguro's work thus stands as a testament to literature's enduring relevance in illuminating human experience and the enigmatic nature of time itself. Overall, an in-depth exploration of time and its variants in literature leads to a more comprehensive understanding of life, fostering interdisciplinary connections and a holistic view of the world.

Screened Coulomb interaction in insulators with strong disorder.

We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.

Aging transition in coupled quantum oscillators.

Aging transition is an emergent behavior observed in networks consisting of active (self-oscillatory) and inactive (non-self-oscillatory) nodes, where the network transits from a global oscillatory state to an oscillation collapsed state when the fraction of inactive oscillators surpasses a critical value. However, the aging transition in quantum domain has not been studied yet. In this paper we investigate the quantum manifestation of aging transition in a network of active-inactive quantum oscillators. We show that, unlike classical case, the quantum aging is not characterized by a complete collapse of oscillation but by sufficient reduction in the mean boson number. We identify a critical "knee" value in the fraction of inactive oscillators around which quantum aging occurs in two different ways. Further, in stark contrast to the classical case, quantum aging transition depends upon the nonlinear damping parameter. We also explain the underlying processes leading to quantum aging that have no counterpart in the classical domain.

Quantum Manifestation of the Classical Bifurcation in the Driven Dissipative Bose-Hubbard Dimer.

We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose-Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.

Quantum manifestations in electronic properties of bilayer phosphorene nanoribbons.

Recently, a new edge structure named ZZ(U) has been evidenced as the lowest-energy structure for bilayer phosphorene nanoribbons (PNRs). Owing to strong quantum confinement effects and edge states, width and edge are the two most important factors that influence the properties of PNRs in nanosized microelectronics. In this study, we systematically investigated the evolution of the electronic properties of bilayer PNRs with different edge configurations as the widths vary. The four types of edges explored include ZZ(Pristine), ZZ(Klein), ZZ(Tube), and newly found ZZ(U). As the widths change from 14 to 40 Å, the ZZ(Pristine) are always metallic with edge states penetrating the Fermi level, while the others are semiconductors. The edge states in ZZ(Klein) are located in the two lowest conduction bands. However, in ZZ(U), the edge states are nearly hidden in the bulk band structure, and its carrier transportation exhibits almost perfect 2D layers, nearly eliminating the U-edge influence. Our results pave the way for phosphorene's utilization in electronics and optoelectronics.

Relativistic quantum scarring, spin-induced phase, and quantization in a symmetric Dirac billiard system

Thirty-five years ago, Sir Michael Berry and his collaborator Mondragon studied the behaviors of neutrino, a massless relativistic quantum particle, in a classically chaotic billiard—the neutrino billiard problem. To celebrate Sir Michael Berry’s eightieth birthday, here we report results on the role of geometric symmetries of the billiard system in relativistic quantum scarring. In particular, we investigate a Dirac billiard system with a four-fold rotational symmetry whose classical dynamics are fully chaotic. The system is described by the massless Dirac equation in the fundamental domain that consists of one fourth of the full billiard, with proper boundary conditions on the symmetry lines to preserve the physical properties under the symmetry operations. We show that the relativistic quantum characteristics of spin induced phase play a fundamental role in the quantum behaviors of the Dirac particle in the billiard. We find that the peaks in the length spectra are due to the interference of states circling the fundamental domain orbits (FDOs) in opposite propagating directions, which can be constructive or destructive depending on the accumulated phases. In addition, we derive the quantization conditions of the scarring states about the unstable periodic orbits within the fundamental domain from the phase along the FDOs. Our work is a vivid demonstration that relativistic quantum scarring, or more generally quantum manifestations of classical chaos, can be fully understood by analyzing the behaviors of the geometric phase—a powerful approach in modern physics pioneered by Sir Michael Berry.

Quantum computing and computational law

ABSTRACT Quantum computing technology will greatly enhance the abilities of the emerging field of computational law to express, model, and operationalise law in algorithmic form. Foreshadowing the harnessing of the power of quantum computing technology by the legal sector, this essay targets, with reference to computational complexity theory, the categories of computational problems which quantum computers are better equipped to deal with than are classical computers (‘quantum supremacy’). Subsequently, the essay demarcates the possible contours of legal ‘quantum supremacy’ by showcasing three anticipated legal fields of quantum technology: optimisation problems, burdens of proof, and machine learning. Acknowledging that the exact manifestation of quantum computing technology in the legal sector is as yet difficult to predict, the essay posits that the meaningful utilisation of quantum computing technology at a later stage presupposes a creative imagination of possible use-cases at the present.

The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators

We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova–Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index mu ) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.

Correspondence between classical and quantum resonances

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li⇆Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to ℏ=0 unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit ℏ→0. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.

SU(3)-skein algebras and webs on surfaces

The \(SU_3\)-skein algebra of a surface F is spanned by isotopy classes of certain framed graphs in \(F\times I\) called 3-webs subject to the skein relations encapsulating relations between \(U_q(sl(3))\)-representations. It is expected that their theory parallels that of the Kauffman bracket skein algebras. We make the first step towards developing that theory by proving that the reduced \(SU_3\)-skein algebra of any surface of finite type is finitely generated. We achieve that result by developing a theory of canonical forms of webs in surfaces. Specifically, we show that for any ideal triangulation of F every reduced 3-web can be uniquely decomposed into unions of pyramid formations of hexagons and disjoint arcs in the faces of the triangulation with possible additional “crossbars” connecting their edges along the ideal triangulation. We show that such canonical position is unique up to “crossbar moves”. That leads us to an associated system of coordinates for webs in triangulated surfaces (counting intersections of the web with the edges of the triangulation and their rotation numbers inside of the faces of the triangulation) which determine a reduced web uniquely. Finally, we relate our skein algebras to \({\mathcal {A}}\)-varieties of Fock–Goncharov and to \(\text {Loc}_{SL(3)}\)-varieties of Goncharov–Shen. We believe that our coordinate system for webs is a manifestation of a (quantum) mirror symmetry conjectured by Goncharov–Shen.

Quantum Information in Neural Systems

Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.

Quantized Dihedral Energy as Signature of Chemical Bond Breaking and Potential Applications in Large Bio-Molecules

Growing evidence for quantized dihedral energy emerges as interesting topic to explore chemical bond breaking event at fundamental level. Recent quantum computational studies on rivastigmine and water dimer system indicate the technique has potential to predict many useful quantum-based molecular simulations as well as prediction of results in single molecule force and torque spectroscopy experiments (https://doi.org/10.1080/07391102.2019.1708462). While molecular mechanics based dihedral energy always continuous, quantum-mechanical energies are discreet and the break-up conditions in molecular geometry or chemical-bond breaking show evidence for that as appeared in singularities or quantized feature of dihedral energy. In general, due to thermal background spectroscopic or other quantum signature of the molecule conformers are well masked to be detectable. However, under suitable condition of bond-breaking the corresponding dihedral energy parameter indeed show quantum manifestations as recently reported in water dimer system as well (DOI: 10.21203/rs.3.rs-40070/v1, under review). Recent studies have conclusively indicated the results can potentially provide very useful avenues both for theoretical and experimental setting to understand fundamental molecular bond breaking process by implementing single molecule force and torque spectroscopy to complement the theoretical predictions here. In this work we will present our most recent results on Binol system as its unique structure has been found to be an excellent molecule for the proof of concepts here. Besides results from several semi-quantum techniques, we will outline proposed experimentations and also further ab initio based results on the system and also proposed logical extension to large bio-macromolecular cases.

Quantum manifestations of homogeneous and inhomogeneous oscillation suppression states.

We study the quantum manifestations of homogeneous and inhomogeneous oscillation suppression states in coupled identical quantum oscillators. We consider quantum van der Pol oscillators coupled via weighted mean-field diffusive coupling and, using the formalism of open quantum systems, we show that, depending on the coupling and the density of mean-field, two types of quantum amplitude death occurs, namely, squeezed and nonsqueezed quantum amplitude death. Surprisingly, we find that the inhomogeneous oscillation suppression state (or the oscillation death state) does not occur in the quantum oscillators in the classical limit. However, in the deep quantum regime we discover an oscillation death-like state which is manifested in the phase space through the symmetry-breaking bifurcation of the Wigner function. Our results also hint toward the possibility of the transition from quantum amplitude death to oscillation death state through the "quantum" Turing-type bifurcation. We believe that the observation of quantum oscillation death state will deepen our knowledge of symmetry-breaking dynamics in the quantum domain.

Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.

Dimerization and N\xe9el Order in Different Quantum Spin Chains Through a Shared Loop Representation

The ground-states of the spin-S antiferromagnetic chain H_{{text {AF}}} with a projection-based interaction and the spin-1/2 XXZ-chain H_{{text {XXZ}}} at anisotropy parameter Delta =cosh (lambda ) share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar Q-state Potts model at sqrt{Q}= 2S+1 =2cosh (lambda ). The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for H_{{text {AF}}} at all S> 1/2, and Néel order for H_{{text {XXZ}}} at lambda >0. The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil–Copin–Li–Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray–Spinka of the discontinuity of the phase transition for Q>4. Altogether, the quantum manifestation of the change between Q=4 and Q>4 is a transition from a gapless ground-state to a pair of gapped and extensively distinct ground-states.

Quantum Computing and Algorithmic Law

Quantum computing technology will greatly enhance the abilities of the emerging field of computational law to express, model, and operationalize law in algorithmic form. In anticipation of the legal sector’s utilization of quantum computing technology, this essay identifies, with reference to computational complexity theory, the categories of computational problems which quantum computers are better equipped to deal with than are classical computers (‘quantum supremacy’). Subsequently, the essay demarcates the possible contours of legal ‘quantum supremacy’ by showcasing three anticipated legal fields of quantum technology: optimization problems, standards of proof, and machine learning. Acknowledging that the exact manifestation of quantum computing technology in the legal sector remains difficult to predict, the essay posits that the meaningful utilization of quantum computing technology at a later stage presupposes the creative imagination of possible use-cases at the present.

Manifestation of classical nonlinear dynamics in optomechanical entanglement with a parametric amplifier

Cavity optomechanical system involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the former regime, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regular periodic oscillation to period-doubling motion, in which cases the light-mechanical entanglement can be well studied by the logarithm negativity and can manifest the dynamical transition in the classical nonlinear dynamics. Moreover, the optomechanical entanglement shows a second-order transition characteristic at the critical parametric gain. For the latter regime, the kind of normal mode splitting comes up in the laser detuning dependence of optomechanical entanglement, which is induced by the squeezing of the optical and mechanical hybrid modes and finds no classical correspondence. The OPA assisted optomechanical systems therefore offer a simple way to study and exploit quantum manifestations of classical nonlinear dynamics.

Manifestations of chaos in relativistic quantum systems - A study based on out-of-time-order correlator

Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.

On a possible quantum manifestation of the perihelion advance in a hydrogen-like atom

In a static and spherically symmetric case, by following an analog procedure for obtaining a Reissner–Nordstrom solution, thanks to the use of both the Einstein-type equation for an electromagnetic field as well as the Maxwell equation in curved space–time, we managed to find the Schwarzschild-like solution outside a charged sphere Q in interaction with a test charged particle q at an atomic scale where the gravitational force is negligibly small compared to the electrostatic force. Then, in the context of an extension of the equivalence principle to the electromagnetic interaction, we have studied the hydrogen atom. At the atomic scale, where quantum effects can no longer be ignored and the concept of trajectory is abandoned, the corrective terms derived from the geodesic equation for the electron are used within a perturbation theory. At the first order, these radial corrections of the Hamiltonian can partially remove the degeneracy of Bohr’s levels through a Lamb-like shift of the energy levels (2s) and (2p), estimated to E(2s) – E(2p) = 2.4595087102 × 10−4 eV. To match the experimental value of the Lamb shift, 4.372 × 10−6 eV, we have postulated the existence of an electromagnetic background that would describe statistically the vacuum energy by the introduction of a “cosmological”-like constant in the Einstein-like equation for electromagnetism. We have pointed out a divergence when n → +∞ in energy corrections due to a “cosmological” constant that technically could be overcome by the use of a cutoff as well as the renormalization of the electron’s mass.