Recent publications
In this research, we comprehensively investigate the thermodynamic properties of the Kiselev black hole and its holographic counterpart. Our investigation yields the thermodynamic product relations for the Kiselev black hole in environments permeated by dust and radiation. We establish that similar to Einstein’s gravity scenarios, the product of area (or entropy) in both contexts retains mass independence, suggesting its potential universality. In addition, we deduce bounds for the black hole’s entropy at both the inner and outer horizons. We also unveil an asymmetry between the central charges of the left and right-moving sectors when placed within the framework of universal thermodynamic principles. This asymmetry paves the way for inferring the central charges in the associated conformal field theory (CFT). Contrary to our initial findings, we observe that the central charges for the left and right-moving sectors in the CFT ultimately conform to uniform values.
Photon-assisted charge transport through a double-barrier laser structure, separated by a region assisted by a magnetic field, is studied. Employing Floquet theory and matrix formalism, the transmission probabilities for the central band and sidebands are calculated. The temporal periodicity of the laser fields creates an infinite number of transmission modes due to the degeneracy of the energy spectrum. The challenge of numerically addressing all modes necessitates the limitation to the first sideband corresponding to energies . A critical phase difference between the two laser fields is found to cancel the transmission through the sidebands due to quantum interference. Varying the width of the region where the magnetic field is applied allows for the suppression of lateral transmission and control over the transmission mode. The intensity of the laser fields also allows for the suppression of Klein tunneling and blocking transmission processes with zero photon exchange, as well as activating transmission processes with photon exchange. The conductance is also affected by changes in the system parameters. Increasing the intensity of the laser field reduces the conductance due to the confinement of the fermions by the laser fields. In addition, increasing the size of the region where the magnetic field is applied reduces the conductance because the increased distance gives the fermions a greater chance of diffusion and increases their interaction with the magnetic field.
We show how the Aharonov–Bohm flux (AB) ϕi and the dual gaps (Δ1, Δ2) can affect the electron scattering in graphene quantum dots (GQDs) of radius r0 in the presence of an electrostatic potential V. After obtaining the solutions of the energy spectrum, we explicitly determine the radial component of the reflected current Jrr , the square modulus of the scattering coefficients ∣cm∣², and the scattering efficiency Q. Different scattering regimes are identified based on physical parameters such as incident energy E, V, r0, dual gaps, and ϕi. In particular, we show that lower values of E are associated with larger amplitudes of Q. Furthermore, it is found that Q exhibits a damped oscillatory behavior with increasing the AB flux. In addition, increasing the external gap Δ1 resulted in higher values of Q. By increasing ϕi, we show that the oscillations in ∣cm∣² disappear for larger values of r0 and are replaced by prominent peaks at certain values of E and angular momentum m. Finally, we show that Jrr displays periodic oscillations of constant amplitude, which are affected by the AB flux.
This study aims to provide general axioms that should hold for any theory of quantum gravity. These axioms imply that spacetime is an emergent structure, which emerges from information. This information cannot occur in spacetime, as spacetime emerges from it, and hence exists in an abstract mathematical Platonic realm. Thus, quantum gravity exists as a formal system in this Platonic realm. Gödel’s theorems apply to such formal systems, and hence they apply to quantum gravity. This limits the existence of a complete consistent theory of quantum gravity. However, we generalize the Lucas-Penrose argument and argue that a non-algorithmic understanding exists in this Platonic realm. It makes it possible to have a complete and consistent theory of quantum gravity.
The Theory of Everything seeks to unify all fundamental forces of nature, including quantum gravity, into a single theoretical framework. This theory would be defined internally using a set of axioms, and this paper proposes a set of axioms for any such theory. Furthermore, for such a theory, all scientific truth would be defined internally as consequences derivable from the rules of such a theory. This paper then examines the implications of Tarski's undefinability theorem on scientific truths derived from such axioms. We demonstrate that Tarski's theorem imposes limitations on any such formal system . However, we also argue that the Lucas-Penrose argument suggests that non-algorithmic understanding can transcend these formal limitations.
The heat engine of magnetic black holes in Einstein–AdS gravity coupled to rational nonlinear electrodynamics, as the working substance, is studied. The dynamical negative cosmological constant is considered as a thermodynamic pressure. We investigate the efficiency of black hole heat engines in extended space thermodynamics for rectangle closed path in the P−V plane and the maximally efficient Carnot cycles. The exact efficiency formula that is written in terms of the mass of the black hole is obtained. It was demonstrated that the black hole efficiency decreases when the nonlinear electrodynamics coupling increases and the black hole efficiency increases if the magnetic charge increases. The relation between the efficiency, event horizon radiuses (entropy), and pressure is obtained. We study an efficiency of the holographic heat engine of a cycle in the vicinity of a critical point. Thus, the heat engine of our model can produce work.
We study the effect of the double potentials (barrier, well) on the Goos–Hänchen (GH) shifts in phosphorene. We determine the solutions of the energy spectrum associated with the five regions that make up our system. By studying the phase shifts, we find that the GH shifts are highly sensitive to the incident energy, the y directional wave vector, the potential heights and widths. To validate our findings, we perform a numerical analysis of the GH shifts as a function of the transmission probability under various conditions. In particular, we observe a consistent pattern in which a positive peak in the GH shift is always followed by a negative valley, a behavior evident at all potential height values. Notably, the energies at which the GH shift changes sign coincide exactly with the points at which transmission drops to zero. In particular, the transmission resonances that occur just before and just after the transmission gap region are strongly correlated with the points at which the GH shift changes sign. This study advances our understanding of how the double potential influences the GH shift behaviors in phosphorene. The ability to fine-tune the GH shifts by changing system parameters suggests potential applications in optical and electronic devices using this two-dimensional material.
In this series of papers, we present a set of methods to revive quantum geometrodynamics which encountered numerous mathematical and conceptual challenges in its original form promoted by Wheeler and De Witt. In this paper, we introduce the regularization scheme on which we base the subsequent quantization and continuum limit of the theory. Specifically, we employ the set of piecewise constant fields as the phase space of classical geometrodynamics, resulting in a theory with finitely many degrees of freedom of the spatial metric field. As this representation effectively corresponds to a lattice theory, we can utilize well-known techniques to depict the constraints and their algebra on the lattice. We are able to compute the lattice corrections to the constraint algebra. This model can now be quantized using the usual methods of finite-dimensional quantum mechanics, as we demonstrate in the following paper. The application of the continuum limit is the subject of a future publication.
Extracellular diffusion coupled with degradation is considered a dominant mechanism behind the establishment of morphogen gradients. However, the fundamental nature of these biophysical processes, visa viz, the Bicoid (Bcd) morphogen gradient, remains unclear. Fluorescence correlation spectroscopy has recently revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo. Here, we show that these observations are best fitted by a model fundamentally based on quantum mechanics. It is thus hypothesized that the transient quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. Furthermore, simulating the associated probability distribution for the model shows that the observed non-zero concentration of the Bcd molecules in the posterior-most parts of the embryo is a result of non-Gaussian distribution characteristic to quantum evolution. We conclude that with the Bcd gradient being essentially a one-dimensional problem, a simple one-dimensional model suffices for its analysis.
We consider magnetic graphene quantum dots (MGQDs) and study the impact of the Aharonov–Bohm (AB) flux and gap on the scattering process of electrons. Our emphasis is on the finite lifetimes of quasi-bound states arising from the interaction between electrons and the magnetic field within MGQDs. Initially, we calculate the scattering coefficients, scattering efficiency, and probability density by ensuring the continuity of eigenspinors at the boundary of MGQDs. The results indicate that as the gap increases, the quasi-bound states reach higher maxima. We show that an increase in AB-flux leads to a generation of quasi-bound states requiring less magnetic field, and the scattering efficiency starts to take non-zero values at smaller MGQD sizes. The analysis of probability density shows that the quasi-bound states, corresponding to non-resonantly excited scattering modes, exhibit a significant improvement in the concentrated density at MGQDs. The improvement is a result of reducing the diffraction phenomenon and suppressing the Klein effect through an increase in AB-flux and gap. This increases the probability of retaining the electron for a longer period of time.
We study the tunneling effect of two different junctions based on graphene. Firstly, we consider gapped monolayer graphene (MLG) bridging AA-bilayer graphene (BLG), and secondly, AB stacking. These two systems display a significant decrease in transmission in both setups, showing the adjustability of conductance through gap size manipulation. Furthermore, we identify distinct characteristics in both stackings, including Fano resonances and Fabry-Pérot-like oscillations. Examining conductance as a function of BLG region width gives away varying peaks in the conductance profile for both stackings, exhibiting diverse periods and shapes. We demonstrate that under specific parameter conditions, tunneling leads to zero conductance, contrasting with the case without bias. The coexistence of gap and bias introduces a complex pattern in conductance peaks, reflecting fluctuations in amplitude and frequency. Notably, our findings indicate that the gap induces a noteworthy shift in the conductance profile in AB stacking, suggesting a modification of electronic properties. In AA stacking, minima are particularly evident in the conductance profile, especially for small bias values.
We study the tunneling behavior of Dirac fermions in graphene subjected to a double barrier potential profile created by spatially overlapping laser fields. By modulating the graphene sheet with an oscillating structure formed from two laser barriers, we aim to understand how the transmission of Dirac fermions is influenced by such a light-induced electric potential landscape. Using the Floquet method, we determine the eigenspinors of the five regions defined by the barriers applied to the graphene sheet. Applying the continuity of the eigenspinors at barrier edges and using the transfer matrix method, we establish the transmission coefficients. These allow us to show that oscillating laser fields generate multiple transmission modes, including zero-photon transmission aligned with the central band ε and photon-assisted transmission at sidebands ε + l ϖ, with l = 0, ± 1, ⋯ and frequency ϖ. For numerical purposes, our attention is specifically directed towards transmissions related to zero-photon processes (l = 0), along with processes involving photon emission (l = 1) and absorption (l = − 1). We find that transmission occurs only when the incident energy is above the threshold energy ε > k y + 2ϖ, with transverse wave vector k y . We find that the variation in distance d 1 separating two barriers of widths d 2 − d 1 suppresses one transmission mode. Additionally, we show that an increase in laser intensity modifies transmission sharpness and amplitude.
RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intricacies of these sequences. We have previously devised a mathematical approach for defining a "healthy" sequence. This sequence is characterized by having at most four distinct nucleotides (denoted as nt ≤ 4). It serves as the generator of a group denoted as f p. The desired properties of this sequence are as follows: f p should be close to a free group of rank nt − 1, it must be aperiodic, and f p should not have isolated singularities within its SL 2 (C) character variety (specifically within the corresponding Groebner basis). Now, let us explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S 4 2. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI Equation. In certain cases, S 4 2 degenerates, in the sense that two punctures collapse, resulting in a "wild" dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find many applications including cancer research and the investigation of neurodegenative diseases.
We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters-the number of cells, barrier/well width, and barrier heights-on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry.
We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras.
This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the E8 root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of planar grids in three dimensions, with the grid spacing of each following a Fibonacci chain. It was found to be closely related to a five-fold compound of 3D sections taken from the 4D Elser–Sloane quasicrystal (ESQC), which is derived via a cut-and-project process from E8. More recently, a direct cut-and-project from E8 has been found which yields the FIG (presented in another paper of this series). The present paper focuses not on the full quasicrystal, but on the relationship between the root polytope of E8 (Gosset’s 421 polytope) and the core polyhedron generated in the FIG, a compound of 20 tetrahedra referred to simply as a 20-Group. In particular, the H3 symmetry of the FIG can be seen as a five-fold or “golden” composition of tetrahedral symmetry (referring to the characteristic appearance of the golden ratio). This is shown to mirror a connection between tetrahedral and five-fold symmetries present in the 421. Indeed, the rotations that connect tetrahedra contained within the 421 are shown to induce, in a certain natural way, the tetrahedron orientations in the 20-Group.
Background an objectives
Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between “healthy” nucleotide sequences and disrupted sequences that may be associated with various diseases. In this paper, we extend our efforts to the study of messenger RNA (mRNA) metabolism, showcasing the power of our approach.
Methods
To achieve this, we used: (a) infinite (finitely generated) groups , with generators representing the distinct nucleotides and a relation between them [e.g., the consensus sequence in the mRNA translation (i), the poly(A) tail in item (ii), and the microRNA seed in item (iii)]; (b) aperiodicity theory, which connects healthy groups to free groups of rank r and their profinite completion , and (c) the representation theory of groups over the space-time-spin group SL2(C), highlighting the role of surfaces with isolated singularities in the character variety.
Results
We investigate (1) mRNA translation in prokaryotes and eukaryotes, (2) polyadenylation in eukaryotes, which is crucial for nuclear export, translation, stability, and splicing of mRNA, (3) microRNAs involved in RNA silencing and post-transcriptional regulation of gene expression, and (4) identification of disrupted sequences that could lead to potential illnesses.
Conclusion
Our approach could potentially contribute to the understanding of the molecular mechanisms underlying various diseases and help develop new diagnostic or therapeutic strategies.
This paper introduces a new kind of quasicrystal by Fibonacci-spacing a multigrid of a certain symmetry, like H2, H3, T3, etc. Multigrids of a certain symmetry can be used to generate quasicrystals, but multigrid vertices are not a quasicrystal due to arbitrary closeness. By Fibonacci-spacing the grids, the structure transit into an aperiodic order becomes a quasicrystal itself. Unlike the quasicrystal generated by the dual-grid method, this kind of quasicrystal does not live in the dual space of the grid space. It is the grid space itself and possesses quasicrystal properties, except that its total number of vertex types are not finite and fixed for the infinite size of the quasicrystal but bounded by a slowly logarithmic growing number. A 2D example, the Fibonacci pentagrid, is given. A 3D example, the Fibonacci icosagrid (FIG), is also introduced, as well as its subsets, the Fibonacci tetragrid (FTG). The FIG can be thought of as a golden composition of five sets of FTGs. The golden composition procedure is another way to transit a random structure into aperiodic order, and the associated rotational angle is the same as the angle that resolves the geometric frustration for the H3 tetrahedral clusters. The FIG resembles another quasicrystal that is the same golden composition of five quasicrystals that are cut and projected and sliced from the E8 lattice. This leads to further exploration in mapping the FIG to the E8 lattice, and the results will be published following this paper.
In this letter, we propose a novel statistical method to measure which system is better suited to probe small deviations from the usual quantum behavior. Such deviations are motivated by a number of theoretical and phenomenological motivations, and various systems have been proposed to test them. We propose that measuring deviations from quantum mechanics for a system would be easier if it has a higher Kullback–Leibler divergence. We show this explicitly for a non-local Scr"{o}dinger equation and argue that it will hold for any modification to standard quantum behavior. Thus, the results of this letter can be used to classify a wide range of theoretical and phenomenological models.
The symmetries of a Riemann surface Σ \ {a i } with n punctures a i are encoded in its fundamental group π 1 (Σ). Further structure may be described through representations (homomorphisms) of π 1 over a Lie group G as globalized by the character variety C = Hom(π 1 , G)/G. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere Σ = S (4) 2 and the 'space-time-spin' group G = SL 2 (C). In such a situation, C possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface V a,b,c,d (x, y, z) with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or P V I); and (iii) there exists a finite set of 1 (Cayley-Picard)+3 (continuous platonic)+45 (icosahedral) solutions of P V I. In this paper, we feature the parametric representation of some solutions of P V I : (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups f p encountered in TQC or DNA/RNA sequences are proposed.
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