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38 pages, 1412 KB  
Article
A Framework for Understanding the Impact of Integrating Conceptual and Quantitative Reasoning in a Quantum Optics Tutorial on Students’ Conceptual Understanding
by Paul D. Justice, Emily Marshman and Chandralekha Singh
Educ. Sci. 2025, 15(10), 1314; https://doi.org/10.3390/educsci15101314 - 3 Oct 2025
Abstract
We investigated the impact of incorporating quantitative reasoning for deeper sense-making in a Quantum Interactive Learning Tutorial (QuILT) on students’ conceptual performance using a framework emphasizing integration of conceptual and quantitative aspects of quantum optics. In this investigation, we compared two versions of [...] Read more.
We investigated the impact of incorporating quantitative reasoning for deeper sense-making in a Quantum Interactive Learning Tutorial (QuILT) on students’ conceptual performance using a framework emphasizing integration of conceptual and quantitative aspects of quantum optics. In this investigation, we compared two versions of the QuILT that were developed and validated to help students learn various aspects of quantum optics using a Mach Zehnder Interferometer with single photons and polarizers. One version of the QuILT is entirely conceptual while the other version integrates quantitative and conceptual reasoning (hybrid version). Performance on conceptual questions of upper-level undergraduate and graduate students who engaged with the hybrid QuILT was compared with that of those who utilized the conceptual QuILT emphasizing the same concepts. Both versions of the QuILT focus on the same concepts, use a scaffolded approach to learning, and take advantage of research on students’ difficulties in learning these challenging concepts as well as a cognitive task analysis from an expert perspective as a guide. The hybrid and conceptual QuILTs were used in courses for upper-level undergraduates or first-year physics graduate students in several consecutive years at the same university. The same conceptual pre-test and post-test were administered after traditional lecture-based instruction in relevant concepts and after student engaged with the QuILT, respectively. We find that the post-test performance of physics graduate students who utilized the hybrid QuILT on conceptual questions, on average, was better than those who utilized the conceptual QuILT. For undergraduates, the results showed differences for different classes. One possible interpretation of these findings that is consistent with our framework is that integrating conceptual and quantitative aspects of physics in research-based tools and pedagogies should be commensurate with students’ prior knowledge of physics and mathematics involved so that students do not experience cognitive overload while engaging with such learning tools and have appropriate opportunities for metacognition, deeper sense-making, and knowledge organization. In the undergraduate course in which many students did not derive added benefit from the integration of conceptual and quantitative aspects, their pre-test performance suggests that the traditional lecture-based instruction may not have sufficiently provided a “first coat” to help students avoid cognitive overload when engaging with the hybrid QuILT. These findings suggest that different groups of students can benefit from a research-based learning tool that integrates conceptual and quantitative aspects if cognitive overload while learning is prevented either due to students’ high mathematical facility or due to their reasonable conceptual facility before engaging with the learning tool. Full article
31 pages, 5301 KB  
Article
Comprehensive Computational Study of a Novel Chromene-Trione Derivative Bioagent: Integrated Molecular Docking, Dynamics, Topology, and Quantum Chemical Analysis
by P. Sivaprakash, A. Viji, S. Krishnaveni, K. M. Kavya, Deokwoo Lee and Ikhyun Kim
Int. J. Mol. Sci. 2025, 26(19), 9661; https://doi.org/10.3390/ijms26199661 - 3 Oct 2025
Abstract
This work thoroughly investigated the compound 4-(2,5-Dimethoxyphenyl)-3,4-dihydrobenzo[g]chromene-2,5,10-trione (DMDCT) using molecular docking, quantum chemical analysis, and vibrational spectroscopy methodology. The medicinal chemistry group has been particularly interested in chromene and benzochromene derivatives due to their wide range of pharmacological actions, including anticancer, antibacterial, anti-inflammatory, [...] Read more.
This work thoroughly investigated the compound 4-(2,5-Dimethoxyphenyl)-3,4-dihydrobenzo[g]chromene-2,5,10-trione (DMDCT) using molecular docking, quantum chemical analysis, and vibrational spectroscopy methodology. The medicinal chemistry group has been particularly interested in chromene and benzochromene derivatives due to their wide range of pharmacological actions, including anticancer, antibacterial, anti-inflammatory, antioxidant, antiviral, and neuroprotective capabilities. In this connection, DMDCT has been explored to evaluate its biological, electrical, and structural properties. DFT using the B3LYP functional and 6–31G basis was established to conduct theoretical computations with the Gaussian 09 program. The findings from these computations provide insight into the following topics: NBO interactions, optimal molecular geometry, Mulliken charge distribution, frontier molecular orbitals, and MEP. Second-order perturbation theory has been used to assess stabilization energies arising from donor–acceptor interactions. Furthermore, general features such as chemical hardness, softness, and electronegativity were studied. The results suggest that DMDCT has stable electronic configurations and biologically relevant active sites. This integrated experimental and theoretical study supports the potential of DMDCT as a practical scaffold for future therapeutic applications and contributes valuable information regarding its vibrational and electronic behavior. Full article
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26 pages, 1838 KB  
Article
Modeling the Emergence of Insight via Quantum Interference on Semantic Graphs
by Arianna Pavone and Simone Faro
Mathematics 2025, 13(19), 3171; https://doi.org/10.3390/math13193171 - 3 Oct 2025
Abstract
Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this [...] Read more.
Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this work, we propose a computational model of insight generation grounded in continuous-time quantum walks over weighted semantic graphs, where nodes represent conceptual units and edges encode associative relationships. By exploiting the principles of quantum superposition and interference, the model enables the probabilistic amplification of semantically distant but contextually relevant concepts, providing a plausible account of non-local transitions in thought. The model is implemented using standard Python 3.10 libraries and is available both as an interactive fully reproducible Google Colab notebook and a public repository with code and derived datasets. Comparative experiments on ConceptNet-derived subgraphs, including the Candle Problem, 20 Remote Associates Test triads, and Alternative Uses, show that, relative to classical diffusion, quantum walks concentrate more probability on correct targets (higher AUC and peaks reached earlier) and, in open-ended settings, explore more broadly and deeply (higher entropy and coverage, larger expected radius, and faster access to distant regions). These findings are robust under normalized generators and a common time normalization, align with our formal conditions for transient interference-driven amplification, and support quantum-like dynamics as a principled process model for key features of insight. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
15 pages, 339 KB  
Article
Enhancing Variational Informational Principles: A Complexified Approach with Arbitrary Order Norms
by D. Bernal-Casas and José M. Oller
Mathematics 2025, 13(19), 3160; https://doi.org/10.3390/math13193160 - 2 Oct 2025
Abstract
This paper offers an innovative exploration of variational informational principles by incorporating complexification and studying norms of arbitrary order, thereby surpassing the limitations of the conventional L2 norm. For years, variational principles have been vital for deriving fundamental results in both physics [...] Read more.
This paper offers an innovative exploration of variational informational principles by incorporating complexification and studying norms of arbitrary order, thereby surpassing the limitations of the conventional L2 norm. For years, variational principles have been vital for deriving fundamental results in both physics and information theory; however, our proposed framework represents a significant advancement by utilizing complex variables to enhance our understanding of information measures. By employing complex numbers, we introduce a sophisticated structure that captures phase information, thereby significantly improving the potential applicability and scope of variational principles. The inclusion of norms of arbitrary order further expands the scope of optimization problems in information theory, leading to the potential for more creative solutions. Our findings indicate that this extended framework not only maintains the essential characteristics of traditional variational principles but also reveals valuable insights into the complex interplay between complexity, information, and optimization. We conclude with a thoughtful discussion of potential applications and future research directions, emphasizing the transformative impact that complexified variational principles, together with norms of arbitrary order, could have on the study of quantum dynamics. Full article
17 pages, 828 KB  
Article
Quantum Coherence and Mixedness in Hydrogen Atoms: Probing Hyperfine Structure Dynamics Under Dephasing Constraints
by Kamal Berrada and Smail Bougouffa
Symmetry 2025, 17(10), 1633; https://doi.org/10.3390/sym17101633 - 2 Oct 2025
Abstract
We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical [...] Read more.
We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Quantum coherence is quantified through the l1-norm measures, while purity is evaluated to assess mixedness. Results demonstrate that coherence exhibits oscillatory decay modulated by the dephasing rate, with antiparallel spin states showing greater resilience against noise compared to parallel configurations. These findings highlight the interplay between coherent hyperfine dynamics and environmental dephasing, offering insights into preserving quantum resources in atomic systems for applications in quantum information science. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Quantum Mechanics)
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15 pages, 2496 KB  
Article
Structures, Interactions, and Antimicrobial Activity of the Shortest Thanatin Peptide from Anasa tristis
by Swaleeha Jaan Abdullah, Jia Sheng Guan, Yuguang Mu and Surajit Bhattacharjya
Int. J. Mol. Sci. 2025, 26(19), 9571; https://doi.org/10.3390/ijms26199571 - 30 Sep 2025
Abstract
Antimicrobial peptides (AMPs), also referred to as host defense peptides, are promising molecules in the development of the next generation of antibiotics against drug-resistant bacterial pathogens. Thanatin comprises a family of naturally occurring cationic AMPs derived from several species of insects. The first [...] Read more.
Antimicrobial peptides (AMPs), also referred to as host defense peptides, are promising molecules in the development of the next generation of antibiotics against drug-resistant bacterial pathogens. Thanatin comprises a family of naturally occurring cationic AMPs derived from several species of insects. The first thanatin, 21 residues long, was identified from the spined soldier bug, and more thanatin peptides have been discovered in recent studies. The 16-residue thanatin from Anasa tristis, or Ana-thanatin, represents the shortest sequence in the family. However, the antimicrobial activity and mechanistic process underpinning bacterial cell killing have yet to be reported for Ana-thanatin peptide. In this work, we examined the antibacterial activity, structures, and target interactions of Ana-thanatin. Our results demonstrated that Ana-thanatin exerts potent antibiotic activity against strains of Gram-negative and Gram-positive bacteria. Biophysical studies demonstrated that Ana-thanatin interacts with LPS outer membrane and can permeabilize the OM barrier in the process. Atomic-resolution structures of the peptide in free solution and in complex with lipopolysaccharide (LPS) micelle were solved by NMR, determining canonical β-sheet structures. Notably, in complex with LPS, the β-sheet structure of the peptide was better defined in terms of the packing of amino acid residues. Further, MD simulations demonstrated rapid binding of the Ana-thanatin peptide with the LPS molecules within the lipid bilayers. These studies have revealed structural features which could be responsible for LPS-OM disruption of the Gram-negative bacteria. In addition, NMR heteronuclear single quantum coherence (HSQC) studies have demonstrated that Ana-thanatin can strongly interact with the LPS transport periplasmic protein LptAm, potentially inhibiting OM biogenesis. Taken together, we surmise that the Ana-thanatin peptide could serve as a template for the further development of novel antibiotics. Full article
(This article belongs to the Collection Feature Papers in Molecular Biophysics)
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20 pages, 1156 KB  
Article
Developing Up-Scale Allogeneic Chondrocyte Therapies Using Juvenile Donor Cartilage
by Charlotte H. Hulme, Jade Perry, Helen S. McCarthy, Tian Lan, Thavisha Ranasinghe, Nigel Kiely, Robert Freeman, Jonathan Wright and Karina T. Wright
Int. J. Mol. Sci. 2025, 26(19), 9566; https://doi.org/10.3390/ijms26199566 - 30 Sep 2025
Abstract
Allogeneic chondrocyte therapies present an attractive alternative to existing autologous therapies for the repair of cartilage defects, enabling the selection of optimal donor cells and streamlined manufacturing processes. This study investigates the potential of juvenile chondrocytes derived from human infantile (aged 0–4 y) [...] Read more.
Allogeneic chondrocyte therapies present an attractive alternative to existing autologous therapies for the repair of cartilage defects, enabling the selection of optimal donor cells and streamlined manufacturing processes. This study investigates the potential of juvenile chondrocytes derived from human infantile (aged 0–4 y) polydactyly digits and the iliac apophysis for cartilage repair using Good Manufacturing Practice bioreactor expansion. Iliac apophysis (n = 4) and polydactyly tissues (n = 4) were assessed histologically. Chondrocytes were isolated enzymatically and cultured using standard tissue culture plastic (TCP) methodology. Upon sufficient cell expansion, chondrocytes were seeded into the Quantum® bioreactor system or onto TCP (±vitronectin coating). The manufactured chondrocytes growth rates, total cell yields, chondrogenic pellet forming capacity (GAG/DNA, histology), immunoprofiles (flow cytometry) and gene expression (RT-qPCR) were assessed. Equivalent chondrocyte numbers were isolated from polydactyly and iliac apophysis donors per wet weight of tissue. Quantum®-expanded chondrocytes from both sources yielded comparable cell numbers; however, growth was slowed in the Quantum® compared to TCP. Polydactyly and iliac apophysis-derived chondrocytes expressed chondrocyte cell surface markers (CD166, CD44, CD151, SOX9) and formed chondrogenic pellets. Quantum® bioreactor expansion did not alter, gene expression or capacity to form glycosaminoglycans (GAGs (normalised to DNA content)) compared to matched TCP expansion. Juvenile cartilage donors are a promising chondrocyte source for the development of an allogeneic therapy. This novel study expanding juvenile chondrocytes in the Quantum® GMP-compliant bioreactor suggests that culture conditions may need modification to improve growth, whilst retaining cartilage forming capacity. Full article
(This article belongs to the Special Issue Ligament/Tendon and Cartilage Tissue Engineering and Reconstruction)
21 pages, 2160 KB  
Article
Highly Stable Supramolecular Donor–Acceptor Complexes Involving (Z)-, (E)-di(3-pyridyl)ethylene Derivatives as Weak Acceptors: Structure—Property Relationships
by Artem I. Vedernikov, Valeriy V. Volchkov, Mikhail N. Khimich, Mikhail Y. Mel’nikov, Fedor E. Gostev, Ivan V. Shelaev, Victor A. Nadtochenko, Lyudmila G. Kuz’mina, Judith A. K. Howard, Asya A. Efremova, Mikhail V. Rusalov and Sergey P. Gromov
Molecules 2025, 30(19), 3920; https://doi.org/10.3390/molecules30193920 - 29 Sep 2025
Abstract
The Z-isomer of N,N’-diammoniopropyl derivative of di(3-pyridyl)ethylene was synthesized. The structure and stability of complexes between this non-planar weak acceptor (A, (Z)-2) and a planar strong donor, the E-isomer of bis(18-crown-6)stilbene (D, (E [...] Read more.
The Z-isomer of N,N’-diammoniopropyl derivative of di(3-pyridyl)ethylene was synthesized. The structure and stability of complexes between this non-planar weak acceptor (A, (Z)-2) and a planar strong donor, the E-isomer of bis(18-crown-6)stilbene (D, (E)-1), were studied using X-ray diffraction, 1H NMR spectroscopy, and optical spectroscopy, including 1H NMR and spectrofluorimetric titrations. In MeCN, the components form a very stable pseudocyclic bimolecular complex (logKD·A = 8.48) due to homoditopic coordination of the ammonium groups of the acceptor to the crown moieties of the donor through numerous hydrogen bonds. Intrasupramolecular photo-driven electron transfer (ET) in the isomeric complexes of (E)-1 with (E)- and (Z)-2 was studied using steady-state absorption and fluorescence spectroscopy with time-resolved pulse absorption spectroscopy. It was found that back ET is approximately two times faster in complex (E)-(Z)-2 than in closely related (E)-(E)-2. Meanwhile, it is ~67 times slower in complex (E)-(E)-2 than in the isomeric complex based on N,N’-diammoniopropyl derivative of (E)-di(4-pyridyl)ethylene. Quantum chemical (DFT, TD-DFT) calculations suggest the actual photorelaxation pathway for the complexes under study. Full article
(This article belongs to the Section Photochemistry)
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34 pages, 5443 KB  
Article
Quantum and Topological Dynamics of GKSL Equation in Camel-like Framework
by Sergio Manzetti and Andrei Khrennikov
Entropy 2025, 27(10), 1022; https://doi.org/10.3390/e27101022 - 28 Sep 2025
Abstract
We study the dynamics of von Neumann entropy driven by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, focusing on its camel-like behavior—a hump-like entropy evolution reflecting the system’s adaptation to its environment. Within this framework, we analyze quantum correlations under decoherence and environmental interaction for three [...] Read more.
We study the dynamics of von Neumann entropy driven by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, focusing on its camel-like behavior—a hump-like entropy evolution reflecting the system’s adaptation to its environment. Within this framework, we analyze quantum correlations under decoherence and environmental interaction for three sets of quantum states. Our results show that the sign of the entanglement entropy’s derivative serves as an indicator of the system’s drift toward either classical or quantum information exchange—an insight relevant to quantum error correction and dissipation in quantum thermal machines. We parameterize quantum states using both single-parameter and Bloch-sphere representations, where the angle θ on the Bloch sphere corresponds to the state’s position. On this sphere, we construct gradient and basin maps that partition the dynamics of quantum states into stable and unstable regions under decoherence. Notably, we identify a Braiding ring of decoherence-unstable states located at θ=3π4; these states act as attractors under a constructed Lyapunov function, illustrating the topological and dynamical complexity of quantum evolution. Finally, we propose a testable experimental setup based on camel-like entropy and discuss its connection to the theoretical framework of this entropy behavior. Full article
(This article belongs to the Special Issue Entanglement Entropy in Quantum Field Theory)
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29 pages, 7233 KB  
Article
No-Signaling in Steepest Entropy Ascent: A Nonlinear, Non-Local, Non-Equilibrium Quantum Dynamics of Composite Systems Strongly Compatible with the Second Law
by Rohit Kishan Ray and Gian Paolo Beretta
Entropy 2025, 27(10), 1018; https://doi.org/10.3390/e27101018 - 28 Sep 2025
Abstract
Lindbladian formalism models open quantum systems using a ‘bottom-up’ approach, deriving linear dynamics from system–environment interactions. We present a ‘top-down’ approach starting with phenomenological constraints, focusing on a system’s structure, subsystems’ interactions, and environmental effects and often using a non-equilibrium variational principle designed [...] Read more.
Lindbladian formalism models open quantum systems using a ‘bottom-up’ approach, deriving linear dynamics from system–environment interactions. We present a ‘top-down’ approach starting with phenomenological constraints, focusing on a system’s structure, subsystems’ interactions, and environmental effects and often using a non-equilibrium variational principle designed to enforce strict thermodynamic consistency. However, incorporating the second law’s requirement—that Gibbs states are the sole stable equilibria—necessitates nonlinear dynamics, challenging no-signaling principles in composite systems. We reintroduce ‘local perception operators’ and show that they allow to model signaling-free non-local effects. Using the steepest-entropy-ascent variational principle as an example, we demonstrate the validity of the ‘top-down’ approach for integrating quantum mechanics and thermodynamics in phenomenological models, with potential applications in quantum computing and resource theories. Full article
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27 pages, 601 KB  
Review
Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimir–Polder Forces in and out of Thermal Equilibrium
by Galina L. Klimchitskaya and Vladimir M. Mostepanenko
Physics 2025, 7(4), 44; https://doi.org/10.3390/physics7040044 - 26 Sep 2025
Abstract
We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder forces. After a brief summary of the properties [...] Read more.
We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within the Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency, which is present in the transverse response function of graphene. An application of the response functions of graphene to the calculation of the equilibrium Casimir force between two graphene sheets and the Casimir–Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir–Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined. Full article
(This article belongs to the Section Condensed Matter Physics)
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14 pages, 263 KB  
Article
PT-Symmetric Dirac Inverse Spectral Problem with Discontinuity Conditions on the Whole Axis
by Rakib Feyruz Efendiev, Davron Aslonqulovich Juraev and Ebrahim E. Elsayed
Symmetry 2025, 17(10), 1603; https://doi.org/10.3390/sym17101603 - 26 Sep 2025
Abstract
We address the inverse spectral problem for a PT-symmetric Dirac operator with discontinuity conditions imposed along the entire real axis—a configuration that has not been explicitly solved in prior literature. Our approach constructs fundamental solutions via convergent recursive series expansions and establishes their [...] Read more.
We address the inverse spectral problem for a PT-symmetric Dirac operator with discontinuity conditions imposed along the entire real axis—a configuration that has not been explicitly solved in prior literature. Our approach constructs fundamental solutions via convergent recursive series expansions and establishes their linear independence through a constant Wronskian. We derive explicit formulas for transmission and reflection coefficients, assemble them into a PT-symmetric scattering matrix, and demonstrate how both spectral and scattering data uniquely determine the underlying complex-valued, discontinuous potentials. Unlike classical treatments, which assume smoothness or limited discontinuities, our framework handles full-axis discontinuities within a non-Hermitian setting, proving uniqueness and providing a constructive recovery algorithm. This method not only generalizes existing inverse scattering theory to PT-symmetric discontinuous operators but also offers direct applicability to optical waveguides, metamaterials, and quantum field models where gain–loss mechanisms and zero-width resonances are critical. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2025)
13 pages, 1623 KB  
Article
The Photodynamic Antibacterial Potential of New Tetracationic Zinc(II) Phthalocyanines Bearing 4-((Diethylmethylammonium)methyl)phenoxy Substituents
by Gennady Meerovich, Dmitry Bunin, Ekaterina Akhlyustina, Igor Romanishkin, Vladimir Levkin, Sergey Kharnas, Maria Stepanova, Alexander Martynov, Victor Loschenov, Yulia Gorbunova and Marina Strakhovskaya
Int. J. Mol. Sci. 2025, 26(19), 9414; https://doi.org/10.3390/ijms26199414 - 26 Sep 2025
Abstract
Photodynamic inactivation and antimicrobial photodynamic therapy (PDI/APDT) based on the toxic properties of reactive oxygen species (ROS), which are generated by a number of photoexcited dyes, are promising for preventing and treating infections, especially those associated with drug-resistant pathogens. The negatively charged bacterial [...] Read more.
Photodynamic inactivation and antimicrobial photodynamic therapy (PDI/APDT) based on the toxic properties of reactive oxygen species (ROS), which are generated by a number of photoexcited dyes, are promising for preventing and treating infections, especially those associated with drug-resistant pathogens. The negatively charged bacterial cell surface attracts polycationic photosensitizers, which contribute to the vulnerability of the bacterial plasma membrane to ROS. The integrity of the plasma membrane is critical for the viability of the bacterial cell. Polycationic phthalocyanines are regarded as promising photosensitizers due to their high quantum yields of ROS generation (mainly singlet oxygen), high extinction coefficients in the far-red spectral range, and low dark toxicity. For application in PDI/APDT, the wide range of possibilities of modifying the chemical structure of phthalocyanines is particularly valuable, especially by introducing various peripheral and non-peripheral substituents into the benzene rings. Depending on the type and location of such substituents, it is possible to obtain photosensitizers with different photophysical properties, photochemical activity, solubility in an aqueous medium, biocompatibility, and tropism for certain structures of photoinactivation targets. In this study, we tested novel water-soluble Zn (II) phthalocyanines bearing four 4-((diethylmethylammonium)methyl)phenoxy substituents with symmetric and asymmetric charge distributions for photodynamic antibacterial activity and compared them with those of water-soluble octacationic zinc octakis(cholinyl)phthalocyanine. The obtained results allow us to conclude that the studied tetracationic aryloxy-substituted Zn(II) phthalocyanines effectively bind to the oppositely charged cell wall of the Gram-negative bacteria E. coli. This finding is supported by data on bacteria’s zeta potential neutralization in the presence of phthalocyanine derivatives and fluorescence microscopy images of stained bacterial cells. Asymmetric substitution influences the aggregation and fluorescent characteristics but has little effect on the ability of the studied tetracationic phthalocyanines to sensitize the bioluminescent E. coli K12 TG1 strain. Both symmetric and asymmetric aryloxy-substituted phthalocyanines are no less effective in PDI than the water-soluble zinc octakis(cholinyl)phthalocyanine, a photosensitizer with proven antibacterial activity, and have significant potential for further studies as antibacterial photosensitizers. Full article
(This article belongs to the Special Issue New Molecular Insights into Antimicrobial Photo-Treatments)
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22 pages, 6052 KB  
Article
Dynamics of Complex Systems and Their Associated Attractors in a Multifractal Paradigm of Motion
by Vlad Ghizdovat, Monica Molcalut, Florin Nedeff, Valentin Nedeff, Diana Carmen Mirila, Mirela Panainte-Lehăduș, Dragos-Ioan Rusu, Maricel Agop and Decebal Vasincu
Fractal Fract. 2025, 9(10), 623; https://doi.org/10.3390/fractalfract9100623 - 25 Sep 2025
Abstract
In this paper we analyze complex systems dynamics using a multifractal framework derived from Scale Relativity Theory (SRT). By extending classical differential geometry to accommodate non-differentiable, scale-dependent behaviors, we formulate Schrödinger-type equations that describe multifractal geodesics. These equations reveal deep analogies between quantum [...] Read more.
In this paper we analyze complex systems dynamics using a multifractal framework derived from Scale Relativity Theory (SRT). By extending classical differential geometry to accommodate non-differentiable, scale-dependent behaviors, we formulate Schrödinger-type equations that describe multifractal geodesics. These equations reveal deep analogies between quantum mechanics and macroscopic complex dynamics. A key feature of this approach is the identification of hidden symmetries governed by multifractal analogs of classical groups, particularly the SL(2ℝ) group. These symmetries help explain universal dynamic behaviors such as double period dynamics, damped dynamics, modulated dynamics, or chaotic dynamics. The resulting framework offers a unified geometric and algebraic perspective on the emergence of order within complex systems, highlighting the fundamental role of fractality and scale covariance in nature. Full article
(This article belongs to the Section Complexity)
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23 pages, 901 KB  
Article
Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits
by Mathieu Beau
Entropy 2025, 27(10), 996; https://doi.org/10.3390/e27100996 - 24 Sep 2025
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Abstract
We propose a general and experimentally accessible framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution. Defined from the rate of population change in a target state, the TF distribution can be reconstructed through repeated projective measurements at [...] Read more.
We propose a general and experimentally accessible framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution. Defined from the rate of population change in a target state, the TF distribution can be reconstructed through repeated projective measurements at discrete times on independently prepared systems, thus avoiding Zeno inhibition. In monotonic regimes, it admits a clear interpretation as a time-of-arrival (TOA) or time-of-departure (TOD) distribution. We apply this approach to optimize time-dependent Hamiltonians, analyze shortcut-to-adiabaticity (STA) protocols, study non-adiabatic features in the dynamics of a three-level time-dependent detuning model, and derive a transition-based quantum speed limit (TF-QSL) for both closed and open quantum systems. We also establish a lower bound on temporal uncertainty and examine decoherence effects, demonstrating the versatility of the TF framework for quantum control and diagnostics. This method provides both a conceptual tool and an experimental protocol for probing and engineering quantum dynamics in discrete-state platforms. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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