Quantum Mechanical Model Research Articles

Supersymmetric quantum mechanics and the Riemann hypothesis

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the vanishing ground state energies in this model. The model provides a natural form of supersymmetry.

Molecular Structure Related to an S = 5/2 High-Spin S2 State Manganese Cluster of Photosystem II Investigated by Q-Band Pulse EPR Spectroscopy.

The high-spin S2 state of the photosynthetic oxygen-evolving cluster Mn4CaO5, corresponding to the g = 4.1 signal for X-band electron paramagnetic resonance (EPR), was investigated using Q-band pulsed EPR, which detected a main peak at g = 3.10 and satellite peaks at 5.25, 4.55, and 2.80. We evaluated the spin state as the zero-field splitting of D = 0.465 cm-1 and E/D = 0.245 with S = 5/2. The temperature dependence of the T1 relaxation time revealed that the excited-state energy was 28.7 cm-1 higher than that of the S = 5/2 ground state. By comparing present quantum mechanical (QM) calculation models, a closed-cubane structure with the protonation state of two oxygens, W1 (= OH-) and W2 (= H2O), was the most probable structure for the S = 5/2 state. The three-pulse electron spin-echo envelope modulation (ESEEM) detected the nuclear signal, which was assigned to nitrogen as His332 ligated to the Mn1 ion. The obtained hyperfine constant for the nitrogen signal was significantly reduced from that in the S = 1/2 low-spin state. These results indicate that the S = 5/2 spin state arises from the closed-cubane structure.

Quantum optomagnetics in graphene

Graphene can be magnetized through nonlinear response of its orbital angular momentum to an intense circularly polarized light. This optomagnetic effect can be well exemplified by the inverse Faraday effect (IFE) where an optically-generated DC magnetization leads to graphene’s optical activity. We provide a single-particle quantum mechanical model of an IFE in graphene by solving Schrödinger’s equation in the presence of a renormalized Hamiltonian near a Dirac point in the presence of circularly polarized monochromatic light. We derive an analytical expression for DC magnetization based on non-perturbative and dressed states of quasi-electrons where their energy spectrum is isotropically gapped by the circularly polarized light. Optical rotatory power is then computed through the gyroelectric birefringence where a measurable polarization rotation angle under moderate and intense optical radiations is predicted.

How to Compute Atomistic Insight in DFT Clusters: The REG-IQA Approach.

The relative energy gradient (REG) method is paired with the topological energy partitioning method interacting quantum atoms (IQA), as REG-IQA, to provide detailed and unbiased knowledge on the intra- and interatomic interactions. REG operates on a sequence of geometries representing a dynamical change of a system. Its recent application to peptide hydrolysis of the human immunodeficiency virus-1 (HIV-1) protease (PDB code: 4HVP) has demonstrated its full potential in recovering reaction mechanisms and through-space electrostatic and exchange-correlation effects, making it a compelling tool for analyzing enzymatic reactions. In this study, the computational efficiency of the REG-IQA method for the 133-atom HIV-1 protease quantum mechanical system is analyzed in every detail and substantially improved by means of three different approaches. The first approach of smaller integration grids for IQA integrations reduces the computational overhead by about a factor of 3. The second approach uses the line-simplification Ramer-Douglas-Peucker (RDP) algorithm, which outputs the minimal number of geometries necessary for the REG-IQA analysis for a predetermined root mean squared error (RMSE) tolerance. This cuts the computational time of the whole REG analysis by a factor of 2 if an RMSE of 0.5 kJ/mol is considered. The third approach consists of a "biased" or "unbiased" selection of a specific subset of atoms of the whole initial quantum mechanical model wave-function, which results in more than a 10-fold speed-up per geometry for the IQA calculation, without deterioration of the outcome of the REG-IQA analysis. Finally, to show the capability of these approaches, the findings gathered from the HIV-1 protease system are also applied to a different system named haloalcohol dehalogenase (HheC). In summary, this study takes the REG-IQA method to a computationally feasible and highly accurate level, making it viable for the analysis of a multitude of enzymatic systems.

Sub-picosecond collapse of molecular polaritons to pure molecular transition in plasmonic photoswitch-nanoantennas

Molecular polaritons are hybrid light-matter states that emerge when a molecular transition strongly interacts with photons in a resonator. At optical frequencies, this interaction unlocks a way to explore and control new chemical phenomena at the nanoscale. Achieving such control at ultrafast timescales, however, is an outstanding challenge, as it requires a deep understanding of the dynamics of the collectively coupled molecular excitation and the light modes. Here, we investigate the dynamics of collective polariton states, realized by coupling molecular photoswitches to optically anisotropic plasmonic nanoantennas. Pump-probe experiments reveal an ultrafast collapse of polaritons to pure molecular transition triggered by femtosecond-pulse excitation at room temperature. Through a synergistic combination of experiments and quantum mechanical modelling, we show that the response of the system is governed by intramolecular dynamics, occurring one order of magnitude faster with respect to the uncoupled excited molecule relaxation to the ground state.

Environment assisted quantum model for studying RNA-DNA-error correlation created due to the base tautomery

The adaptive mutation phenomenon has been drawing the attention of biologists for several decades in evolutionist community. In this study, we propose a quantum mechanical model of adaptive mutation based on the implications of the theory of open quantum systems. We survey a new framework that explain how random point mutations can be stabilized and directed to be adapted with the stresses introduced by the environments according to the microscopic rules dictated by constraints of quantum mechanics. We consider a pair of entangled qubits consist of DNA and mRNA pair, each coupled to a distinct reservoir for analyzing the spreed of entanglement using time-dependent perturbation theory. The reservoirs are physical demonstrations of the cytoplasm and nucleoplasm and surrounding environments of mRNA and DNA, respectively. Our predictions confirm the role of the environmental-assisted quantum progression of adaptive mutations. Computing the concurrence as a measure that determines to what extent the bipartite DNA-mRNA can be correlated through entanglement, is given. Preventing the entanglement loss is crucial for controlling unfavorable point mutations under environmental influences. We explore which physical parameters may affect the preservation of entanglement between DNA and mRNA pair systems, despite the destructive role of interaction with the environments.

Quantum description of free electron laser radiation and nonlinear amplitude equations

A relativistic quantum mechanical model to describe the quantum free electron laser dynamics has been developed. Neglecting the spin of electrons in the impacting beam, this model is based on the Klein–Gordon equation coupled to the Poisson equation for the space-charge potential and the wave equation for the transverse components of the radiation field. Furthermore, a system of coupled nonlinear envelope equations for the slowly varying amplitudes of the electron beam distribution and the radiation field has been derived. The fundamental system of basic equations has been cast into a suitable hydrodynamic formulation. In the framework of the hydrodynamic representation, a new dispersion relation has been derived and analyzed in both the quantum and the quasi-classical regimes, where the space-charge oscillations of the electron beam are taken into account.

Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling.

This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. It further sheds light on the applicability, utility, and efficiency of the mixed quantum-classical dynamics (MQCD) formalism, which starts off with the MQCLE, in probing spectroscopy and dynamics of condensed systems, whereby quantum mechanics and classical mechanics are combined systematically. The author has been exploring and implementing MQCD to investigate electron-phonon coupling effects on electronic dephasing in harmonic and anharmonic systems by calculating linear and nonlinear optical transition analytically and numerically dipole moment time correlation functions in an MQC environment, thereby presenting an in depth spectral profile analysis and their shape and symmetry. The distinctive capability of the MQC time correlation functions is that ergodicity and stationarity properties are inherently satisfied as part of the mixed quantum-classical dynamics (MQCD) framework, unlike classical correlation functions. While some research groups have applied MQCLE to calculate vibrational spectra to study hydrogen-bonded complexes in a MQC environment and other groups calculated Optical response function to probe electron transfer dynamics using the basis mapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, the same framework is employed to study dissipative systems in the MQC limit, whereby the zero-phonon line adopts the correct width and eliminates its asymmetry. While the full quantum mechanical model, like the multimode Brownian oscillator (MBO) model, yields the correct width and inaccurate shape in the low-temperature limit, the MQCD formalism seems to produce an accurate zero-phonon profile. Nonlinear optical signals are also reviewed in MQC media to show the applicability and utility of this approach. The vibronic optical response functions developed here will account for geometry change, frequency change, and anharmonicity upon electronic excitation to accurately probe electronic dephasing, electron-phonon coupling, shape, and symmetry of profiles and present differences and similarities to the MBO model on pure electronic dephasing. Frequency change and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. This is an additional unique result obtained by the author to further demonstrate the applicability and utility of this approach over other approximation schemes in probing electronic dephasing including that of the MBO model.

De Sitter space, extremal surfaces, and time entanglement

We refine previous investigations on de Sitter space and extremal surfaces anchored at the future boundary $I^+$. Since such surfaces do not return, they require extra data or boundary conditions in the past (interior). In entirely Lorentzian de Sitter spacetime, this leads to future-past timelike surfaces stretching between $I^\pm$. Apart from an overall $-i$ factor (relative to spacelike surfaces in $AdS$) their areas are real and positive. With a no-boundary type boundary condition, the top half of these timelike surfaces joins with a spacelike part on the hemisphere giving a complex-valued area. Motivated by these, we describe two aspects of "time-entanglement" in simple toy models in quantum mechanics. One is based on a future-past thermofield double type state entangling timelike separated states, which leads to entirely positive structures. Another is based on the time evolution operator and reduced transition amplitudes, which leads to complex-valued entropy.

Role of Preaggregation in Single-Molecule Photoredox Catalysis

We investigate the role of preaggregation among photocatalyst and substrate in the paradigmatic molecular dye rhodamine 6G by means of fluorescence correlation experiments and quantum-mechanical modeling. By varying the substrate concentration, we experimentally confirm earlier conclusions that consecutive photoelectron transfer between rhodamine 6G and a model substrate molecule is not diffusion limited, raising puzzling questions regarding the mechanisms underlying its established photocatalytic activity. By theoretically exploring alternative explanations for ultrafast excited-state charge transfer, it is indeed found that preaggregation between photocatalyst and substrate is required to reach charge-transfer rates similar to those experimentally observed. Electrostatic as well as dispersive interactions are found to be most important for the molecular attraction involved in preaggregation. We show that tuning these contributions by chemical design alters the binding energies of photocatalyst–substrate assemblies. This suggests that reaction rates can be adjusted by adapting the composition of the species involved in preaggregation, which appears as an appealing concept in photocatalysis.

Wormhole model for Neon-20

A quantum mechanical model for the Neon-20 nucleus is developed that allows for the splitting of a bipyramidal structure of five alpha-particles into an alpha-particle and an Oxygen-16 nucleus. The geometry of the configuration space is assumed to be a 3-dimensional spatial wormhole, and on the wormhole background there is an attractive short-range potential. This leads to a radial Schrödinger equation of the Heun form, which simplifies for threshold bound states to an associated Legendre equation that has explicit solutions. The energies of the true bound states for all spin/parities are numerically calculated, and match those of the well-established Kπ=0+ and Kπ=0− rotational bands of Neon-20, and certain higher bands.

Teaching and Learning Optics in High School: From Fermat to Feynman

In this article, we analyze the basis of a proposal that allows teaching the notions of reflection, refraction, interference and diffraction from a unified perspective, using Fermat’s variational principle, recovered by Richard Feynman in his formulation of the paths sum for quantum mechanics. This allows reconsidering the notions of geometrical and physical optics, using the probabilistic and unified model of quantum mechanics by means of mathematical notions that are accessible to high school students.

An objective collapse model without state dependent stochasticity

The impossibility of describing measurement in quantum mechanics while using a quantum mechanical model for the measurement machine, remains one of its central problems. Objective collapse theories attempt to resolve this problem by proposing alterations to Schrödinger’s equation. Here, we present a minimal model for an objective collapse theory that, in contrast to previous proposals, does not employ state dependent stochastic terms in its construction. It is an explicit proof of principle that it is possible for Born’s rule to emerge from a stochastic evolution in which no properties of the stochastic process depend on the state being evolved. We propose the presented model as a basis from which more realistic objective collapse theories can be constructed.

Ultrafast quantum path interferometry to determine the electronic decoherence time of the electron-phonon coupled system in n -type gallium arsenide

Quantum coherence is the key to new quantum technologies, although the details of decoherence processes and times are still not well understood in solids. We demonstrate how to measure the decoherence time of electronic excited states in $n$-type gallium arsenide ($n$-GaAs) crystals using a relative-phase locked double pulse excitation method and quantitatively evaluate with a simple model including temperature dependence. The interference patterns of both electronic and phonon coherence are observed in $n$-GaAs using ultrafast quantum path interferometry with $\ensuremath{\pi}/4$ polarized femtosecond pulses, via the amplitude of longitudinal optical phonons as a function of pump-pump delay. The electronic coherence shows uplifting and splitting in the collapse and revival of the electronic interference, which is sensitive to temperature, and these features are well reproduced using a simple quantum mechanical model. The decoherence time is determined using quantum calculations, from the splitting and uplifting in the interference shape, to be $27.8\ifmmode\pm\else\textpm\fi{}0.5, 23.0\ifmmode\pm\else\textpm\fi{}0.3$, and $12.9\ifmmode\pm\else\textpm\fi{}0.3$ fs at 10, 90, and 290 K, respectively. The temperature dependence of the decoherence time is well reproduced by the density of electrons in the conduction band with the group velocity of the photoinduced electrons.

Schrödinger Operators with Oblique Transmission Conditions in {mathbb R}^2

In this paper we study the spectrum of self-adjoint Schrödinger operators in L^2(mathbb {R}^2) with a new type of transmission conditions along a smooth closed curve Sigma subseteq mathbb {R}^2. Although these oblique transmission conditions are formally similar to delta '-conditions on Sigma (instead of the normal derivative here the Wirtinger derivative is used) the spectral properties are significantly different: it turns out that for attractive interaction strengths the discrete spectrum is always unbounded from below. Besides this unexpected spectral effect we also identify the essential spectrum, and we prove a Krein-type resolvent formula and a Birman-Schwinger principle. Furthermore, we show that these Schrödinger operators with oblique transmission conditions arise naturally as non-relativistic limits of Dirac operators with electrostatic and Lorentz scalar delta -interactions justifying their usage as models in quantum mechanics.

Singularity in the electron-core potential as a gateway to accurate multielectron ionization spectra in strongly driven atoms

We demonstrate a general three-dimensional semiclassical model as a powerful technique for the study of correlated multi-electron escape in atoms driven by infrared laser pulses at intensities where electron-electron correlation prevails. We do so in the context of triple ionization of strongly driven Ne. We show that a drawback of other current quantum mechanical and classical models of triple ionization is that they soften the Coulomb potential of each electron with the core. The model we employ fully accounts for the singularity in the Coulomb potentials of a recolliding electron with the core and a bound electron with the core as well as for the interaction of a recolliding with a bound electron. Our model treats approximately only the interaction between bound electrons through the use of effective potentials. These effective potentials ensure that no artificial autoionization takes place as a result of the full treatment of the electron-core potential. We demonstrate the accuracy of our model by obtaining triple ionization distributions of the sum of the final electron momenta which we find to be in very good agreement with experiments. Also, we explain the main features of these momenta distributions in terms of the prevalent pathways of correlated three-electron escape in Ne. We also show that the different ionization pathways prevailing in three-electron escape in strongly driven Ne versus Ar give rise to different momenta distributions in these two atoms.

Hydration shell effects in ac-driven single-molecule junctions

We propose a quantum-mechanical model to calculate the current through a single molecular junction immersed in a solvent and surrounded by a thin shell of bound water under an applied ac voltage. The solvent plus hydration shell are captured by a dielectric continuum model for which the resulting spectral density is determined. Here the dielectric properties, e.g., the Debye relaxation time and the dielectric constant, of the bulk solvent and the hydration shell as well as the shell thickness directly enter. We determine the charge current through the molecular junction under an ac voltage in the sequential tunneling regime where we solve a quantum master equation by a real-time diagrammatic technique. Interestingly, the Fourier components of the charge current show an exponential-like decline when the hydration shell thickness increases. Finally, we apply our findings to binary solvent mixtures with varying volume fractions and find that the current is highly sensitive to both the hydration shell thickness as well as the volume fraction of the solvent mixture, giving rise to possible applications as shell and concentration sensors on the molecular scale.

A gravitationally induced decoherence model using Ashtekar variables

We consider the coupling of a scalar field to linearised gravity and derive a relativistic gravitationally induced decoherence model using Ashtekar variables. The model is formulated at the gauge invariant level using suitable geometrical clocks in the relational formalism, broadening existing gauge invariant formulations of decoherence models. For the construction of the Dirac observables we extend the known observable map by a kind of dual map where the role of clocks and constraints is interchanged. We also discuss a second choice of geometrical clocks existing in the ADM literature. Then we apply a reduced phase space quantisation on Fock space and derive the final master equation choosing a Gibbs state for the gravitational environment and using the projection operator technique. The resulting master equation is not automatically of Lindblad type, a starting point sometimes assumed for phenomenological models, but still involves a residual time dependence at the level of the effective operators in the master equation due to the form of the correlation functions that we express in terms of thermal Wightman functions. Furthermore, we discuss why in the model analysed here the application of a second Markov approximation in order to obtain a set of time independent effective system operators is less straightforward than in some of the quantum mechanical models.

A refreshing perspective on electrochromic materials: Phenoxazine as an opportune moiety towards stable and efficient electrochromic polyimides

In our attempt to develop appealing EC materials, here we address the electrochromic materials field by employing the aryl-substituted phenoxazine (POZ) as a new member of triarylamine family with excellent potential for electrochromic applications. Thus, a simple synthetic strategy was followed to build a novel POZ-based diamine that was further used in polycondensation reaction with commercially available aromatic dianhydrides to develop three novel polyimides (PIs). Complementarily, POZ-based model compounds were synthesized to get insights into the electrochemical and electrochromic behavior of the synthesized PIs. With the support of the computational quantum mechanical modeling methods (Density-Functional Theory – DFT and Time-Dependent (TD)–DFT), the mechanism responsible for the absence of the dimerization process upon POZ oxidation was established. Without resorting to any structural modification to block the para position of POZ, the present PIs demonstrated exquisite electrochemical and electrochromic performance, including high redox stability during 100 repetitive cyclic voltammetry scans, unique deep-purple coloration during oxidation, high optical contrast, up to 62%, response time below 6.5 s for coloring and 5.1 s for bleaching, excellent electrochromic efficiency, up to 193 cm2/C and a maximum 21% decay of the electrochromic efficiency after 500 cycles. The most efficient EC polyimide was used as an active layer in electrochromic prototype devices to survey the full applicative potential of these PIs. The devices rendered an optical contrast of 51%, 7.9 s for coloring, and 7.2 s for bleaching, electrochromic efficiency of 178 cm2/C, and decay of the electrochromic efficiency of 6.1% after 100 cycles, placing for the first time the POZ-based PIs among the perspective electrochromic materials.

Li+ intercalation current generation in amorphous and crystalline MoS2: Experiment and theory

In this work, crystalline and amorphous nano-MoS2 materials for effective Li+-intercalation current generation have been synthesized. The effect of disordering on the structural and electrochemical properties of nano-MoS2 has been systematically investigated by multiple characterizations: transmission electron microscopy (TEM), X-ray diffraction method and electrochemical measurements. Thermodynamic and kinetic peculiarities of intercalation processes have been studied. Dependences of the change in Gibbs’ free energy of the intercalation reaction on the extent of ‘guest’ lithium loading are analyzed. The distinctive feature of disordered structures is their ability to show colossal lithium ‘guest’ load, which ensures the specific capacity of the material in cathode processes up to ~2500 mAh·g-1 under the discharge not less than 2.6 V relative to lithium. The diffusion coefficient of lithium cations in the structure of disordered nano-MoS2 is two orders of magnitude higher than that in the crystalline MoS2. A quantum-mechanical model of the observed phenomena is suggested.