Conformational Tuning of Magnetic Interactions in Coupled Nanographenes.

Phenalenyl (C13H9) is an open-shell spin-1/2 nanographene. Using scanning tunneling microscopy (STM) inelastic electron tunneling spectroscopy (IETS), covalently bonded phenalenyl dimers have been shown to feature conductance steps associated with singlet-triplet excitations of a spin-1/2 dimer with antiferromagnetic exchange. Here, we address the possibility of tuning the magnitude of the exchange interactions by varying the dihedral angle between the two molecules within a dimer. Theoretical methods ranging from density functional theory calculations to many-body model Hamiltonians solved within different levels of approximation are used to explain STM-IETS measurements of phenalenyl dimers on a hexagonal boron nitride (h-BN)/Rh(111) surface, which exhibit signatures of twisting. By means of first-principles calculations, we also propose strategies to induce sizable twist angles in surface-adsorbed phenalenyl dimers via functional groups, including a photoswitchable scheme. This work paves the way toward tuning magnetic couplings in carbon-based spin chains and two-dimensional lattices.

Self-consistent field method for open-shell systems within the density-matrix functional theory.

The unrestricted Hartree-Fock method is extended to correlation calculation within the density-matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin-orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi-Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O 2 .

Transient Study of Photoluminescence in Nanowaveguides Doped with Quantum Emitters and Metallic Nanoparticles.

We have studied the time-dependent optical properties of nanowaveguides containing an ensemble of noninteracting quantum emitters and interaction metallic nanoparticles. We have developed a theory for transient photoluminescence (PL) and exciton population density using the density matrix method. In our theory, we have included the effect of the dipole-dipole interaction (DDI) between metallic nanoparticles along with the effect of the surface plasmon polaritons (SPPs) created by metallic nanoparticles. We compared our theory with the transient PL experiments of nanohybrids fabricated from CdSe/ZnS quantum dots and an Ag nanorod array. A good agreement between theory and PL experiment is found. We have also examined the transient behavior of the photoluminescence in the presence of the DDI and SPP couplings. It is observed that the number of transient PL oscillations increases as the DDI coupling increases. The width of the transient peaks also increases as the amount of the DDI coupling increases. Finally, we predicted that the peaks of the transient PL oscillation split from one peak to two peaks as the intensity of the DDI coupling reaches the strong coupling limit. The strong coupling limit is defined when the DDI coupling is larger than the PL decay rates. This finding can be used to fabricate nano switches by using one peak as the OFF position and two peaks as the ON position. The above findings also suggest the transient plasmonic properties of nanowaveguides can be controlled by the SPP and DDI couplings. These findings have potential applications in the development of transient nanoscale plasmonic devices such as nano detectors and optical nano switches.

Charge Transfer in He+ - He → He(1s4l, l ≥ 2) - He+ Collisions in Intermediate Energy Range.

The anticrossing spectra of the helium line λ1s4l D3,F-1s2p P3=447.2 nm emitted after electron capture by He+ ions in He+-He collisions were measured for projectile energies of 10-29 keV. Furthermore, considering the excited states' time evolution, the theoretical intensity functions were calculated. The electric field and density distributions of the target He atoms in the collision volume were taken into account, and by fitting the theoretical intensities to the measured ones, the post-collisional states of the charge-transferred He atoms were determined. The results indicate that for the intermediate projectile energy range, the electronic charge distributions were asymmetric, but the electric dipole moments did not change, as in the case of the target atoms excited directly in the collisions. This result shows that the Paul trap mechanism may play an important role in the charge transfer excitation in this energy range.

The Role of Bond Functions in Describing Intermolecular Electron Correlation for Van der Waals Dimers: A Study of (CH4)2 and Ne2.

We present a study of the intermolecular interactions in van der Waals complexes of methane and neon dimers within the framework of the CCSD method. This approach was implemented and applied to calculate and examine the behavior of the contracted two-particle reduced density matrix (2-RDM). It was demonstrated that the region near the minimum of the two-particle density matrix correlation part, corresponding to the primary bulk of the Coulomb hole contribution, exerts a significant influence on the dispersion interaction energetics of the studied systems. As a result, the bond functions approach was applied to improve the convergence performance for the intermolecular correlation energy results with respect to the size of the atomic basis. For this, substantial acceleration was achieved by introducing an auxiliary basis of bond functions centered on the minima of the 2-RDM. For both methane and neon dimers, this general conclusion was confirmed with a series of CCSD calculations for the 2-RDM and the correlation energies.

Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium.

In this work, we lay the foundations for computing the behavior of a quantum heat engine whose working medium consists of an ensemble of non-harmonic quantum oscillators. In order to enable this analysis, we develop a method based on the Schrödinger picture. We investigate different possible choices on the basis of expanding the density operator, as it is crucial to select a basis that will expedite the numerical integration of the time-evolution equation without compromising the accuracy of the computed results. For this purpose, we developed an estimation technique that allows us to quantify the error that is unavoidably introduced when time-evolving the density matrix expansion over a finite-dimensional basis. Using this and other ways of evaluating a specific choice of basis, we arrive at the conclusion that the basis of eigenstates of a harmonic Hamiltonian leads to the best computational performance. Additionally, we present a method to quantify and reduce the error that is introduced when extracting relevant physical information about the ensemble of oscillators. The techniques presented here are specific to quantum heat cycles; the coexistence within a cycle of time-dependent Hamiltonian and coupling with a thermal reservoir are particularly complex to handle for the non-harmonic case. The present investigation is paving the way for numerical analysis of non-harmonic quantum heat machines.

Maximum Geometric Quantum Entropy.

Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes' information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles.

Density-functional theory (DFT) and time-dependent DFT study of the chemical and physical origins of key photoproperties of end-group derivatives of a nonfullerene acceptor molecule for bulk heterojunction organic solar cells.

As emphasized in a recent review article (Chem. Rev. 2022, 122, 14180), organic solar cell (OSC) photoconversion efficiency has been rapidly evolving with results increasingly comparable to those of traditional inorganic solar cells. Historically, OSC performance improvement focused first on the morphology of P3HT: PC 61 BM solar cells then went through different stages to shift lately interest towards nonfullerene acceptors (NFAs) as a replacement of PC 61 BM acceptor (ACC) molecule. Here, we use density-functional theory (DFT) and time-dependent DFT to investigate four novel NFAs of A-D-A (acceptor-donor-acceptor) form derived from the recently synthesized IDIC-4Cl (Dyes Pigm. 2019, 166, 196). Our level of theory is carefully evaluated for IDIC-4Cl and then applied to the four novel NFAs in order to understand how chemical modifications lead to physical changes in cyclic voltammetry (CV) frontier molecular orbital energies and absorption spectra in solution. Finally we design and apply a new type of Scharber plot for NFAs based upon some simple but we think reasonable assumptions. Unlike the original Scharber plots where a larger DON band gap favors a larger PCE, our modified Scharber plot reflects the fact that a smaller ACC band gap may favor PCE by filling in gaps in the DON acceptor spectrum. We predict that only the candidate molecule with the least good acceptor A, with the highest frontier molecular orbital energies, and one of the larger CV lowest unoccupied molecular orbital (LUMO) - highest unoccupied molecular orbital (HOMO) gaps, will yield a PM6:ACC PCE exceeding that of the parent IDIC-4Cl ACC. This candidate also shows the largest oscillator strength for the primary 1 (HOMO, LUMO) charge- transfer transition and the largest degree of delocalization of charge transfer of any of the ACC molecules investigated here.

Optical Physical Mechanisms of Helicene Carbon Nanohoop with Möbius Topology.

Optical and spectral properties of carbon nanohoop with Möbius topology is of great interest in nano-science and nano-technology. And it can be imagined that it has a lot of unexpected potential application prospects. However, theoretical calculations based on some figure-of-eight helicene carbon nanohoop with Möbius topology are still insufficient. Therefore, in this paper, we theoretically study the optical and spectral properties of figure-of-eight helicene carbon nanohoop with Möbius topology. Optical and spectral properties are analyzed with visualization method of transition density matrix and charge density difference, which reveal the unique characterization of carbon nanohoop with Möbius topology. Our results can not only deepen the understanding of the optical physical mechanisms of the nanorings with mobius carbons, but also provide deeper insight on optical properties and potential design on optical nanodevices.

Quantum Phase Diagram of a Frustrated Spin-1/2 Ferro-Antiferromagnetic Normal Ladder.

In this work, we consider a frustrated two-leg spin-1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin-1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non-collinear ferrimagnetic (NCF), m - 1 / 4 ${m - 1/4}$ , antiferromagnetic and dimer phases. The  quantum phase diagram is constructed for the Heisenberg spin-1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the  stability of m - 1 / 4 ${m - 1/4}$ phase and calculate the pitch angle θ ${\left( \theta \right)}$ in the NCF phase.

Random projection ensemble classification with high-dimensional time series.

Multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. We propose new random projection ensemble classifiers with high-dimensional MTS. The method first applies dimension reduction in the time domain via randomly projecting the time-series variables into some low-dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space. Our contributions are twofold: (i) We derive optimal weighted majority voting schemes for pooling information from the base classifiers for multiclass classification and (ii) we introduce new base frequency-domain classifiers based on Whittle likelihood (WL), Kullback-Leibler (KL) divergence, eigen-distance (ED), and Chernoff (CH) divergence. Both simulations for binary and multiclass problems, and an Electroencephalogram (EEG) application demonstrate the efficacy of the proposed methods in constructing accurate classifiers with high-dimensional MTS.

Terahertz Fingerprint of Monolayer Wigner Crystals.

The strong Coulomb interaction in monolayer semiconductors represents a unique opportunity for the realization of Wigner crystals without external magnetic fields. In this work, we predict that the formation of monolayer Wigner crystals can be detected by their terahertz response spectrum, which exhibits a characteristic sequence of internal optical transitions. We apply the density matrix formalism to derive the internal quantum structure and the optical conductivity of the Wigner crystal and to microscopically analyze the multipeak shape of the obtained terahertz spectrum. Moreover, we predict a characteristic shift of the peak position as a function of charge density for different atomically thin materials and show how our results can be generalized to an arbitrary two-dimensional system.

Shaped Microwave Field in a Three-Level Closed Loop Dense Atomic System.

In this work, we investigate the atomic properties of a three-level system under the effect of a shaped microwave field. The system is simultaneously driven by a powerful laser pulse and a weak constant probe that drives the ground state to an upper level. Meanwhile, an external microwave field drives the upper state to the middle transition with shaped waveforms. Hence, two situations are considered: one in which the atomic system is controlled by a strong laser pump and a classical constant microwave field, and another in which both the microwave and pump laser fields are shaped. Finally, for sake of comparison, we investigate the tanh-hyperbolic, the Gaussian and the power of the exponential microwave form in the system. Our results reveal that shaping the external microwave field has a significant impact on the absorption and dispersion coefficient dynamics. In comparison with the classical scenario, where usually the strong pump laser is considered to have a major role in controlling the absorption spectrum, we show that shaping the microwave field leads to distinct results.

Quantum State Assignment Flows.

This paper introduces assignment flows for density matrices as state spaces for representation and analysis of data associated with vertices of an underlying weighted graph. Determining an assignment flow by geometric integration of the defining dynamical system causes an interaction of the non-commuting states across the graph, and the assignment of a pure (rank-one) state to each vertex after convergence. Adopting the Riemannian-Bogoliubov-Kubo-Mori metric from information geometry leads to closed-form local expressions that can be computed efficiently and implemented in a fine-grained parallel manner. Restriction to the submanifold of commuting density matrices recovers the assignment flows for categorical probability distributions, which merely assign labels from a finite set to each data point. As shown for these flows in our prior work, the novel class of quantum state assignment flows can also be characterized as Riemannian gradient flows with respect to a non-local, non-convex potential after proper reparameterization and under mild conditions on the underlying weight function. This weight function generates the parameters of the layers of a neural network corresponding to and generated by each step of the geometric integration scheme. Numerical results indicate and illustrate the potential of the novel approach for data representation and analysis, including the representation of correlations of data across the graph by entanglement and tensorization.

Hermitian and Unitary Almost-Companion Matrices of Polynomials on Demand.

We introduce the concept of the almost-companion matrix (ACM) by relaxing the non-derogatory property of the standard companion matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and generally complex polynomial. The greater flexibility inherent in the ACM concept, compared to CM, allows the construction of ACMs that have convenient matrix structures satisfying desired additional conditions, compatibly with specific properties of the polynomial coefficients. We demonstrate the construction of Hermitian and unitary ACMs starting from appropriate third-degree polynomials, with implications for their use in physical-mathematical problems, such as the parameterization of the Hamiltonian, density, or evolution matrix of a qutrit. We show that the ACM provides a means of identifying the properties of a given polynomial and finding its roots. For example, we describe the ACM-based solution of cubic complex algebraic equations without resorting to the use of the Cardano-Dal Ferro formulas. We also show the necessary and sufficient conditions on the coefficients of a polynomial for it to represent the characteristic polynomial of a unitary ACM. The presented approach can be generalized to complex polynomials of higher degrees.

MRSCloud: A cloud-based MRS tool for basis set simulation.

PURPOSE: The purpose of this study is to present a cloud-based spectral simulation tool "MRSCloud," which allows MRS users to simulate a vendor-specific and sequence-specific basis set online in a convenient and time-efficient manner. This tool can simulate basis sets for GE, Philips, and Siemens MR scanners, including conventional acquisitions and spectral editing schemes with PRESS and semi-LASER localization at 3 T. METHODS: The MRSCloud tool was built on the spectral simulation functionality in the FID-A software package. We added three extensions to accelerate computation (ie, one-dimensional projection method, coherence pathways filters, and precalculation of propagators). The RF waveforms were generated based on vendors' generic pulse shapes and timings. Simulations were compared within MRSCloud using different numbers of spatial resolution (21 × 21, 41 × 41, and 101 × 101). Simulated metabolite basis functions from MRSCloud were compared with those generated by the generic FID-A and MARSS, and a phantom-acquired basis set from LCModel. Intraclass correlation coefficients were calculated to measure the agreement between individual metabolite basis functions. Statistical analysis was performed using R in RStudio. RESULTS: Simulation time for a full PRESS basis set is approximately 11 min on the server. The interclass correlation coefficients ICCs were at least 0.98 between MRSCloud and FID-A and were at least 0.96 between MRSCloud and MARSS. The interclass correlation coefficients between simulated MRSCloud basis spectra and acquired LCModel basis spectra were lowest for glutamine at 0.68 and highest for N-acetylaspartate at 0.96. CONCLUSIONS: Substantial reductions in runtime have been achieved. High ICC values indicated that the accelerating features are running correctly and produce comparable and accurate basis sets.

Giant Spin Lifetime Anisotropy and Spin-Valley Locking in Silicene and Germanene from First-Principles Density-Matrix Dynamics.

Through first-principles real-time density-matrix (FPDM) dynamics simulations, we investigated spin relaxation due to electron-phonon and electron-impurity scatterings with spin-orbit coupling (SOC) in two-dimensional Dirac materials silicene and germanene at finite temperatures. We discussed the applicability of conventional descriptions of spin relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared to the FPDM method, which is determined by a complex interplay of intrinsic SOC, external fields, and scattering strength. For example, the electric field dependence of the spin lifetime by FPDM is close to the DP mechanism for silicene at room temperature but similar to the EY mechanism for germanene. Because of its stronger SOC strength and buckled structure in contrast to graphene, germanene has a giant spin lifetime anisotropy and spin-valley locking effect under nonzero Ez and low temperatures. More importantly, germanene has a long spin lifetime (∼100 ns at 50 K) and an ultrahigh carrier mobility, making it advantageous for spin-valleytronic applications.

Quantum Mutual Information, Fragile Systems and Emergence.

In this paper, we present an analytical description of emergence from the density matrix framework as a state of knowledge of the system, and its generalized probability formulation. This description is based on the idea of fragile systems, wherein the observer modifies the system by the measurement (i.e., the observer effect) in order to detect possible emergent behavior. We propose the use of a descriptor, based on quantum mutual information, to calculate if subsystems of systems have inner correlations. This may contribute to a definition of emergent systems in terms of emergent information.

Canonical Density Matrices from Eigenstates of Mixed Systems.

One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits.

We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole-dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.