Density Matrix Research Articles

Plasma performance and operational space with an RMP-ELM suppressed edge

The operational space and global performance of plasmas with edge-localized modes (ELMs) suppressed by resonant magnetic perturbations (RMPs) are surveyed by comparing AUG, DIII-D, EAST, and KSTAR stationary operating points. RMP-ELM suppression is achieved over a range of plasma currents, toroidal fields, and RMP toroidal mode numbers. Consistent operational windows in edge safety factor are found across devices, while windows in plasma shaping parameters are distinct. Accessed pedestal parameters reveal a quantitatively similar pedestal-top density limit for RMP-ELM suppression in all devices of just over 3×1019 m−3. This is surprising given the wide variance of many engineering parameters and edge collisionalities, and poses a challenge to extrapolation of the regime. Wide ranges in input power, confinement time, and stored energy are observed, with the achieved triple product found to scale like the product of current, field, and radius. Observed energy confinement scaling with engineering parameters for RMP-ELM suppressed plasmas are presented and compared with expectations from established H and L-mode scalings, including treatment of uncertainty analysis. Different scaling exponents for individual engineering parameters are found as compared to the established scalings. However, extrapolation to next-step tokamaks ITER and SPARC find overall consistency within uncertainties with the established scalings, finding no obvious performance penalty when extrapolating from the assembled multi-device RMP-ELM suppressed database. Overall this work identifies common physics for RMP-ELM suppression and highlights the need to pursue this no-ELM regime at higher magnetic field and different plasma physical size.

Modulating *OOH Adsorption on RuO2 for Efficient and Durable Acidic Water Oxidation Electrocatalysis.

Acidic water electrolysis is of considerable interest due to its higher current density operation and energy conversion efficiency, but its real industrial application is highly limited by the shortage of efficient, stable, and cost-effective acidic oxygen evolution reaction (OER) electrocatalysts. Here,an electrocatalyst consisting of Ni-implanted RuO2 supported is reported on α-MnO2 (MnO2/RuO2-Ni) that shows high activity and remarkable durability in acidic OER. Precisely, the MnO2/RuO2-Ni catalyst shows an overpotential of 198mV at a current density of 10mA cm-2 and can operate continuously and stably for 400h (j = 10mA cm-2) without any obvious attenuation of activity, making it one of the best-performing acid-stable OER catalysts. Experimental results, in conjunction with density functional theory calculations, demonstrate that the interface electron transfer effect from RuO2 to MnO2, further enhanced by Ni incorporation, effectively modulates the adsorption of OOH* and significantly reduces the overpotential, thereby enhancing catalytic activity and durability.

Accelerating Density Matrix Embedding with Stochastic Density Fitting Theory: An Application to Hydrogen Bonded Clusters.

In this work, we demonstrate how using semistochastic density fitting (ss-DF) can accelerate self-consistent density matrix embedding theory (DMET) calculations by reducing the number of auxiliary orbitals in the three-indexed DF integrals. This reduction results in significant time savings when building the Hartree-Fock (HF) Coulomb and Exchange Matrices and in transforming integrals from the atomic orbital (AO) basis to the embedding orbital (EO) basis. We apply ss-DF to a range of hydrogen-bonded clusters to showcase its effectiveness. First, we examine how the amount of deterministic space impacts the quality of the calculation in a (H2O)10 cluster. Next, we test the computational efficiency of ss-DF compared to deterministic DF (d-DF) in water clusters containing 6-30 water molecules using a triple-ζ basis set. Finally, we perform numerical structural optimizations on water and hydrogen fluoride clusters, revealing that DMET can recover weak interactions using a back-transformed energy formula. This work demonstrates the potential of using stochastic resolution of identity in quantum embedding theories and highlights its capability to recover weak interactions effectively.

Entanglement in flavored scalar scattering

We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.

A Formulation of Quantum Fluid Mechanics and Trajectories

Abstract A formalism of classical mechanics is given for time-dependent many-body states of quantum
mechanics, describing both fluid flow and point mass trajectories. The familiar equations of
energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity
equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent
Schroedinger equation, respectively, where the Schroedinger equation is in density matrix form.
For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for
quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and
fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations
of fluid mechanics, respectively. Generalizations of the energy and Euler equations are
derived to obtain equations that are in the same form as they are in classical mechanics. The
fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local
variable mass. Over all space mass is conserved. The variable mass is a necessary condition for
the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross
flows are examined, where velocity directions are changed without changing the kinetic energy.
For one-electron atoms, the velocity modification gives closed orbits for trajectories, and
mass conservation, vortexes, and density stratification for fluid flows. For many body states,
Under certain conditions, and by hypotheses, Euler equations of orbital-flows are
obtained. One-body Schroedinger equations that are a generalization of the Hartree-Fock
equations are also obtained. These equations contain a quantum Coulomb's law, involving the
2-body pair function of reduced density matrix theory that replace the charge densities.

Using the Haken-Strobl-Reineker Model to Determine the Temperature Dependence of the Diffusion Coefficient.

Stochastic quantum Liouville equations (SQLE) are widely used to model energy and charge dynamics in molecular systems. The Haken-Strobl-Reineker (HSR) SQLE is a particular paradigm in which the dynamical noise that destroys quantum coherences arises from a white noise (i.e., constant-frequency) spectrum. A system subject to the HSR SQLE thus evolves to its "high-temperature" limit, whereby all the eigenstates are equally populated. This result would seem to imply that the predictions of the HSR model, e.g., the temperature dependence of the diffusion coefficient, have no validity for temperatures lower than the particle bandwidth. The purpose of this paper is to show that this assumption is incorrect for translationally invariant systems. In particular, provided that the diffusion coefficient is determined via the mean-squared-displacement, considerations about detailed-balance are irrelevant. Consequently, the high-temperature prediction for the temperature dependence of the diffusion coefficient may be extrapolated to lower temperatures, provided that the bath remains classical. Thus, for diagonal dynamical disorder the long-time diffusion coefficient, D∞(T) = c1/T, while for both diagonal and off-diagonal disorder, D∞(T) = c1/T + c2T, where c2 ≪ c1. An appendix discusses an alternative interpretation from the HSR model of the "quantum to classical" dynamics transition, whereby the dynamics is described as stochastically punctuated coherent motion.

Resource theory of Kirkwood-Dirac imaginarity

As an extension of classical probability distribution, the Kirkwood-Dirac distribution (KDD) was discussed by Kirkwood in 1933 and Dirac 1945, independently. Recently, it has been proved that nonclassical values (negative and non-real values) of the KDD have the ability of outperforming their classical counterparts in quantum computation, quantum measurement and so on. In this work, by dividing quantum states into KD-real (KD-free) and KD-imaginary (KD-resource) ones based on the KDD of a state, we establish a resource theory for KD-imaginarity with respect to a pair of bases (A, B), called the resource theory of Kirkwood-Dirac imaginarity. This theory is different from the resource theory of imaginarity of quantum states with respect to one basis A, where the free states are those that have real density matrices under the basis A.

Efficient fidelity estimation: alternative derivation and related applications

In [Phys. Rev. A 107 012427 (2023)], Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum states ρ and σ, i.e., F(ρ,σ)≔Trρσρ2 , can be written in a simplified form as F(ρ,σ)=Trρσ2 . In this article, we give an alternative proof of this result, using a function power series expansion and the properties of the trace function. Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

Topologically protected entanglement switching around exceptional points

The robust operation of quantum entanglement states is crucial for applications in quantum information, computing, and communications1–3. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.

ARTIFICIAL CRISES IN FINANCIAL MARKETS: PROBLEMS OF DIAGNOSIS AND PREVENTION

Purpose: The aim of this study is to diagnose and prevent crises in the country's financial markets by managing the connectedness of the attacked market with other. Theoretical Framework: Non-statistical changes in the largest connected markets and the parameters of the attacked market's connection with them. There is a need to consider ways to counter crises by managing the connection of the attacked market with other financial markets in the country. Design/Methodology/Approach: Methods for diagnosing crises are proposed to identify signs of a man-made crisis and strategies for its prevention. The proposed approach will prevent the actions of unscrupulous private financial market operators who want to receive unscrupulous income, stimulating volatility. Findings: Among the most important results, it was determined that there are serious shortcomings in the organization and structure of financial markets that require active government intervention. The state can not only legislative and administrative, but also financial methods prevent the actions of dishonest operators or minimize the consequences of the crises caused by them. Research, Practical & Social implications: This study makes it possible to identify signs of an artificial crisis and strategies for its prevention. Using the data of this study, the state operator in the financial markets can distribute its financial, administrative and informational resources in turn against its opponents and thus have a significant advantage over each of them. Originality/Value: The value of the study lies in the fact that various methods for diagnosing financial crises are offered by studying non-statistical changes in the largest connected markets and the parameters of the attacked market's connection with them. Using this information, the state can minimize the consequences of artificial financial crises.

Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies.

In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density functional theory (DFT) and density matrix renormalization group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ( ), density profiles ( ), and average entanglement entropies ( ) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices, and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems, there is a clear hierarchy between the deviations, , and all the deviations decrease with the chain size; for superlattices and harmonic confinement, the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general, increasing the number of impurities in the unit cell represents lower precision in the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications. The DFT calculations were performed using the standard Kohn-Sham scheme within the BALDA approach. It integrated the numerical Bethe-Ansatz (BA) solution of the Hubbard model as the homogeneous density functional within a local-density approximation (LDA) for the exchange-correlation energy. The DMRG algorithms were implemented using the ITensor library, which is based on the matrix product states (MPS) ansatz. The calculations were performed until the energy reaches convergence of at least .

Color image hiding with invisible visual cryptography

In this paper, we propose a wavelength multiplexing image hiding system based on color invisible visual cryptography (CIVC). The image is divided into red, green, and blue channels. Each channel turns into several meaningful share images, different from the random, meaningless share images in visual cryptography (VC), and these are concealed within phase keys. The acquired single-channel share images, once synthesized into a color image and subjected to incoherent superposition, enable the extraction of the secret color image. Optical experiments are presented to demonstrate the feasibility and effectiveness of the proposed method.

Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory.

Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.

Painlevé Kernels and Surface Defects at Strong Coupling

AbstractIt is well established that the spectral analysis of canonically quantized four-dimensional Seiberg–Witten curves can be systematically studied via the Nekrasov–Shatashvili functions. In this paper, we explore another aspect of the relation between $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories in four dimensions and operator theory. Specifically, we study an example of an integral operator associated with Painlevé equations and whose spectral traces are related to correlation functions of the 2d Ising model. This operator does not correspond to a canonically quantized Seiberg–Witten curve, but its kernel can nevertheless be interpreted as the density matrix of an ideal Fermi gas. Adopting the approach of Tracy and Widom, we provide an explicit expression for its eigenfunctions via an $${{\,\mathrm{O(2)}\,}}$$ O ( 2 ) matrix model. We then show that these eigenfunctions are computed by surface defects in $${{\,\mathrm{SU(2)}\,}}$$ SU ( 2 ) super Yang–Mills in the self-dual phase of the $$\Omega $$ Ω -background. Our result also yields a strong coupling expression for such defects which resums the instanton expansion. Even though we focus on one concrete example, we expect these results to hold for a larger class of operators arising in the context of isomonodromic deformation equations.

Ising meson spectroscopy on a noisy digital quantum simulator

Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Interstitial Strengthening of a Cast and Wrought Ni-Based Heavy Density Matrix Alloy by Carbon Addition

Interstitial Strengthening of a Cast and Wrought Ni-Based Heavy Density Matrix Alloy by Carbon Addition

Synergistic charge-transfer dynamics of rigid fused and unfused backbone with donors lead to promising photovoltaic properties of diazaborinine-based chromophores

Herein, a series of diazaborinin based derivatives (FABD1–FABD8) having D-π-D configuration was designed by inserting different types of rigid fused and unfused π-bridges into reference molecule (FABR) to explore their photovoltaic characteristics. To determine the optoelectronic and charge transport characteristics of these analogues, DFT/TD-DFT based calculations were conducted at the MPW1PW91/6-31G (d,p) level. For this, various analyses were performed such as transition density matrix (TDM), global reactivity parameters (GRP), open-circuit voltage (Voc), optical properties (UV–Vis), binding energy (Eb), hole-electron and frontier molecular orbital (FMO) energies. Their insights indicate that a rigid fused π-bridge greatly lowers the band gap as compared to an unfused π-spacers. Particularly, FABD7 showed the lowest energy gap of 2.20 eV owing to the presence of a rigid fused central core as compared to FABR with a band gap of 2.65 eV. Similarly, the entitled designed derivatives demonstrated a redshift absorption in the range of 585.7–704.6 nm while FABR is reported with 558.7 nm in the solvent phase. Furthermore, these derivatives displayed significant Voc with blending of PC61BM acceptor. This observation was also supported by DOS and TDM based insights. Interestingly, FABD7 seemed as a viable photovoltaic material due to its strong optical properties and small band gaps. These results uncover that the designed chromophores may be considered as efficient to enhance the performance of OSCs.

Dense QCD2 with matrix product states

We study one-flavor SU(2) and SU(3) lattice QCD in (1 + 1) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction.

We introduce a new method to remove the one-electron self-interaction error in approximate density functional calculations on an orbital-by-orbital basis, as originally proposed by Perdew and Zunger [Phys. Rev. B 1981, 23, 5048]. This method is motivated by a recent proposal by Pederson et al. [J. Chem. Phys. 2014, 140, 121103] to remove self-interaction that employs orbitals derived from the real-space density matrix, known as FLOSIC (Fermi Löwdin orbitals self-interaction correction). However, instead of Fermi Löwdin orbitals, our scheme utilizes columns of the density matrix to determine localized orbitals, like the localization procedure proposed by Fuemmeler et al. [J. Chem. Theory Comput. 2023, 19, 8572]. The new method, dubbed DOCSIC for density matrix as orbital coefficients self-interaction correction, contrasts with traditional Perdew-Zunger or FLOSIC in that it does not incorporate additional optimization parameters, and, unlike the average density self-interaction correction of Ciofini et al. [Chem. Phys. Lett. 2003, 380, 12], it makes use of localized orbitals. Another advantage of DOCSIC is that it can be implemented as a mean-field formalism. We show details of the self-consistent generalized Kohn-Sham implementation, some illustrative results, and we finally highlight its advantages and limitations.

A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed balance are revisited in terms of the supersymmetric quantum Hamiltonian H that can be obtained from the Markov generator via a similarity transformation. We first focus on the large deviations at level 2 for the empirical density p^(C) of the configurations C seen during a trajectory over the large time window [0,T] , and rewrite the explicit Donsker–Varadhan rate function as the matrix element I[2][p^(.)]=⟨p^|H|p^⟩ involving the square-root ket |p^⟩ . (The analog formula is also discussed for reversible diffusion processes as a comparison.) We then consider the explicit rate functions at higher levels, in particular for the joint probability of the empirical density p^(C) and the empirical local activities a^(C,C′) characterizing the density of jumps between two configurations (C,C′) . Finally, the explicit rate function for the joint probability of the empirical density p^(C) and of the empirical total activity A^ that represents the total density of jumps of a long trajectory is written in terms of the two matrix elements ⟨p^|H|p^⟩ and ⟨p^|Hoff|p^⟩ , where Hoff represents the off-diagonal part of the supersymmetric Hamiltonian H. This general framework is then applied to pure or random spin chains with single-spin-flip or two-spin-flip transition rates, where the supersymmetric Hamiltonian H corresponds to quantum spin chains with local interactions involving Pauli matrices of two or three neighboring sites. It is then useful to introduce the quantum density matrix ρ^=|p^⟩⟨p^| associated with the empirical density p^(.) in order to rewrite the various rate functions in terms of reduced density matrices involving only two or three neighboring sites.