Article
Mathematics, Applied
Lothar Reichel, Miodrag M. Spalevic
Summary: The estimation of quadrature error in Gauss quadrature rules for approximating integrals is important in scientific computing. Anti-Gauss quadrature rules and averaged rules have been developed as improved approximations. Recent research has shown that these averaged rules can achieve higher accuracy than expected. This paper discusses methods to modify averaged rules to ensure their internal nodes.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Physics, Mathematical
Jeremy Faupin, Marius Lemm, Israel Michael Sigal
Summary: The dynamics of the Bose-Hubbard model on general lattices are considered, and a Lieb-Robinson bound is proved for observables with separated supports. A maximal velocity bound for particle transport through an initially empty region is obtained, extending to long-range hopping. The techniques used originate in the proofs of maximal velocity bounds for Schrodinger operators and scattering theory in non-relativistic QED.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Condensed Matter
Hao Fu, Mingqiu Luo, Peiqing Tong
Summary: The Lieb-Robinson bound (LRB) is numerically studied in one-dimensional noninteracting many-electron systems with disordered and quasiperiodic on-site potentials. For the short-range hopping system, a logarithmic light cone is found in the presence of a disordered on-site potential, which decreases with increasing disorder strength. In the long time limit, the bound does not change with time. For the generalized Fibonacci quasiperiodic system, a power-law light cone is observed, with the exponent decreasing as the strength of the potential increases. It is also found that the exponent is larger for the first class of GFQ system compared to the second class with the same potential. Lastly, the effects of long-range hopping on the LRB are discussed.
PHYSICA B-CONDENSED MATTER
(2022)
Article
Mathematics, Applied
J. Alahmadi, M. Pranic, L. Reichel
Summary: The paper discusses the technique proposed by Golub and Meurant for computing error bounds for Stieltjes integrals, as well as an extension of this technique that addresses the situation where derivatives of the integrand change sign. By using different quadrature rules, upper and lower error bounds for the functional are effectively evaluated in such cases.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Bernardo de la Calle Ysern, Miodrag M. Spalevic
Summary: This paper presents a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with reduced polynomial exactness compared to the corresponding Kronrod extension. The algorithm is based on determining an associated Jacobi matrix and finding the nodes and weights as the matrix's eigenvalues and eigenvectors, similar to the Golub-Welsch algorithm.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Alessandro Michelangeli, Nicola Santamaria
Summary: This article proves that for a mixture of interacting Bose gases initially prepared in a regime of condensation, observables of disjoint sets of particles of each species have correlation functions that remain asymptotically small in the total number of particles and display a controlled growth in time.
ASYMPTOTIC ANALYSIS
(2022)
Article
Mathematics, Applied
J. Alahmadi, M. Pranic, L. Reichel
Summary: This paper focuses on computing approximations of matrix functionals of the form F(A) := v(T) f (A)v, where A is a large symmetric positive definite matrix, v is a vector, and f is a Stieltjes function. The paper proposes using rational Gauss quadrature rules and develops rational Gauss-Radau and rational anti-Gauss rules. These rules can be used to determine upper and lower bounds, or approximate upper and lower bounds, for F(A). In cases where the function f has singularities close to the spectrum of A, the use of rational Gauss rules is beneficial.
NUMERISCHE MATHEMATIK
(2022)
Article
Mathematics, Applied
Gerard Meurant, Petr Tichy
Summary: In this paper, we discuss the use of the conjugate gradient (CG) method to solve systems of linear algebraic equations with a real symmetric positive definite matrix A. We analyze the behavior of the Gauss-Radau upper bound on the A-norm of the error and its relationship with the prescribed underestimate mu. We also explain a phenomenon observed during computations where the upper bound loses accuracy in later CG iterations. We propose an adaptive strategy for improving the accuracy of the upper bounds in previous iterations.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
D. Lj Djukic, R. M. Mutavdzic Djukic, L. Reichel, M. M. Spalevic
Summary: This paper investigates the internal property of averaged and generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the third and fourth kinds, and demonstrates that truncated variants have internal property.
NUMERICAL ALGORITHMS
(2023)
Article
Physics, Mathematical
Martin Gebert, Alvin Moon, Bruno Nachtergaele
Summary: This study considers a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. Commutator bounds for its Heisenberg dynamics, which incorporate the coupling strengths of the impurities, are proven. The results apply to both finite volume and thermodynamic limit scenarios, and can be used to improve Lieb-Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution.
REVIEWS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Idrissa Kayijuka, Suliman Alfaqeih, Turgut Ozis
Summary: This paper introduces a method for computing singular and highly oscillatory integrals, by transforming the integrals into problems of integration on [0, infinity) and using the generalized Gauss-Laguerre rule or constructing Gauss rules relative to a Freud weights function. MATHEMATICA programming code, algorithms and illustrative numerical examples are provided to test the efficiency of the presented experiments.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Mathematics, Applied
Mukesh Gupta, Jai Prakash Shukla, B. K. Singh
Summary: Our study aims to investigate the dynamical behavior of the quantum model of Bateman-Burgers equation using a new hybrid semidiscretization technique, nCB-DQT-RK scheme. The nCB-DQT-RK scheme combines traditional differential quadrature technique (DQT) with modified cubic B-splines (nCB) as a basis for discretizing spatial derivatives, and SSP-RK scheme for temporal discretization. The efficiency and effectiveness of the nCB-DQT-RK results are demonstrated numerically and graphically, showing improved accuracy and spatial convergence compared to existing techniques using traditional cubic B-splines and its modifications.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Information Systems
Giorgio Taricco
Summary: This study addresses the problem of evaluating the performance of short codes used in Ultra-Reliable Low-Latency Communications. It proposes an alternative method called Random-Coding Union Bounds (RCUB) and compares its accuracy with Gaussian and saddlepoint approximations.
IEEE WIRELESS COMMUNICATIONS LETTERS
(2022)
Article
Mathematics, Applied
D. R. JANDRLIC, D. M. KRTINIC, L. J. V. MIHIC, A. V. PEJCEV, M. M. SPALEVIC
Summary: In this paper, we propose a numerical method for evaluating the error terms in Gaussian quadrature formulae with the Legendre weight function. Inspired by previous work, we derive an explicit formula for the kernel and identify the points on an ellipse where the maximum modulus of the kernel is attained. We also provide effective error bounds for this quadrature formula when used with analytic integrands.
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
(2022)
Article
Chemistry, Physical
Clemens Vittmann, R. Kevin Kessing, James Lim, Susana F. Huelga, Martin B. Plenio
Summary: This study investigates the nonequilibrium dynamics of electron transmission from a straight waveguide to a helix with spin-orbit coupling. Transmission is found to be spin-selective, leading to large spin polarizations of the itinerant electrons. The degree of spin selectivity depends on the width of the interface region, and no polarization is observed for single-point couplings. The study identifies interface structure and conservation of momentum as crucial factors for chiral-induced spin selectivity, and confirms the robustness of this mechanism against static disorder.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2022)
Article
Physics, Multidisciplinary
Eldad Bettelheim, Aditya Banerjee, Martin B. Plenio, Susana F. Huelga
Summary: The statistical mechanics characterization of finite subsystems embedded in an infinite system is a fundamental question in quantum physics. In this study, a mathematical framework based on the Riemann-Hilbert approach is developed to address this problem in the one-dimensional case, where the finite system consists of two disjoint intervals and is analyzed in the thermodynamic limit. The method is demonstrated to be useful for computing the change in the entanglement and negativity spectra, providing insights into the quantum correlation structure and extent in fermionic systems subject to local environments.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Astronomy & Astrophysics
Kirill Streltsov, Julen Simon Pedernales, Martin Bodo Plenio
Summary: In this study, we investigate the interaction between a harmonic oscillator and a two-level test mass mediated by a local operations and classical communication channel. We demonstrate that a signature, claimed to be exclusive to channels that can transmit quantum information, is generated. By providing an explicit example based on a measurement-and-feedback channel, we explain the failure of the previous proof and discuss the potential applications of setups of this type in testing the nature of gravitational interaction and the fundamental implications an LOCC model of gravity may have in black hole physics.
Article
Physics, Multidisciplinary
Julen S. Pedernales, Kirill Streltsov, Martin B. Plenio
Summary: Feynman suggested in 1957 that the quantum or classical nature of gravity can be evaluated through testing the gravitational interaction of source masses in superposition. However, the weakness of this interaction in proposed matter-wave interferometry experiments requires special initial states. This study tackles the challenge by using a massive body as an amplifying mediator, resulting in a stronger and independent interaction between test systems.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
F. Caycedo-Soler, A. Mattioni, J. Lim, T. Renger, S. F. Huelga, M. B. Plenio
Summary: Numerically exact simulations reveal that multimode vibronic mixing in model photosynthetic systems strongly affects optical responses and facilitates coherent dynamics. The generation, transport, and trapping of excitons in pigment-protein complexes (PPCs) are crucial for photosynthesis. The inclusion of full multi-mode vibronic dynamics in numerical calculations of linear spectra leads to significant corrections to electronic parameter estimation. These effects are relevant to the discussion on the origin of long-lived oscillations in multidimensional nonlinear spectra.
NATURE COMMUNICATIONS
(2022)
Article
Chemistry, Multidisciplinary
Yingke Wu, Priyadharshini Balasubramanian, Zhenyu Wang, Jaime A. S. Coelho, Mateja Prslja, Reiner Siebert, Martin B. Plenio, Fedor Jelezko, Tanja Weil
Summary: This study demonstrates the use of sub-10 nm-sized fluorescent nanodiamonds as catalysts for the decomposition of H2O2 and the production of radical intermediates at the nanoscale. The nitrogen-vacancy quantum sensors inside the nanodiamonds are employed to quantify these radicals. This method can be used as self-reporting H2O2 sensors with molecular-level sensitivity and nanoscale spatial resolution.
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
(2022)
Article
Physics, Multidisciplinary
Felix Ahnefeld, Thomas Theurer, Dario Egloff, Juan Mauricio Matera, Martin B. Plenio
Summary: In this paper, we investigate a sequential variant of Shor's algorithm and quantitatively explore the role of coherence. By using the framework of dynamical resource theories, we determine the lower and upper bounds of the success probability of the protocol and find that coherence is the quantum resource that determines its performance within the fixed structure considered.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Mathematical
Giovanni Ferrari, Ludovico Lami, Thomas Theurer, Martin B. Plenio
Summary: In this study, we examine asymptotic state transformations in continuous variable quantum resource theories. We prove that lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation rates in these settings. We provide applications to optical nonclassicality, entanglement, and quantum thermodynamics resource theories. Our findings offer computable upper bounds for asymptotic transformation rates, including those achievable with linear optical elements.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Chemistry, Physical
Clemens Vittmann, James Lim, Dario Tamascelli, Susana F. Huelga, Martin B. Plenio
Summary: This study examines the role of delocalized phonon modes in electron transport in chiral structures and demonstrates that spin selectivity can originate from spin-dependent energy and momentum conservation in electron-phonon scattering events. The degree of spin polarization, however, depends on environmental factors and the presence of external driving fields. The parametric dependence allows for experimentally testable predictions of the model.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Physics, Multidisciplinary
Patrick Barthel, Patrick H. Huber, Jorge Casanova, Inigo Arrazola, Dorna Niroomand, Theeraphot Sriarunothai, Martin B. Plenio, Christof Wunderlich
Summary: We demonstrate the experimental implementation of a two-qubit phase gate using a radio frequency controlled trapped-ion quantum processor. The gate is generated by applying a pulsed dynamical decoupling sequence to the ions' carrier transitions, allowing for tunable and high-fidelity phase shift. The gate's performance is robust against various sources of error and holds potential for fast gate speeds.
NEW JOURNAL OF PHYSICS
(2023)
Article
Physics, Multidisciplinary
Alejandro D. Somoza, Nicola Lorenzoni, James Lim, Susana F. Huelga, Martin B. Plenio
Summary: The role of vibrational motion in the charge dynamics of donor-acceptor networks in organic photovoltaics is investigated using non-perturbative simulations. The study addresses the challenge of simulating large electronic-vibrational systems and identifies conditions under which underdamped vibrational motion induces efficient charge separation. The results provide insights into coupling mechanisms and the role of entropic effects, offering a toolbox for designing efficient charge separation pathways in artificial nanostructures.
COMMUNICATIONS PHYSICS
(2023)
Article
Physics, Multidisciplinary
Alastair Marshall, Thomas Reisser, Phila Rembold, Christoph Mueller, Jochen Scheuer, Martin Gierse, Tim Eichhorn, Jakob M. Steiner, Patrick Hautle, Tommaso Calarco, Fedor Jelezko, Martin B. Plenio, Simone Montangero, Ilai Schwartz, Matthias M. Mueller, Philipp Neumann
Summary: This paper utilizes photoexcited triplet state of pentacene-doped naphthalene crystals to polarize surrounding protons and enhance nuclear magnetic resonance signals. Optimal control pulses designed with REDCRAB and a strategy called ARISE are introduced to improve the performance of hyperpolarization sequences.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Optics
Julen S. Pedernales, Martin B. Plenio
Summary: This study designs a method that utilizes spatial correlations to reduce the impact of perturbations from distant sources on the visibility of matter-wave interference patterns, and develops a general framework for correcting the multipole expansion of environmental potential fields. This method works for stochastic field fluctuations at any timescale and does not require quantum correlations.
Article
Quantum Science & Technology
Theodoros Ilias, Dayou Yang, Susana F. Huelga, Martin B. Plenio
Summary: This study proposes a protocol for criticality-enhanced sensing by continuously observing the emitted radiation quanta. The study establishes a scaling theory for the global quantum Fisher information and derives universal scaling laws related to critical exponents. The findings suggest that the precision scaling of continuous detection of emitted quanta exceeds that of direct measurement, indicating the metrological value of this approach in dissipative criticality.
Article
Optics
Giovanni Spaventa, Susana F. Huelga, Martin B. Plenio
Summary: This study combines the concepts of quantum resource theory and divisibility classes of quantum channels to prove that memory effects can increase the efficiency of photoisomerization, which is not achievable under purely thermal Markovian evolution. This provides rigorous evidence that memory effects can serve as a resource in quantum thermodynamics at the nanoscale.