Article
Quantum Science & Technology
Hari Krovi
Summary: We present generalized and improved quantum algorithms for inhomogeneous linear and nonlinear ordinary differential equations (ODE) over prior work. Our algorithm for linear ODEs can handle many non-diagonalizable matrices, including singular matrices, and is exponentially faster than previous bounds for certain diagonalizable matrices. We apply our linear ODE algorithm to nonlinear differential equations using Carleman linearization, resulting in an exponential improvement in error dependence and the ability to handle any sparse matrix with a negative log-norm, without the requirement of normality.
Article
Optics
A. Ciamei, S. Finelli, A. Cosco, M. Inguscio, A. Trenkwalder, M. Zaccanti
Summary: We report on the realization of a degenerate mixture of ultracold fermionic lithium and chromium atoms, and demonstrate the control of density and degeneracy of the components, as well as the lithium-to-chromium density ratio.
Article
Multidisciplinary Sciences
Raphael Jannin, Yuri van der Werf, Kees Steinebach, Hendrick L. Bethlem, Kjeld S. E. Eikema
Summary: The Pauli exclusion principle has a significant impact on the structure of matter and particle interaction. Recent experiments have confirmed the existence of Pauli blockade in an optically trapped Fermi gas of He-3.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Jin-Peng Liu, Herman Oie Kolden, Hari K. Krovi, Nuno F. Loureiro, Konstantina Trivisa, Andrew M. Childs
Summary: The paper presents a quantum algorithm for dissipative quadratic n-dimensional ordinary differential equations, allowing for an exponential improvement in complexity over existing quantum algorithms. The method involves Carleman linearization and provides a lower bound on the worst-case complexity for general quadratic differential equations, showing potential applications in realistic epidemiological models and fluid dynamics.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Physics, Multidisciplinary
Marcel Duda, Xing-Yan Chen, Andreas Schindewolf, Roman Bause, Jonas von Milczewski, Richard Schmidt, Immanuel Bloch, Xin-Yu Luo
Summary: The interplay of quantum statistics and interactions in atomic Bose-Fermi mixtures results in a phase transition from a polaronic to a molecular phase, leading to the emergence of a molecular Fermi gas. This represents a new phenomenon complementary to the Bose-Einstein condensate/Bardeen-Cooper-Schrieffer crossover observed in Fermi systems. By tuning interspecies interactions, heteronuclear molecules can be generated in the quantum-degenerate regime.
Article
Mathematics, Applied
Alok Shukla, Prakash Vedula
Summary: A hybrid classical-quantum approach based on Walsh-Hadamard basis functions for solving nonlinear ordinary differential equations is proposed. The computation of the Walsh-Hadamard transform of arbitrary vectors is central to this approach, which is achieved using quantum Hadamard gates and various operations. The proposed hybrid approach shows a significantly lower computational complexity for the Walsh-Hadamard transform compared to the Fast Walsh-Hadamard transform, and it also provides satisfactory results for solving nonlinear differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Astronomy & Astrophysics
Jai-chan Hwang, Hyerim Noh
Summary: In this paper, we present the first-order post-Newtonian (1PN) approximations for a general imperfect fluid and an axion as a coherently oscillating massive scalar field in the cosmological context. For the axion, we derive the Schrodinger and Madelung hydrodynamic formulations using the Klein transformation and Madelung transformation, respectively, in an exact covariant way and to 1PN order. The complete sets of 1PN formulations are obtained without fixing the temporal gauge condition. We investigate the linear instability in cosmology and the static limit for both fluid and axion, independently of the gauge condition to 1PN order, thus ensuring gauge invariance.
Article
Physics, Multidisciplinary
Cheng Xue, Yu-Chun Wu, Guo-Ping Guo
Summary: The study presents a quantum algorithm based on the homotopy perturbation method for solving n-dimensional nonlinear dissipative ordinary differential equations (ODEs), providing exponential improvement over the best classical algorithms or previous quantum algorithms.
NEW JOURNAL OF PHYSICS
(2021)
Article
Physics, Multidisciplinary
Xin-Yuan Gao, D. Blume, Yangqian Yan
Summary: This work investigates the finite-temperature loss rate of single-component Fermi gases with weak interactions, and validates the applicability of the theoretical model through experimental results.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics, Applied
Damiao J. Araujo, Boyan Sirakov
Summary: In this paper, we obtain optimal boundary and global regularity estimates for viscosity solutions of fully nonlinear elliptic equations with degenerate ellipticity at critical points. We show that the solutions are C1,alpha on the boundary of the domain, where the optimal and explicit value of alpha depends only on the regularity of the boundary data and the degree of elliptic degeneracy, independent of the elliptic operator. We also obtain sharp global estimates, using a different method from previous results.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2023)
Article
Mathematics, Applied
Paul Bosch, Jose M. Rodriguez, Jose M. Sigarreta
Summary: In this paper, the authors work with a general formulation of Caputo-type fractional derivative and study oscillatory solutions of differential equations involving these derivatives. They extend the Kamenev-type oscillation criterion proposed by Baleanu et al. in 2015 and prove results on the existence and uniqueness of solutions for many equations. Finally, they provide some examples to enhance their study.
Article
Mathematics, Applied
Sumiya Baasandorj, Sun-Sig Byun, Jehan Oh
Summary: We establish the C1 regularity for certain degenerate/singular fully nonlinear elliptic equations with minimal assumptions on the associated operators.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Musa Cakmak
Summary: In this study, a collocation method based on Fibonacci polynomials is used to approximately solve a class of nonlinear pantograph differential equations. The unknown coefficients of the approximate solution function are calculated through a nonlinear algebraic system obtained via collocation points. The proposed method is validated by testing its performance using absolute error functions and comparing the results with exact solutions and other existing methods in literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Fluids & Plasmas
Pavel A. Andreev
Summary: The study focuses on spin-electron-acoustic waves in degenerate electron gases and presents a relativistic hydrodynamic model to investigate linear and nonlinear waves, including solitons. The model considers the evolution of partial concentrations, velocity fields, average reverse relativistic gamma factors, and flux of gamma factors. The research finds that relativistic effects reduce the phase velocity of spin-electron-acoustic waves and cause the dispersion curves of spin-electron-acoustic and Langmuir waves to approach each other in the relativistic limit. Additionally, the study demonstrates the spin dependence of the amplitude and width of relativistic spin-electron-acoustic solitons, as well as the transformation of bright solitons into dark solitons under relativistic effects.
PHYSICS OF PLASMAS
(2022)
Article
Computer Science, Interdisciplinary Applications
R. Au-Yeung, A. J. Williams, V. M. Kendon, S. J. Lind
Summary: This study presents a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. By encoding the SPH operators and domain discretization in a quantum register, and performing SPH summation via an inner product of quantum registers, the algorithm shows promising results in classical testing and solution of partial differential equations. This work lays a foundation for efficient simulations of complex engineering problems on gate-based quantum computers.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Physics, Multidisciplinary
Eldad Bettelheim
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Multidisciplinary
S. S. Seidov, S. Mukhin
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Multidisciplinary
Eldad Bettelheim
Summary: We use the Bethe ansatz technique and functional approach to exactly compute the matrix element of the field operator in the Lieb-Liniger model in the thermodynamic limit for any coupling constant c, and compare our results to known semiclassics at the limit c -> 0.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
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
Physics, Multidisciplinary
Eldad Bettelheim, Naftali R. Smith, Baruch Meerson
Summary: We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model by uncovering and exploiting complete integrability of the underlying equations. We solve these equations using the Zakharov-Shabat inverse scattering method adapted for the derivative nonlinear Schrodinger equation. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Condensed Matter
Sergei Mukhin
Summary: The study proposes the origin of the pseudogap and superconducting behaviors in high-T-c superconductors based on the formation of Euclidean Q-balls, explaining the relationship between Q-balls and superconducting condensates at the superconducting transition temperature.
Article
Physics, Multidisciplinary
Sergei I. Mukhin
Summary: This study investigates Euclidean Q-ball type solutions carrying Cooper/local-pair condensates in a model of high-Tc superconductors. The solutions are found in a finite volume filled with oscillating in Matsubara time semiclassical electronic spin/charge densities. The study explores the formation mechanism of these solutions and analyzes their existence and properties in superconducting materials.
Article
Physics, Condensed Matter
Sergei Mukhin
Summary: It is proposed that the Q-ball mechanism can be detected using micro X-ray diffraction, as it exhibits inverse correlations between the size and scattering intensities of the Q-ball charge-density-wave (CDW) fluctuations. The Q-ball charge Q represents the number of condensed elementary bosonic excitations in a CDW fluctuation. The self-consistent attraction between these excitations inside Euclidean Q-balls is triggered by the simultaneous condensation of Cooper/local pairs. Predictions derived from this picture, such as the inverse proportionality between Q-ball volume V and X-ray scattering intensity and the temperature dependence of superconducting Q-balls, fit well with recent X-ray diffraction data.
Article
Physics, Multidisciplinary
Eldad Bettelheim
Summary: We employ the Riemann-Hilbert approach to study the logarithmic negativity of two macroscopic intervals of free fermions, and find non-zero logarithmic negativity. The calculations show a specific magnitude result under certain filling and interval size conditions.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Optics
S. I. Mukhin, A. Mukherjee, S. S. Seidov
Summary: Analytic expression for the frequency dependence of transmission coefficient of microwave cavity coupled to transmission line with superradiant condensate is obtained, showing sharp transmission drops that reflect the condensate's frequencies spectrum. These findings pave the way for direct detection of the emergence of superradiant condensates in quantum metamaterials. The results are based on the analytic solutions of the nonlinear semiclassical dynamics of superradiant photonic condensate in the Dicke model, which describes ensemble of dipolar-coupled two-level atoms to electromagnetic field in the microwave cavity. In the ground state, the semiclassical coordinate of the superradiant condensate either oscillates in one of the two degenerate minima of its potential energy or traverses between them over the saddle point, depending on the coupling strength. An experimental setup is proposed for measuring the breakdown of the normal phase of the Dicke model through coupling with the transmission line. Additionally, the semiclassical motion of the superradiant condensate can be mapped to the nodding of an unstable LaGrange sleeping top, making the Dicke model an analog device for modeling mechanical systems dynamics.
Article
Physics, Multidisciplinary
S. I. Mukhin, A. Mukherjee, S. S. Seidov
Summary: The analytic solution of the semiclassical dynamics equations of the Dicke model in a superradiant state is presented, revealing that the amplitudes of the superradiant photonic condensate and coherent population of two-level atomic array in the microwave cavity can be expressed via Jacobi elliptic functions of real time. The existence of an adiabatic invariant of motion in the strongly coupled system is also manifested. The periodic beatings of the photonic and atomic coherent state amplitudes are shifted in time, indicating an effect of bound luminosity where energy stored in the two-level system is suddenly converted into photonic condensate that illuminates the cavity for half a period before plunging into darkness again.
JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS
(2021)
Article
Physics, Fluids & Plasmas
Boris Kheyfets, Sergei Mukhin, Timur Galimzyanov
Article
Materials Science, Multidisciplinary
S. Mukhin, T. R. Galimzyanov
Article
Physics, Fluids & Plasmas
Boris Kheyfets, Timur Galimzyanov, Sergei Mukhin
Proceedings Paper
Physics, Applied
P. I. Karpov, S. I. Mukhin
MOSCOW INTERNATIONAL SYMPOSIUM ON MAGNETISM (MISM 2017)
(2018)
