General form of s , t , and u symmetric polynomials and heavy quarkonium physics
Not Available
Ma, Yan-Qing↗
SEARCH · Engineering Papers
Results for “General Physics”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Physical generalizations of the Rényi entropy
We present a new type of generalization of the Rényi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of [Formula: see text]-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Rényi entropy as an integral of the thermal entropy of hyperbolic black holes in [Formula: see text]-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Rényi entropy that suggests itself in that light. In the field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For [Formula: see text], it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems.
Astronomy & Astrophysics↗
Grassmann phase space theory and the Jaynes–Cummings model
The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are often developed. However, atomic spin operators satisfy the standard angular momentum commutation rules rather than the commutation rules for bosonic annihilation and creation operators, and are in fact second order combinations of fermionic annihilation and creation operators. Though phase space methods in which the fermionic operators are represented directly by c-number phase space variables have not been successful, the anti-commutation rules for these operators suggest the possibility of using Grassmann variables—which have similar anti-commutation properties. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of phase space methods in quantum optics to treat fermionic systems by representing fermionic annihilation and creation operators directly by Grassmann phase space variables is rather rare. This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the TLA) can be used to treat the Jaynes–Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker–Planck equation involving both left and right Grassmann differentiations can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, in which the correspondence rules for the bosonic operators are non-standard and hence the Fokker–Planck equation is also unusual. Initial conditions, such as those above for initially uncorrelated states, are discussed and used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enable the six coupled equations for the new c-number functions–that are also equivalent to the canonical Grassmann distribution function–to be solved analytically, based on an ansatz from an earlier paper by Stenholm. It is then shown that the distribution function is exactly the same as that determined from the well-known solution based on coupled amplitude equations. In quantum–atom optics theories for many atom bosonic and fermionic systems are needed. With large atom numbers, treatments must often take into account many quantum modes—especially for fermions. Generalisations of phase space distribution functions of phase space variables for a few modes to phase space distribution functionals of field functions (which represent the field operators, c-number fields for bosons, Grassmann fields for fermions) are now being developed for large systems. For the fermionic case, the treatment of the simple two mode problem represented by the Jaynes–Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for fermionic applications in quantum–atom optics. -- Highlights: •Novel phase space theory of the Jaynes–Cummings model using Grassmann variables. •Fokker–Planck equations solved analytically. •Results agree with the standard quantum optics treatment. •Grassmann phase space theory applicable to fermion many-body problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity
Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e. , the principle of least action on a Finsler manifold.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Physical Processes in the MAGO/MFT Systems
The Monograph is devoted to theoretical discussion of the physical effects, which are most significant for the alternative approach to the problem of controlled thermonuclear fusion (CTF): the MAGO/MTF approach. The book includes the description of the approach, its difference from the major CTF systems—magnetic confinement and inertial confinement systems. General physical methods of the processes simulation in this approach are considered, including plasma transport phenomena and radiation, and the theory of transverse collisionless shock waves, the surface discharges theory, important for such kind of research. Different flows and magneto-hydrodynamic plasma instabilities occurring in the frames of this approach are also considered. In virtue of the general physical essence of the considered phenomena the presented results are applicable to a wide range of plasma physics and hydrodynamics processes. The book is intended for the plasma physics and hydrodynamics specialists, post-graduate students, and senior students-physicists.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nuclear Astrophysics through simulations of neutron star mergers using Monte‐Carlo neutrino radiation transport (DE-SC0020435 Final Technical Report)
Neutron star mergers are an important source of information for nuclear physics. Except for black holes, neutron stars are the densest macroscopic objects known to exist in the Universe. They provide us with a remarkable laboratory to study the poorly understood high-density states of matter, complementing the study of heavy nuclei performed by nuclear physics experiments on Earth. Collisions of neutron stars are of particular interest. They are among the most energetic events observable in the Universe, powering a broad range of signals across the electromagnetic spectrum as well as gravitational wave signals. These signals contain important information about the properties of extremely dense matter. Colliding neutron stars additionally eject large amounts of neutron-rich material into the surrounding interstellar medium -- material that then undergoes rapid neutron-capture (r-process) nucleosynthesis, the mechanism thought to be responsible for the production of about half of the heavy nuclei. In order to understand current and future observations of neutron star mergers, we need reliable models for the signals that they power. An important component in the construction of such models are numerical simulations of colliding neutron stars. These simulations are costly, running for multiple months on supercomputers, and require the inclusion of complex physics (general relativity, magnetohydrodynamics, neutrino physics, nuclear reactions). In this document, we describe the development of new methods for the treatment of neutrinos in merger simulations, as well as the first simulations capable of evolving the equations of neutrino radiation transport directly and their impact on our understanding of neutron star mergers and more broadly in nuclear astrophysics. We also discuss additional work performed in the study of nucleosynthesis and neutrino physics in neutron star mergers as part of Early Career Award DE-SC0020435.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
The neutrino gravitational memory from a core collapse supernova: phenomenology and physics potential
General Relativity predicts that the passage of matter or radiation from an asymmetrically-emitting source should cause a permanent change in the local space-time metric. This phenomenon, called the gravitational memory effect, has never been observed, however supernova neutrinos have long been considered a promising avenue for its detection in the future. With the advent of deci-Hertz gravitational wave interferometers, observing the supernova neutrino memory will be possible, with important implications for multimessenger astronomy and for tests of gravity. In this work, we develop a phenomenological (analytical) toy model for the supernova neutrino memory effect, which is overall consistent with the results of numerical simulations. This description is then generalized to several case studies of interest. We find that, for a galactic supernova, the dimensionless strain, h(t), is of order ~ 10 -22 - 10 -21 , and develops over a typical time scale that varies between ~ 0.1 - 10 s, depending on the time-evolution of the anisotropy of the neutrino emission. The characteristic strain, h c (f), has a maximum at a frequency f max ~ Script $\mathcal{O}$(10 -1 ) - Script $\mathcal{O}$(1) Hz. The detailed features of the time- and frequency-structure of the memory strain will inform us of the matter dynamics near the collapsed core, and allow to distinguish between different stellar collapse scenarios. Next generation gravitational wave detectors like DECIGO and BBO will be sensitive to the neutrino memory effect for supernovae at typical galactic distances and beyond; with Ultimate DECIGO exceeding a detectability distance of 10 Mpc
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The Epstein–Glaser causal approach to the light-front QED{sub 4}. I: Free theory
In this work we present the study of light-front field theories in the realm of the axiomatic theory. It is known that when one uses the light-cone gauge pathological poles (k{sup +}){sup −n} arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have the correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use of rigorous mathematical machinery of the distributional theory combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how the analytic representation for propagators arises by requiring general physical properties within the framework of Wightman’s formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar and fermionic fields, as well as for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein–Glaser causal method in order to have a mathematical rigorous description of the free propagators of the theory, allowing us to discuss a general treatment for propagators of the type (k{sup +}){sup −n}. Afterwards, we show that at given conditions our results reproduce known prescriptions in the literature. - Highlights: • We develop the analytic representation for propagators in Wightman’s framework. • We make use of the analytic representation to obtain equal-time (anti)commutation relations in the light-front. • We derive the free Feynman propagators for the light-front quantum electrodynamics in the Epstein–Glaser approach. • We determine a general expression for the propagator associated to the light-cone poles (k{sup +}){sup −n} in the causal approach.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. As a result, we present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Bootstrap and amplitudes: a hike in the landscape of quantum field theory
This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories. We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic quantum field theories. Here, the first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the CP 1 model with the Fubini-Study metric arising from re-summation of the n-point interaction terms derived from amplitudes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multilayer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely, the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such a model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.
97 MATHEMATICS AND COMPUTING↗
Peakompactons: Peaked compact nonlinear waves
This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly by reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K # (n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mapping of spin wave propagation in a one-dimensional magnonic crystal
The formation and evolution of spin wave band gaps in the transmission spectrum of a magnonic crystal have been studied. A time and space resolved magneto inductive probing system has been used to map the spin wave propagation and evolution in a geometrically structured yttrium iron garnet film. Experiments have been carried out using (1) a chemically etched magnonic crystal supporting the propagation of magnetostatic surface spin waves, (2) a short microwave pulsed excitation of the spin waves, and (3) direct spin wave detection using a movable magneto inductive probe connected to a synchronized fast oscilloscope. The results show that the periodic structure not only modifies the spectra of the transmitted spin waves but also influences the distribution of the spin wave energy inside the magnonic crystal as a function of the position and the transmitted frequency. These results comprise an experimental confirmation of Bloch′s theorem in a spin wave system and demonstrate good agreement with theoretical observations in analogue phononic and photonic systems. Theoretical prediction of the structured transmission spectra is achieved using a simple model based on microwave transmission lines theory. Here, a spin wave system illustrates in detail the evolution of a much more general physical concept: the band gap.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Global magnetohydrodynamic instabilities in the L-2M stellarator
Analysis of global magnetohydrodynamic (MHD) instabilities in the L-2M stellarator (Prokhorov General Physics Institute, Russian Academy of Sciences) is presented. The properties of free-boundary equilibria states are outlined, the stability conditions for small-scale modes are briefly discussed, and the number of trapped particles is estimated. All the magnetic configurations under study are stable against ballooning modes. It is shown that global ideal internal MHD modes can be found reliably only in Mercier unstable plasmas. In plasma that is stable with respect to the Mercier criterion, global unstable modes that are localized in the vicinity of the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) can be found. The radial structure of all perturbations under study is almost entirely determined by the poloidal coupling of harmonics. The results of calculations are compared with the available experimental data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The Holographic Entropy Cone
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Controlling the quantum dynamics of a mesoscopic spin bath in diamond
Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Formation and Acceleration of Uniformly-Filled Ellipsoidal Electron Bunches Obtained via Space-Charge-Driven Expansion from a Cesium-Telluride Photocathode
Abstract Not Provided
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Scientific and Technical Basis of Application of Nanostructured Materials Science and Nanoelectronics in Systems of Electromechanical Energy Converters for Special Purposes
We consider the current state of a completely new area of science; microsystem electromechanics. Тhe wide spectra of its practical applications and prospects for further development are analyzed. We discuss in detail two main directions of creating micro- and nanoelectromechanical converters as basic elements of microsystem electromechanics: “top down” and “down top.” We also describe the main technological methods in constructing basic functional elements of microsystem electromechanics, areas of their application in traditional and new technologies (information and computer technologies, medicine, aerospace, rocket and artillery systems, etc.). At the same time, we discuss some key issues of generalized physical and mathematical modeling of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). A new generalized approach is proposed to study dynamic and energy characteristics of MEMS and NEMS as complex dynamic systems with binary conjugate subsystems. Based on proposed theoretical principles and models, the possibilities of studying electrophysical characteristics of biological nanostructures have been considered.
77 NANOSCIENCE AND NANOTECHNOLOGY↗