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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Applications of Noether conservation theorem to Hamiltonian systems

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Electric fields at finite temperature

Partial differential equations for the electric potential at finite temperature, taking into account the thermal Euler–Heisenberg contribution to the electromagnetic Lagrangian are derived. This complete temperature dependence introduces quantum corrections to several well known equations such as the Thomas–Fermi and the Poisson–Boltzmann equation. Our unified approach allows at the same time to derive other similar equations which take into account the effect of the surrounding heat bath on electric fields. We vary our approach by considering a neutral plasma as well as the screening caused by electrons only. The effects of changing the statistics from Fermi–Dirac to the Tsallis statistics and including the presence of a magnetic field are also investigated. Some useful applications of the above formalism are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Kinklike structures in models of the Dirac–Born–Infeld type

The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac–Born– Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root restricting the field evolution and including additional powers in derivatives of the scalar field, controlled by a real parameter. In order to obtain topological solutions analytically, we propose a first-order framework that simplifies the equation of motion ensuring solutions that are linearly stable. This is implemented using the deformation method, and we introduce examples presenting two categories of potentials, one having polynomial interactions and the other with nonpolynomial interactions. We also explore how the Dirac–Born–Infeld kinetic term affects the properties of the solutions. In particular, we note that the kinklike solutions are similar to the ones obtained through models with standard kinetic term and canonical potential, but their energy densities and stability potentials vary according to the parameter introduced to control the new models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Soliton solutions in two-dimensional Lorentz-violating higher derivative scalar theory

This paper shows a new approach to obtain analytical topological defects of a 2D Myers–Pospelov Lagrangian for two scalar fields. Such a Lagrangian presents higher-order kinetic terms, which lead us to equations of motion which are non-trivial to be integrated. Here we describe three possible scenarios for the equations of motion, named by timelike, spacelike and lightlike respectively. We started our investigation with a kink-like traveling wave Ansatz for the free theory, which led us to constraints for the dispersion relations of each scenario. We also introduced a procedure to obtain analytical solutions for the general theory in the three mentioned scenarios. We exemplified the procedure and discussed the behavior of the defect solutions carefully. It is remarkable that the methodology presented in this study led to analytical models, despite the complexity of the equations of motion derived from the 2D Myers–Pospelov Lagrangian. The methodology here tailored can be applied to several Lagrangians with higher-order derivative terms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Contact manifolds and dissipation, classical and quantum

Motivated by a geometric decomposition of the vector field associated with the Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact Hamiltonian systems for the description of dissipative-like dynamical systems in the context of (non-necessarily exact) contact manifolds. In particular, we show how this class of dynamical systems naturally emerges in the context of Lagrangian Mechanics and in the case of nonlinear evolutions on the space of pure states of a finite-level quantum system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Variational formulation of classical and quantum models for intense laser pulse propagation

Highlights: •We consider the theoretical description of intense laser pulses propagating through gases. •We derived reduced models using Lagrangian and Hamiltonian formulations. •We obtain models where the atomic electrons are treated classically or quantum-mechanically. •We derive a number of conserved quantities of the reduced models. -- Abstract: We consider the theoretical description of intense laser pulses propagating through gases. Starting from a first-principles description of both the electromagnetic field and the electron motion within the gas atoms, we derive a hierarchy of reduced models. We obtain a parallel set of models, where the atomic electrons are treated classically on the one hand, and quantum-mechanically on the other. By working consistently in either a Lagrangian formulation or a Hamiltonian formulation, we ensure that our reduced models preserve the variational structure of the parent models. Taking advantage of the Hamiltonian formulation, we deduce a number of conserved quantities of the reduced models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Topological circuits of inductors and capacitors

Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea by analyzing a series of topological circuits consisting purely of inductors (L) and capacitors (C) connected to each other by wires to form periodic lattices. All the examples are treated using a unifying approach based on Lagrangians and the dynamical H-matrix. First, the building blocks and permutation wiring are introduced using simple circuits in one dimension, the SSH transmission line and a braided ladder analogous to the ice-tray model also known as the π-flux ladder. Then, more general building blocks (loops and stars) and wiring schemes (m-shifts) are introduced. The key concepts of emergent pseudo-spin degrees of freedom and synthetic gauge fields are discussed, and the connection to quantum lattice Hamiltonians is clarified. A diagrammatic notation is introduced to simplify the design and presentation of more complicated circuits. These building blocks are then used to construct topological circuits in higher dimensions. The examples include the circuit analog of Haldane’s Chern insulator in two dimensions and quantum Hall insulator in four dimensions featuring finite second Chern numbers. The topological invariants and symmetry protection of the edge modes are discussed based on the H-matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Einstein–Cartan cosmologies

Cosmologies based on General Relativity encompassing an anti-symmetric connection (torsion) can display nice desirable features as the absence of the initial singularity and the possibility of inflation in the early stage of the universe. After briefly reviewing the standard approach to the cosmology with torsion, we generalize it to demonstrate that several theories of torsion gravity are possible using different choices of the diffeomorphic invariants in the Lagrangians. As a result, distinct cosmologies emerge. In all of them it is possible that the universe avoids the initial singularity and passes through an initial accelerated expansion. Differences between these theories are highlighted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Lorentz transformations of the thermodynamic quantities

In modern physics there exist several formulations of relativistic thermodynamics of a moving body. The Planck and Ott formalisms are the main ones. However, it is not clear which one is correct. In the present paper, we have solved this problem. We have required the equivalence of the dynamical Hamiltonian of a system to the fundamental thermodynamic potential in addition to the principle of entropy invariance and derived the first law of thermodynamics from this fundamental potential. We have found that in the case of momentum being an independent variable in the Hamiltonian, the Lorentz transformations of the thermodynamic quantities belong to the Planck formalism. However, if we suppose that the velocity is an independent variable in the Hamiltonian (though it is not correct from the point of view of the relativistic dynamics), the Lorentz transformations of the thermodynamic quantities belong to the Ott formalism. It demonstrates that the Ott formalism cannot be appropriate. Moreover, we have proved that in the Planck description the first law of thermodynamics is covariant and the Legendre transform of the Lagrangian is preserved. However, in the Ott description the first law of thermodynamics is not covariant and the Legendre transform is violated. Thus we have demonstrated that only the Planck formulation of relativistic thermodynamics of a moving body is properly defined and the Ott formalism should be discarded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Particle quantum states with indefinite mass and neutrino oscillations

In this work we develop a mathematical formalism which allows obtaining oscillation formula for neutrino of any energy. We demonstrate that in the ultra-relativistic limit the results obtained in this new approach agree with the previously used phenomenological theory which is only applicable to ultra-relativistic neutrinos. To this end we do the following. The Hilbert spaces of particle states are constructed in such a way that the neutrinos are combined in a multiplet with its components being considered as different quantum states of a single particle. The same is done for the charged leptons and the down- and up-type quarks. In the theory based on the Lagrangian of the fermion sector of the Standard Model modified in accordance with this construction, the phenomenon of neutrino oscillations arises as a direct consequence of the general principles of quantum field theory. Using the example of the pion decay, when the resulting neutrino has to be ultra-relativistic, it is shown that the neutrino states produced in the decay process can be described by a superposition of states with different masses and identical canonical momenta with very high accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Gauge structures: From stabilizer codes to continuum models

Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter. In this paper, we discuss the theory of stabilizer codes as a discrete version of a linear gauge structure, a concept we introduce here. A linear gauge structure captures all the familiar ingredients of U(1) gauge theory including a generalization of charge conservation, Maxwell equations and topological terms. Using this connection, we prove some important results for stabilizer codes which can be used to characterize their error-correction properties. However, this perspective does not depend on any particular Hamiltonian or Lagrangian, which as a consequence is agnostic to the source of the gauge redundancy. Based upon the connection to stabilizer codes, we view the source of the gauge redundancy as an ambiguity in the tensor product structure of the Hilbert space. That is, the gauge provides a set of equivalent but arbitrary ways to factorize the Hilbert space. We apply this formalism to the d=2 and 3 toric code as well as the paradigm fracton models, X-Cube and Haah’s cubic code. From this perspective, we are able to map all these models to some continuum version which captures all or some of the fractonic and topological features of their parent discrete models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Lagrangian formulation of an infinite derivative real scalar field theory in the framework of the covariant Kempf–Mangano algebra in a (D+1)-dimensional Minkowski space–time

In 2017, G. P. de Brito and co-workers suggested a covariant generalization of the Kempf–Mangano algebra in a (D+1)-dimensional Minkowski space–time (Kempf and Mangano, 1997; de Brito et al., 2017). It is shown that reformulation of a real scalar field theory from the viewpoint of the covariant Kempf–Mangano algebra leads to an infinite derivative Klein–Gordon wave equation which describes two bosonic particles in the free space (a usual particle and a ghostlike particle). We show that in the low-energy (large-distance) limit our infinite derivative scalar field theory behaves like a Pais–Uhlenbeck oscillator for a spatially homogeneous field configuration ϕ(t, x-vector )=ϕ(t). Our calculations show that there is a characteristic length scale δ in our model whose upper limit in a four-dimensional Minkowski space–time is close to the nuclear scale, i.e., δ{sub max}∼δ{sub nuclear scale}∼10{sup −15} m. Finally, we show that there is an equivalence between a non-local real scalar field theory with a non-local form factor K(x−y)=−((□{sub x})/((1−((δ{sup 2})/2)□{sub x}){sup 2})) δ{sup (D+1)}(x−y) and an infinite derivative real scalar field theory from the viewpoint of the covariant Kempf–Mangano algebra.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Nonlinear dynamics from linear quantum evolutions

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕ{sub t} of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕ{sub t}. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕ{sub t}. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics

Highlights: • Relativistic Generalized Uncertainty Principle gives Frame independent minimum length. • Quantum Gravity modified Dirac equation from Modified Klein–Gordon Equations. • There exists a Quantum Gravity modified Lagrangian for a spinor field theory. • Feynman vertices contain 2 fermions & up to 5 gauge bosons are allowed. • Minimum length modifies the amplitude of Electrodynamic electron–muon scattering. Continuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Helicity, spin, and infra-zilch of light: A Lorentz covariant formulation

Highlights: • Spin and orbital parts of angular momentum. • The helicity tensor contains the helicity, spin and infra-zilch currents. • The helicity tensor is a Noether current for a duality-symmetric action. • Symmetry generator for the helicity tensor. • The helicity tensor is conserved in Lorenz gauge. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al. (2012), including helicity, spin, as well as the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quasinormal modes for non-minimally coupled scalar fields in regular black hole spacetimes: Grey-body factors, area spectrum and shadow radius

Black hole perturbation theory is a useful approach to study interactions between black holes and fundamental fields. A particular class of black hole solutions arising out of modification of Einstein’s general theory of relativity are regular black holes (RBHs) which can be constructed using a nonlinear electrodynamic Lagrangian. Because of their importance, we are interested in studying the behavior of three kinds of such RBHs under perturbations generated by an external field. Indeed, we investigate the quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs which is non-minimally coupled to the Ricci scalar-tensor of background geometry. We will attempt to find the low-lying quasinormal frequencies of the perturbations by using WKB approximation. We shall also study the relationship between the QNMs and some characteristic properties of black holes such as grey-body factors, area quantization, and shadow radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The repulsive Casimir-type forces in binary mixture of weakly interacting Bose–Einstein condensates gases

Highlights: • The equations of the state of a binary mixture weakly interacting Bose gases are established based on the Lagrangian of the system. • The formulae of the Casimir-type energy and the resulting Casimir-type force are produced from the quantum part of the grand canonical energy. • The results for the Casimir-type effect in the one-field case can be re-obtained by using the results of the two-field case. Within the framework of the quantum field theory (QFT) in the one-loop approximation, we investigate the Casimir-type effect in a mixture of two-component weakly interacting Bose-Einstein condensates (BECs) gases confined between two parallel plates at zero temperature. The Casimir-type forces in the miscible state of BECs for different boundary conditions (BCs) are discovered and compared to each other. The repulsive nature of the Casimir-type force in BECs is defined for the first time. Our calculations are finished in both grand canonical ensemble (GCE) and canonical ensemble (CE).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes

In the present study, a spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. The spectral-difference Raviart-Thomas (SDRT) method was originally proposed by Balan et al. and implemented on triangular-element meshes for invisid flow only. Our present results demonstrated that the SDRT method is stable and high-order accurate in two dimensions (2D) for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes for both inviscid and viscous flows. A stability analysis is also performed for mixed elements. Furthermore, we found our current SDRT scheme is stable for fourth-order accurate spatial discretizations. However, a stable fifth-order SDRT scheme remains to be identified.

97 MATHEMATICS AND COMPUTING↗