Search NASA⌕ Search

SEARCH · Search NASA

Results for “S-matrix theory”

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.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules

We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.

Cohen, S. C.↗
NASA NTRS1996

Mobility of Electron in DNA Crystals by Laser Radiation

The mobility of electrons in laser radiated DNA is closed to the energy transfer and energy migration of a biological molecule. Arrhenius has studied the conductivity of the electrons in a biological molecule. But his result is far from the experimental result and meanwhile the relation between some parameters in his theory and the micro-quantities in DNA is not very clear. In this paper, we propose a new phonon model of electron mobility in DNA and use Lippman-Schwinger equation and S-matrix theory to study the mobility of electrons in DNA crystal. The result is relatively close to the experiment result and some parameters in Arrhenius theory are explained in our work.

Zhang, Kaixi↗
NASA NTRS1985

Interaction potential between a helium atom and metal surfaces

By employing an S-matrix theory for evanescent waves, the repulsive potential between a helium atom and corrugated metal surfaces has been calculated. P-wave interactions and intra-atomic correlation effects were found to be very important. The corrugation part of the interaction potential is much weaker than predicted by the effective-medium theory. Application to Cu, Ni, and Ag (110) surfaces gives good agreement with experiment without any adjustable parameters.

Takada, Y.↗
NASA NTRS1999

Magnetic Photon Splitting: The S-Matrix Formulation in the Landau Representation

Calculations of reaction rates for the third-order QED process of photon splitting gamma yields gamma.gamma in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner [1] presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant, advances beyond the work of [1] by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper- time formulations is demonstrated.

Baring, Matthew G.↗
NASA NTRS1979

Semiclassical theory of electronically nonadiabatic transitions in molecular collision processes

An introductory account of the semiclassical theory of the S-matrix for molecular collision processes is presented, with special emphasis on electronically nonadiabatic transitions. This theory is based on the incorporation of classical mechanics with quantum superposition, and in practice makes use of the analytic continuation of classical mechanics into the complex space of time domain. The relevant concepts of molecular scattering theory and related dynamical models are described and the formalism is developed and illustrated with simple examples - collinear collision of the A+BC type. The theory is then extended to include the effects of laser-induced nonadiabatic transitions. Two bound continuum processes collisional ionization and collision-induced emission also amenable to the same general semiclassical treatment are discussed.

Lam, K. S.↗
DOE OSTI2025

Dynamical coupled-channel models for hadron dynamics

Dynamical coupled-channel (DCC) approaches parametrize the interactions and dynamics of two and more hadrons and their response to different electroweak probes. The inclusion of unitarity, three-body channels, and other properties from scattering theory allows for a reliable extraction of resonance spectra and their properties from data. Here, we review the formalism and application of the ANL-Osaka, the Juelich-Bonn-Washington, and other DCC approaches in the context of light baryon resonances from meson, (virtual) photon, and neutrino-induced reactions, as well as production reactions, strange baryons, light mesons, heavy meson systems, exotics, and baryon-baryon interactions. Finally, we also provide a connection of the formalism to study finite-volume spectra obtained in Lattice QCD, and review applications involving modern statistical and machine learning tools.

Amplitude analysis↗
NASA NTRS1983

Questions on universal constants and four-dimensional symmetry from a broad viewpoint. I

It is demonstrated that there is a flexibility in clock synchronizations and that four-dimensional symmetry framework can be viewed broadly. The true universality of basic constants is discussed, considering a class of measurement processes based on the velocity = distance/time interval, which always yields some number when used by an observer. The four-dimensional symmetry framework based on common time for all observers is formulated, and related processes of measuring light speed are discussed. Invariant 'action functions' for physical laws in the new four-dimensional symmetry framework with the common time are established to discuss universal constants. Truly universal constants are demonstrated, and it is shown that physics in this new framework and in special relativity are equivalent as far as one-particle systems and the S-matrix in field theories are concerned.

Hsu, J. P.↗
DOE OSTI2025

On unitarity of the hypergeometric amplitude

The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with S-matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the (r, m 2 , D) parameter space as non-unitary, and establish another large subset of the (r, m 2 , D) parameter space where all of the residue’s partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1980

Vibration-rotation line shifts for 1 sigma g + H2/V,J/-1S/0/ He computed via close coupling - Temperature dependence

The density shifting of vibration-rotation transitions of H2 perturbed by He was computed (as a function of temperature) with no adjustable parameters. The calculation was carried out using the framework of the impact theory of Baranger with S-matrix elements obtained via close coupling calculations which incorporated the ab initio H2-H2 system potential of Tsapline et al.(1977). Vibrational and rotational inelasticity were neglected in the calculations; nevertheless good agreement with experimental data was obtained, up to moderate temperatures, for the density shift. A much poorer comparison was obtained for the density broadening.

Hahne, G. E.↗
DOE OSTI2025

Splitting regions and shrinking islands from higher point constraints

We study constraints from higher-point amplitudes on 2 → 2 scattering in the context of effective field theory (EFT) using the perturbative numerical S-matrix bootstrap. Specifically, we investigate the class of weakly coupled EFTs with amplitudes that obey the hidden zero and split conditions that are known to hold both for Tr(Φ 3 ) theory and for certain string tree amplitudes, including at 4-point the beta function. Requiring the splitting condition for the 5-point amplitude not only fixes nearly all its contact terms, but it also imposes non-linear constraints among the 4-point EFT Wilson coefficients. When included in the bootstrap, the resulting allowed region consistent with positivity is no longer convex but is restricted to a smaller non-convex region — which has a sharp corner near the string beta function! Assuming the absence of an infinite spin tower at the mass gap, the allowed region bifurcates into a trivial region (with states only above a chosen cutoff) and an island that continues to shrink around the string as more constraints are included in the bootstrap. The numerics indicate that in the absence of single-mass infinite spin towers the string beta function is the unique 4-point amplitude compatible with hidden zero and the 5-point splitting constraints. The analysis provides a prototype example for how features of higher-point amplitudes constrain the bootstrap of 4-point amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

2-loop scattering on superstring and supermembrane in flat space

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

AdS-CFT Correspondence↗
NASA NTRS1986

Origin of gauge invariance in string theory

A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.

Horowitz, G. T.↗
DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗
DOE OSTI2024

Extracting the asymptotic behavior of S-matrix elements from their phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2012

Variance of the Quantum Dwell Time for a Nonrelativistic Particle

Munoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, . . ., of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)]; an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle s time flux and others) is derived.

Hahne, Gerhard↗
DOE OSTI2024

Unitary coupled-channel three-body amplitude with pions and kaons

Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, rearranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems (“isobars”) of all isospins, 𝐼 = 0,1/2,1,3/2,2 , and it also allows for transitions within a given isobar. The 𝑓 0 ⁡(500)⁢(𝜎),𝑓 0 ⁡(980),𝜌⁡(700),𝐾$^{*}_{0}$⁡(700)⁢(𝜅), and 𝐾*⁡(892) resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for 𝑎 1 quantum numbers are shown as a proof of principle for the numerical implementation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗