Search NASA⌕ Search

SEARCH · Search NASA

Results for “1/N Expansion”

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.

9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Failure of the large-N expansion in a bosonic tensor model

We study the tensor model generalization of the quantum p-spherical model in the large-N limit. While the tensor model has the same large-N expansion as the disordered quantum p-spherical model, its ground state is superextensive, in contradiction with large-N perturbation theory. Therefore, the large-N expansion of this model catastrophically fails at arbitrarily large-N, without any obvious signal in perturbation theory.

1/N Expansion↗
DOE OSTI2025

Generalized entropy of gravitational fluctuations

The corrections to holographic entanglement entropy from bulk quantum fields in a classical gravitational background are now well understood. They lead, in particular, to unitary Page curves for evaporating black holes. However, the correct treatment of quantum fluctuations of the metric, including graviton excitations, is a longstanding problem. We provide a gauge-invariant prescription for the generalized entropy of gravitons in anti-de Sitter space in terms of areas and bulk entanglement entropy, generalizing the quantum extremal surface prescription to accommodate fluctuations in the semiclassical spacetime geometry. This task requires a careful treatment of the area operator on the graviton Hilbert space and the definition of a “quantum extremal gauge” in which the extremal surface is unperturbed. It also requires us to determine the correct vacuum modular Hamiltonian for the graviton field, which we fix by requiring that it doesn’t contain a boundary term in extremal gauge. We check our prescription with an explicit computation of the vacuum-subtracted generalized entropy of states containing a graviton in an AdS-Rindler background. Our results exactly match vacuum-subtracted von Neumann entropies for stress-tensor excited states in holographic conformal field theory with d > 2 dimensions. We also use covariant phase space techniques to give a partial proof of our prescription when the entanglement wedge for the background spacetime has a bifurcate Killing horizon. Along the way, we identify a class of perturbative graviton states that have parametrically larger generalized entropy, in the small G N expansion, than any low-energy excitations of an ordinary quantum field.

1/N expansion↗
DOE OSTI2025

All loop scattering as a counting problem

Abstract This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ’t Hooft expansion. We find novel integral formulas for the amplitudes of this theory, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

1/N Expansion↗
DOE OSTI2025

Thermal bootstrap of matrix quantum mechanics

We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, and determine finite temperature observables that interpolate between available analytic results in the low and high temperature limits respectively. We also obtain bootstrap bounds on thermal phase transition as well as preliminary results in the ungauged two-matrix quantum mechanics.

1/N Expansion↗
DOE OSTI2025

Supersymmetry breaking in SYK and the black hole spectrum

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N = 2 Schwarzian theory in which the U(1) R mode becomes massive.

1/N Expansion↗
DOE OSTI2025

All loop scattering for all multiplicity

We study the recently introduced curve integral formalism that defines a new family of formulas for the scattering amplitudes of the colored scalar trϕ 3 theory. We find that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, n, and the loop order, L, is effectively decoupled in these formulas. We derive the curve integrals at tree-level for all n. We then show that, for higher loop-order, it suffices to study the curve integrals for L-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the tree-level results, we find formulas for the all n amplitudes at L loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all n.

1/N Expansion↗
NASA NTRS1981

Temperature variation of the plasma sheet during substorms

The temperature and density of the plasma in the earth's distant plasma sheet at downstream distances of about 20-25 earth radii, are examined during a high geomagnetic disturbance period. It is shown that the plasma sheet cools when magnetospheric substorm expansion is indicated by the AE index. During cooling, the plasma sheet temperature, T, and the number density, N, are related by T proportional to N to the 2/3 power (adiabatic process) in some instances, while by T proportional to 1/N (isobaric process) in other cases. The total plasma and magnetic pressure decreases when T is proportional to 1/N and increases when T is proportional to 1/N. Observation also indicates that the dawn-dusk component of plasma flow is frequently large and comparable to the sunward-tailward flow component near the central plasma sheet during substorms.

Lui, A. T. Y.↗
NASA NTRS1984

New Short Constraint Length, Rate 1/N Convolutional Codes which Minimize Required E Sub B/n Sub o for Given Bit Error Rate

Instead of using the criterion of maximum free distance, (df) or the maximum (df) with minimizing a few first distance profiles, short constraint length rate 1/N convolution codes were searched using a criterion of minimizing required bit energy-to-noise density ratio, E(b)/N(o), for a given value of desired bit error rate (BER), for the goodness of a code. The considered channel was binary antipodal signaling over additive white Gaussian noise and no quantization at the channel output. For the BER calculations, the transfer function bounding technique was used. Partial searches were performed using some known facts and a very useful idea that "good codes generate good codes.'' That is, for a given constraint length K, good rate 1/(N + 1) codes can be found by extending the code generator matrices of good rate 1/N codes. The code search results are tabulated for 3 or = K or = 7 and 2 or = N or = 8. For many pairs of K and N, the new codes are shown to save 0.1 to 0.4 dB in the required E(b)/N(o) compared to previously reported codes. Additionally, the benefits of coding bandwidth expansion are confirmed with the new codes.

Lee, P. J.↗
DOE OSTI2026

Viability of perturbative expansion for quantum field theories on neurons

Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs) [1]. In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number N using scalar ϕ 4 theory in d Euclidean dimensions as an example. We find that the renormalized O(1/N ) corrections to two-and four-point correlators yield perturbative series which are sensitive to the UV cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.

Sen, Srimoyee [Iowa State University, Ames, IA (Un↗