Nonlinearly realized conformal invariance in scale invariant field theories
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
SEARCH · Search NASA
Results for “SCALE INVARIANCE”
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.
Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD
Not Available
Karthik, Nikhil↗
Weyl current, scale-invariant inflation, and Planck scale generation
Scalar fields, $\phi$ i , can be coupled nonminimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including M P =0; (ii) the $\phi$ i have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, K($\phi$ i )=constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale-invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant; (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. Finally, these models are governed by a global Weyl scale symmetry and its conserved current, K μ . At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Binary optical filters for scale invariant pattern recognition
Binary synthetic discriminant function (BSDF) optical filters which are invariant to scale changes in the target object of more than 50 percent are demonstrated in simulation and experiment. Efficient databases of scale invariant BSDF filters can be designed which discriminate between two very similar objects at any view scaled over a factor of 2 or more. The BSDF technique has considerable advantages over other methods for achieving scale invariant object recognition, as it also allows determination of the object's scale. In addition to scale, the technique can be used to design recognition systems invariant to other geometric distortions.
Reid, Max B.↗
Scale-invariant hidden local symmetry, topology change, and dense baryonic matter. II.
Not Available
Paeng, Won-Gi↗
Sea Ice Deformation Is Not Scale Invariant Over Length Scales Greater Than A Kilometer
In March and April 2021, buoys were deployed in the Beaufort Sea, Arctic Ocean, to measure sea-ice horizontal deformation over spatial scales that had not been previously achieved. Geodetic-quality position measurements allowed measurements of strain-rate over lengths from about 200 m to 2 km. Conventional ice-drifters extended spatial coverage up to about 100 km. Past studies find there is multi-fractal behavior for horizontal sea-ice deformation from 10 to 1000 km. Our results demonstrate that such behavior does not hold when including spatial scales below 10 km. We find that sea-ice deformation is not scale in variant between the scale of individual sea-ice floes and aggregates of floes. Therefore, we cannot expect the same physical laws or forcing to describe sea-ice kinematics over these regimes, nor can we assume log-log linear behavior for mean deformation. Using this scaling behavior as a metric to validate models that resolve sea ice floes and their interactions is hence not recommended.
Jennifer K. Hutchings↗
Inflation in a scale-invariant universe
A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale-invariant theory of gravity involving two scalar fields: the spectral indices, the tensor-to-scalar ratio, the level of isocurvature modes, and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale symmetry–broken phase, this theory is well described by a single scalar-field theory. Lastly, ee find the predictions of this theory strongly compatible with current observations.
79 ASTRONOMY AND ASTROPHYSICS↗
An alternative to the Λcdm model: the case of scale invariance
The hypothesis is made that, at large scales where general relativity may be applied, empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor λ of the scale-invariant framework. This relation brings major simplifications in the scale-invariant equations for cosmology, which contain a new term, depending on the derivative of the scale factor, that opposes gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution Ω{sub λ} to the energy density of the universe, satisfying an equation of the form Ω{sub m}+Ω{sub k}+Ω{sub λ}=1. The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters Ω{sub m}<1. Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and Ω{sub m} are performed. The presence of even tiny amounts of matter in the universe tends to kill scale invariance. The point is that for Ω{sub m}=0.3 the effect is not yet completely killed. Models with non-zero density start explosively with a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m–z diagram, and the Ω{sub m} versus Ω{sub λ} plot. Comparisons with observations are also performed for the Hubble constant H{sub 0} versus Ω{sub m}, for the expansion history in the plot H(z)/(z+1) versus redshift z, and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by scale-invariant models, which thus deserve further study.
79 ASTRONOMY AND ASTROPHYSICS↗
No fifth force in a scale invariant universe
We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Observation of Scale Invariance in Two-Dimensional Matter-Wave Townes Solitons
We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons, and a precision test on scale invariance in attractive 2D Boses gases. We induce a shape-controlled modulational instability in an elongated 2D matter-wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities, and observe that the scale-invariant profiles measured at different coupling constants can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies, and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. Here, we confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Time fractals and discrete scale invariance with trapped ions
We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates itself under a rescaling of distance for some scale factor, and a time fractal is a signal that is invariant under the rescaling of time. These features are reminiscent of the Efimov effect, which has been predicted and observed in bound states of three-body systems. We demonstrate that discrete scale invariance in the trapped ion system can be controlled with two independently tunable parameters. We also discuss the extension to n-body states where the discrete scaling symmetry has an exotic heterogeneous structure. Furthermore, the results we present can be realized using currently available technologies developed for trapped ion quantum systems.
74 ATOMIC AND MOLECULAR PHYSICS↗
Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe 5
Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity ( ρ xx ) and the Hall traces ( ρ yx ) of HfTe 5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρ xx and ρ yx show the consistent log B -periodicity with a phase shift. The finding of the log B oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.
magnetoresistance↗
Convergence of variational Monte Carlo simulation and scale-invariant pre-training
We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. Here, we study both the energy minimization phase and the supervised pre-training phase that is commonly used prior to energy minimization. For the energy minimization phase, the standard algorithm is scale-invariant by design, and we provide a proof of convergence for this algorithm without modifications. The pre-training stage typically does not feature such scale-invariance. We propose using a scale-invariant loss for the pretraining phase and demonstrate empirically that it leads to faster pre-training.
97 MATHEMATICS AND COMPUTING↗
Scale-invariant Cosmology and CMB Temperatures as a Function of Redshifts
Cosmological models assuming the scale invariance of the macroscopic empty space show an accelerated expansion, without calling for some unknown particles. Several comparisons between models and observations (tests on distances, m−z diagram, Ω{sub Λ} versus Ω{sub m} plot, age versus H {sub 0}, H(z) versus z, transition braking-acceleration) have indicated an impressive agreement. We pursue the tests with the CMB temperatures T{sub CMB} as a function of redshifts z. CO molecules in DLA systems provide the most accurate excitation temperatures T{sub exc} up to z≈2.7. Such data need corrections for local effects like particle collisions, optical depths, UV radiation, etc., We estimate these corrections as a function of the (CO/H{sub 2}) ratios from far-UV observations of CO molecules in the Galaxy. The results show that it is not sufficient to apply theoretical collisional corrections to get the proper values of T{sub CMB} versus z. Thus, the agreement often found with the standard model may be questioned. The T{sub CMB}(z) relation needs further careful attention and the same for the scale-invariant cosmology in view of its positive tests.
79 ASTRONOMY AND ASTROPHYSICS↗
Scale-invariant density perturbations, anisotropy of the cosmic microwave background, and large-scale peculiar velocity field
The large-scale peculiar velocity field and the large- and intermediate-angular scale anisotropy of the cosmic microwave background are studied in inflationary cosmological models of critical density and containing primordial scale-invariant adiabatic density perturbations. Comparison with recent observations by de Vaucouleurs and Peters Provides tentative support for a cold dark matter scenario in which the dark matter is not appreciably less clustered than the luminous galaxy distribution.
Vittorio, N.↗
Void probability as a function of the void's shape and scale-invariant models
The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.
Elizalde, E.↗
Void probability as a function of the void's shape and scale-invariant models
The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.
Elizalde, E.↗
Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal
Highlights: • We look at the role played by generic scale invariance (GSI) in the phase transition between a U(1) spin liquid and a Fermi liquid. • We identify dangerously irrelevant operators in the renormalization group transformation, involved with the GSI. • We highlight novel mean-field dynamics of this Mott quantum criticality, resulting from the GSI. We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.
36 MATERIALS SCIENCE↗