scholarly journals Axion fragmentation on the lattice

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Enrico Morgante ◽  
Wolfram Ratzinger ◽  
Ryosuke Sato ◽  
Ben A. Stefanek
Keyword(s):  
Energy Dissipation ◽  
Periodic Potential ◽  
Zero Mode ◽  
Stopping Time ◽  
Linear Analysis ◽  
Classical Lattice ◽  
Lattice Simulation ◽  
Field Evolution ◽  
Axion Field

Abstract We analyze the phenomenon of axion fragmentation when an axion field rolls over many oscillations of a periodic potential. This is particularly relevant for the case of relaxion, in which fragmentation provides the necessary energy dissipation to stop the field evolution. We compare the results of a linear analysis with the ones obtained from a classical lattice simulation, finding an agreement in the stopping time of the zero mode between the two within an $$ \mathcal{O}(1) $$ O 1 difference. We finally speculate on the generation of bubbles with different VEVs of the axion field, and discuss their cosmological consequences.

scholarly journals New application of the Killing vector field formalism: modified periodic potential and two-level profiles of the axionic dark matter distribution

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Alexander B. Balakin ◽  
Dmitry E. Groshev
Keyword(s):  
Dark Matter ◽  
Vector Field ◽  
Electric Fields ◽  
Vector Fields ◽  
Periodic Potential ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Covariant Model ◽  
Axion Field ◽  
Field Formalism

Abstract We consider the structure of halos of the axionic dark matter, which surround massive relativistic objects with static spherically symmetric gravitational field and monopole-type magneto-electric fields. We work with the model of pseudoscalar field with the extended periodic potential, which depends on additional arguments proportional to the moduli of the Killing vectors; in our approach they play the roles of model guiding functions. The covariant model of the axion field with this modified potential is equipped with the extended formalism of the Killing vector fields, which is established in analogy with the formalism of the Einstein–Aether theory, based on the introduction of a unit timelike dynamic vector field. We study the equilibrium state of the axion field, for which the extended potential and its derivative vanish, and illustrate the established formalism by the analysis of two-level axionic dark matter profiles, for which the stage delimiters relate to the critical values of the modulus of the timelike Killing vector field.

Analysis of Bloch’s Method in Structures With Energy Dissipation

2010 ◽  
Author(s):  
Farhad Farzbod ◽  
Michael J. Leamy
Keyword(s):  
Energy Dissipation ◽  
Vibration Analysis ◽  
General Framework ◽  
Periodic Potential ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Periodic Systems ◽  
Crystalline Solid ◽  
Structural Damping ◽  
Electron Wave

Bloch analysis was originally developed to solve Schro¨dinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schro¨dinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straight-forward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

Analysis of Bloch’s Method in Structures with Energy Dissipation

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Farhad Farzbod ◽  
Michael J. Leamy
Keyword(s):  
Energy Dissipation ◽  
Periodic Potential ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Periodic Systems ◽  
Crystalline Solid ◽  
Structural Damping ◽  
Electron Wave ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Bloch analysis was originally developed to solve Schrödinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schrödinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straightforward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

scholarly journals Is the Axionic Dark Matter an Equilibrium System?

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 192
Author(s):  
Alexander B. Balakin ◽  
Amir F. Shakirzyanov
Keyword(s):  
Dark Matter ◽  
Equilibrium State ◽  
Periodic Potential ◽  
Basic Function ◽  
Equilibrium System ◽  
Expansion Scalar ◽  
Axion Field ◽  
Matter Model ◽  
Isotropic Cosmological Model ◽  
Dark Matter Model

We consider an axionic dark matter model with a modified periodic potential for the pseudoscalar field in the framework of the axionic extension of the Einstein-aether theory. The modified potential is assumed to be equipped by the guiding function, which depends on the expansion scalar constructed as the trace of the covariant derivative of the aether velocity four-vector. The equilibrium state of the axion field is defined as the state, for which the modified potential itself and its first derivative with respect to the pseudoscalar field are equal to zero. We apply the developed formalism to the homogeneous isotropic cosmological model, and find the basic function, which describes the equilibrium state of the axionic dark matter in the expanding Universe.

scholarly journals Mass transport in Fokker–Planck equations with tilted periodic potential

2019 ◽  
Vol 31 (4) ◽  
pp. 709-736
Author(s):  
MICHAEL HERRMANN ◽  
BARBARA NIETHAMMER
Keyword(s):  
Energy Dissipation ◽  
Periodic Potential ◽  
Temporal Dynamics ◽  
Approximation Error ◽  
Gradient Structure ◽  
Subcritical Regime ◽  
Spatio Temporal ◽  
Fokker Planck Equations ◽  
Double Well Potential ◽  
Fokker Planck

We consider Fokker–Planck equations with tilted periodic potential in the subcritical regime and characterise the spatio-temporal dynamics of the partial masses in the limit of vanishing diffusion. Our convergence proof relies on suitably defined substitute masses and bounds the approximation error using the energy-dissipation relation of the underlying Wasserstein gradient structure. In the appendix, we also discuss the case of an asymmetric double-well potential and derive the corresponding limit dynamics in an elementary way.

scholarly journals Interaction of the axionic dark matter, dynamic aether, spinor and gravity fields as an origin of oscillations of the fermion effective mass

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Alexander B. Balakin ◽  
Anna O. Efremova
Keyword(s):  
Dark Matter ◽  
Effective Mass ◽  
Vector Fields ◽  
Periodic Potential ◽  
Total System ◽  
Field Equations ◽  
Timelike Vector ◽  
Axion Field ◽  
Gravity Fields ◽  
Guiding Function

AbstractIn the framework of the Einstein–Dirac-axion-aether theory we consider the quartet of self-interacting cosmic fields, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark mater, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The key, associated with the mechanism of self-interaction, is installed into the modified periodic potential of the pseudoscalar (axion) field constructed on the base of a guiding function, which depends on one invariant, one pseudo-invariant and two cross-invariants containing the spinor and vector fields. The total system of the field equations related to the isotropic homogeneous cosmological model is solved; we have found the exact solutions for the guiding function for three cases: nonzero, vanishing and critical values of the cosmological constant. Based on these solutions, we obtained the expressions for the effective mass of spinor particles, interacting with the axionic dark matter and dynamic aether. This effective mass is shown to bear imprints of the cosmological epoch and of the state of the cosmic dark fluid in that epoch.

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

Sign in / Sign up

Export Citation Format

Share Document