Hubble-induced phase transitions on the lattice with applications to Ricci reheating

Using 3+1 classical lattice simulations, we follow the symmetry breaking pattern and subsequent non-linear evolution of a spectator field non-minimally coupled to gravity when the post-inflationary dynamics is given in terms of a stiff equation-of-state parameter. We find that the gradient energy density immediately after the transition represents a non-negligible fraction of the total energy budget, steadily growing to equal the kinetic counterpart. This behaviour is reflected on the evolution of the associated equation-of-state parameter, which approaches a universal value 1/3, independently of the shape of non-linear interactions. Combined with kination, this observation allows for the generic onset of radiation domination for arbitrary self-interacting potentials, significantly extending previous results in the literature. The produced spectrum at that time is, however, non-thermal, precluding the naive extraction of thermodynamical quantities like temperature. Potential identifications of the spectator field with the Standard Model Higgs are also discussed.

Axion fragmentation on the lattice

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.

Fuzzy Transforms for Hesitant, Soft or Intuitionistic Fuzzy Sets

Classical F-transform for lattice-valued fuzzy sets can be defined using monadic relation in Zadeh’s monad or, equivalently, as a special semimodule homomorphism. In this paper, we use an analogical approach and by choosing suitable monads and semimodule homomorphisms, we define F-transform for hesitant, intuitionistic or fuzzy soft sets. We prove that these F-transforms naturally extend classical lattice-valued F-transform for lattice-valued fuzzy sets.

Proper static potential in classical lattice gauge theory at finite T

We compute the proper real-time interaction potential between a static quark and antiquark in classical lattice gauge theory at finite temperature. Our central result is the determination of the screened real-part of this potential, and we reconfirm the presence of an imaginary part. The real part is intimately related to the back-reaction of the static sources onto the gauge fields, incorporated via Gauss’s law. Differences in the treatment of static sources in quantum and classical lattice gauge theory are discussed.

Vibrational Spectra of Zeolite Y as a Function of Ion Exchange

Zeolite Y is one of the earliest known and most widely used synthetic zeolites. Many experimental investigations verify the valuable ion exchange capability of this zeolite. In this study, we assessed the effects of ion exchange on its vibrational spectra. We applied classical lattice dynamics methods for IR and Raman intensity calculations. Computed spectra of optimized zeolite Y structures with different cations were compared with experimental data. The spectra obtained in this study are in agreement with previous experimental and computational studies on zeolites from the faujasite group.

A Survey of Solving SVP Algorithms and Recent Strategies for Solving the SVP Challenge

Recently, lattice-based cryptography has received attention as a candidate of post-quantum cryptography (PQC). The essential security of lattice-based cryptography is based on the hardness of classical lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). A number of algorithms have been proposed for solving SVP exactly or approximately, and most of them are useful also for solving CVP. In this paper, we give a survey of typical algorithms for solving SVP from a mathematical point of view. We also present recent strategies for solving the Darmstadt SVP challenge in dimensions higher than 150.