We show that the well-known linear Langevin equation, modeling Brownian motion and leading to a Gaussian stationary distribution of corresponding Fokker-Planck is changed by smallest multiplicative noise. This leads power-law tail for sufficiently large momenta. At finite ratio correlation strength additive noises energy becomes exactly Tsallis distribution.

Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity variability of time data. Building on our previous work linear law-based transformation (LLT) - which improved accuracy by transforming feature space based key data patterns we introduce adaptive (ALT). ALT enhances LLT incorporating variable-length shifted windows, enabling it to capture...

The functional equation governing the renormalization flow of fermionic field theories is investigated in $$d$$ dimensions without introducing auxiliary Bose fields on example Gross–Neveu and Nambu–Jona-Lasinio model. UV-safe fixed points eigenvectors group equations linearized around them are found local potential approximation. results compared carefully with those obtained partial bosonization. do not receive any correction next-to-leading order approximation gradient expansion effective action.

A hierarchy of effective three-dimensional theories finite temperature electroweak matter is studied. First an integration over nonstatic modes leads to theory containing a gauge field ${A}_{i}^{a}$ adjoint Higgs ${A}_{0}^{a}$ and the fundamental ${\ensuremath{\varphi}}_{a}$. We carry out in one-loop approximation, study renormalization effects, estimate quantitatively those terms action which are suppressed by inverse powers temperature. Second, because existence well-separated thermal mass...

We explore formal similarities and mathematical transformation formulas between general trace-form entropies the Gini index, originally used in quantifying income wealth inequalities. utilize notion of gintropy introduced our earlier works as a certain property Lorenz curve drawn map tail-integrated cumulative population fractions. In particular, we rediscover Tsallis’ q-entropy formula related to Pareto distribution. As novel result, express traditional entropy terms reconstruct further...

The second functional derivative of the effective potential pure fermionic field theories is rewritten in a factorized form which facilitates evaluation renormalisation flow rate action Wetterich equation. It applied to Local Potential Approximation cases, when depends on scalar composites built from fermions. procedure demonstrated explicitly example $N_f$-flavor Gross-Neveu model and one-flavor chiral Nambu--Jona-Lasinio model.

Functional renormalization group (FRG) equations are constructed for a simple Yukawa-model with discrete chiral symmetry, including also the effect of nonzero composite fermion background beyond conventional scalar condensate. The evolution effective potential model, generically depending on two invariants, is explored help power series expansions. Systematic investigation class irrelevant operators lower (stability) bound allows non-perturbative extension maximal cutoff value consistent any...

Lattice results show no standard model (SM) electroweak phase transition (EWPT) for Higgs masses approximately 72 GeV, which is below the present experimental limit. Perturbation theory and 3-dimensional simulations indicate an EWPT in minimal supersymmetric SM (MSSM) that strong enough baryogenesis up to m(h) 105 GeV. In this Letter we of our large scale 4-dimensional MSSM simulations. We carried out infinite volume continuum limits found a whose strength agrees well with perturbation...

The lower bound of the shear viscosity to entropy density ratio is examined using an exact representation through states. Under certain assumptions it can be shown that not universal; its value determined by density. Some examples physical systems are discussed in paper where one expect violation conformal $1/4\ensuremath{\pi}$ value.

In this paper we provide a physical picture for the QCD phase transition in terms of qualitative changes spectral functions. Our approach takes into account crossover nature and counts observed strong correlation seen higher order susceptibilities. We demonstrate that hadron resonance gas, which alone describes thermodynamics at temperatures $T<T_c$, will appreciably contribute to total pressure until $T\leq 3T_c$. intermediate regime matter consists strongly correlated excitations,...

We studied different levels of resummations the exactly solvable Bloch-Nordsieck model in order to be able compare approximations with an exact result. one-loop perturbation theory, two-particle-irreducible resummation and Schwinger-Dyson equations truncated a way maintain Ward identities. At all we carefully performed renormalization. found that although does not exhibit infrared sensitivity at mass shell, as theory does, it is still far from solution. The method renormalized equations,...

Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original "microscopic" interacting fermions based on spectral decomposition 2-to-2 scattering amplitude. Functional renormalisation group equations derived exploiting relations expressing equivalence. The effect truncating is investigated quantitatively example non-relativistic two oppositely charged fermi particles.

Resummation, i.e. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized appropriate way. In this paper two methods presented for resummation counterterms: one is a direct method where necessary constructed order by order; other general one, based on renormalization group arguments. Using ${\ensuremath{\Phi}}^{4}$ model, we demonstrate hand that, mass-independent schemes, mass be performed gap equations renormalized...

We point out that in a simple model with multiplicative noise non-Boltzmann–Gibbs distributions power-law tail arise as stationary solutions. compare it to hadronic transverse momentum at RHIC energies and consider average properties of non-conventional quark matter Tsallis distribution the instant hadronization.

We study the renormalization of O(N) model using auxiliary field formalism (Hubbard-Stratonovich transformation) in $1/N$ expansion at finite temperature. provide general strategy for arbitrary order and make a calculation up to next-to-leading order. show that is possible any values condensates, prove temperature independence counterterms, determine cutoff dependence first nontrivial counterterm parts.

In this paper we study the question of effective field assignment to measured or nonperturbatively calculated spectral functions. The straightforward procedure is approximate it by a sum independent Breit-Wigner resonances, and assign an each these resonances. problem with idea that introduces new conserved quantities in free model (the particle numbers), therefore changes symmetry system. We avoid inconsistency representing quantum channel single field, no matter how complicated function...

In this work we provide a numerical method to obtain the Bloch-Nordsieck spectral function at finite temperature in framework of 2PI approximation. We find that results nicely agree with exact one, provided perform coupling constant matching. paper present resulting running constant. This result may apply for behavior QED, too.

A practical method is suggested for performing renormalized 2 particle irreducible (2PI) resummation at finite temperature using specific renormalization schemes. I examine the consistency of such schemes in paper. Advantages proposed are that there no need to solve Bethe-Salpeter equations 2PI resummation, and explicit diagrammatic reducible graphs. The used perform a two-loop ${\ensuremath{\Phi}}^{4}$ model.

In this paper we determine the exact fermionic spectral function of Bloch-Nordsieck model at finite temperature. Analytic results are presented for some special parameters, other values have numerical results. The is and normalizable any nonzero temperature values. real time dependence retarded Green's power-like small times exhibits exponential damping large times. Treating as an infrared regulator, can also give a safe interpretation zero result.

Shear viscosity of the classical ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory is measured using microcanonical simulation. To calculate Kubo formula, we measure energy-momentum tensor correlation function and apply Green-Kubo relation. Given that this a theory, results depend on cutoff, which should be chosen in range temperature. Comparison with experimentally accessible systems also performed.

The scalar mass is determined in the simplest cut-off regularized Yukawa-model whole range of stability potential. Two versions Functional Renormalisation Group (FRG) equations are solved Local Potential Approximation (LPA), where also possible existence a composite fermionic background taken into account. close agreement results with previous studies taking account exclusively effect condensate, supports rather small systematic truncation error FRG due to omission higher dimensional operators.

The goal of this paper is to determine the laws observed trajectories assuming that there a mechanical system in background and using these continue motion plausible way. are represented by neural networks with limited number parameters. training follows Extreme Learning Machine idea. We for different levels embedding, thus we can represent not only equation but also symmetries kinds. In recursive numerical evolution system, require fulfillment all laws, within determined precision. way,...