arXiv subjects

I. G. Marian

Publications and source records attributed to I. G. Marian.

11 recordsLinked to original sources

arXiv2024

Perturbative versus Non-Perturbative Renormalization

Approximated functional renormalization group (FRG) equations lead to regulator-dependent $β$-functions, in analogy to the scheme-dependence of the perturbative renormalization group (pRG) approach. A scheme transformation redefines the couplings to relate the $β$-functions of the FRG method with an arbitrary regulator function to the pRG ones obtained in a given scheme. Here, we consider a periodic sine-Gordon scalar field theory in $d=2$ dimensions and show that the relation of the FRG and pRG approaches is intricate. Although, both the FRG and the pRG methods are known to be sufficient to obtain the critical frequency $β_c^2 =8π$ of the model independently of the choice of the regulator and the renormalization scheme, we show that one has to go beyond the standard pRG method (e.g., using an auxiliary mass term) or the Coulomb-gas representation in order to obtain the $β$-function of the wave function renormalization. This aspect makes the scheme transformation non-trivial. Comparing flow equations of the two-dimensional sine-Gordon theory without any scheme-transformation, i.e., redefinition of couplings, we find that the auxiliary mass pRG $β$-functions of the minimal subtraction scheme can be recovered within the FRG approach with the choice of the power-law regulator with $b=2$, therefore constitutes a preferred choice for the comparison of FRG and pRG flows.

hep-th↗

arXiv2022

Renormalisation of non-differentiable potentials

Non-differentiable potentials, such as the V-shaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouville-type interaction, i.e., an exponential of the V-shaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic self-interaction of an N-component scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near non-analytic points and discuss in this context the role of quantum fluctuations. We then study the renormalisation of such potentials, focusing on the Exact Wilsonian Renormalisation approach, and we discuss how quantum fluctuations smoothen the bare singularity of the potential. Applications of these results to the non-differentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sine-Gordon model in (1+1) dimensions are presented.

hep-th↗

arXiv2022

Vacuum Energy and Renormalization of the Field-Independent Term

Due to its construction, the nonperturbative renormalization group (RG) evolution of the constant, field-independent term (which is constant with respect to field variations but depends on the RG scale $k$) requires special care within the Functional Renormalization Group (FRG) approach. In several instances, the constant term of the potential has no physical meaning. However, there are special cases where it receives important applications. In low dimensions ($d=1$), in a quantum mechanical model, this term is associated with the ground-state energy of the anharmonic oscillator. In higher dimensions ($d=4$), it is identical to the $Λ$ term of the Einstein equations and it plays a role in cosmic inflation. Thus, in statistical field theory, in flat space, the constant term could be associated with the free energy, while in curved space, it could be naturally associated with the cosmological constant. It is known that one has to use a subtraction method for the quantum anharmonic oscillator in $d=1$ to remove the $k^2$ term that appears in the RG flow in its high-energy (UV) limit in order to recover the correct results for the ground-state energy. The subtraction is needed because the Gaussian fixed point is missing in the RG flow once the constant term is included. However, if the Gaussian fixed point is there, no further subtraction is required. Here, we propose a subtraction method for $k^4$ and $k^2$ terms of the UV scaling of the RG equations for $d=4$ dimensions if the Gaussian fixed point is missing in the RG flow with the constant term. Finally, comments on the application of our results to cosmological models are provided.

hep-th↗

arXiv2022

Polarised superlocalization in magnetic nanoparticle hyperthermia

Magnetic hyperthermia is an adjuvant therapy for cancer where injected magnetic nanoparticles are used to transfer energy from the time-dependent applied magnetic field into the surrounding medium. Its main importance is to be able to increase the temperature of the human body locally. This localization can be further increased by using a combination of static and alternating external magnetic fields. For example, if the static field is inhomogeneous and the alternating field is oscillating then the energy transfer and consequently, the heat generation is non-vanishing only where the gradient field is zero which results in superlocalization. Our goal here is to study theoretically and experimentally whether the perpendicular or parallel combination of static and oscillating fields produce a better superlocalization. A considerable polarisation effect in superlocalization for small frequencies and large field strengths which are of great importance in practice is found.

cond-mat.soft↗

arXiv2021

Theory of superlocalized magnetic nanoparticle hyperthermia: rotating versus oscillating fields

The main idea of magnetic hyperthermia is to increase locally the temperature of the human body by means of injected superparamagnetic nanoparticles. They absorb energy from a time-dependent external magnetic field and transfer it into their environment. In the so-called superlocalization, the combination of an applied oscillating and a static magnetic field gradient provides even more focused heating since for large enough static field the dissipation is considerably reduced. Similar effect was found in the deterministic study of the rotating field combined with a static field gradient. Here we study theoretically the influence of thermal effects on superlocalization and on heating efficiency. We demonstrate that when time-dependent steady state motions of the magnetisation vector are present in the zero temperature limit, then deterministic and stochastic results are very similar to each other. We also show that when steady state motions are absent, the superlocalization is severely reduced by thermal effects. Our most important finding is that in the low frequency range ($ω\to 0$) suitable for hyperthermia, the oscillating applied field is shown to result in two times larger intrinsic loss power and specific absorption rate then the rotating one with identical superlocalization ability which has importance in technical realisation.

cond-mat.soft↗

arXiv2020

Renormalization-Group Running Induced Cosmic Inflation

As a contribution to a viable candidate for a standard model of cosmology, we here show that pre-inflationary quantum fluctuations can provide a scenario for the long-sought initial conditions for the inflaton field. Our proposal is based on the assumption that at very high energies (higher than the energy scale of inflation) the vacuum-expectation value (VeV) of the field is trapped in a false vacuum and then, due to renormalization-group (RG) running, the potential starts to flatten out toward low energy, eventually tending to a convex one which allows the field to roll down to the true vacuum. We argue that the proposed mechanism should apply to large classes of inflationary potentials with multiple concave regions. Our findings favor a particle physics origin of chaotic, large-field inflationary models as we eliminate the need for large field fluctuations at the GUT scale. In our analysis, we provide a specific example of such an inflationary potential, whose parameters can be tuned to reproduce the existing cosmological data with good accuracy.

astro-ph.CO↗

arXiv2019

Pseudo-Periodic Natural Higgs Inflation

Inflationary cosmology represents a well-studied framework to describe the expansion of space in the early universe, as it explains the origin of the large-scale structure of the cosmos and the isotropy of the cosmic microwave background radiation. The recent detection of the Higgs boson renewed research activities based on the assumption that the inflaton could be identified with the Higgs field. At the same time, the question whether the inflationary potential can be be extended to the electroweak scale and whether it should be necessarily chosen ad hoc in order to be physically acceptable are at the center of an intense debate. Here, we perform the slow-roll analysis of the so-called Massive Natural Inflation (MNI) model which has three adjustable parameters, the explicit mass term, a Fourier amplitude u, and a frequency parameter $β$, in addition to a constant term of the potential. This theory has the advantage to present a structure of infinite non-degenerate minima and is amenable to an easy integration of high-energy modes. We show that, using PLANCK data, one can fix, in the large $β$-region, the parameters of the model in a unique way. We also demonstrate that the value for the parameters chosen at the cosmological scale does not influence the results at the electroweak scale. We argue that other models can have similar properties both at cosmological and electroweak scales, but with the MNI model one can complete the theory towards low energies and easily perform the integration of modes up to the electroweak scale, producing the correct order-of-magnitude for the Higgs mass.

astro-ph.CO↗

arXiv2018

Efficiency of magnetic hyperthermia in the presence of rotating and static fields

Single-domain ferromagnetic nanoparticle systems can be used to transfer energy from a time-dependent magnetic field into their environment. This local heat generation, i.e., magnetic hyperthermia, receives applications in cancer therapy which requires the enhancement of the energy loss. A possible way to improve the efficiency is to chose a proper type of applied field, e.g., a rotating instead of an oscillating one. The latter case is very well studied and there is an increasing interest in the literature to investigate the former although it is still unclear under which circumstances the rotating applied field can be more favourable than the oscillating one. The goal of this work is to incorporate the presence of a static field and to perform a systematic study of the non-linear dynamics of the magnetisation in the framework of the deterministic Landau-Lifshitz-Gilbert equation in order to calculate energy losses. Two cases are considered: the static field is either assumed to be perpendicular to the plane of rotation or situated in the plane of rotation. In the latter case a significant increase in the energy loss/cycle is observed if the magnitudes of the static and the rotating fields have a certain ratio (e.g. it should be one for isotropic nanoparticles). It can be used to "super-localise" the heat transfer: in case of an inhomogeneous applied static field, tissues are heated up only where the magnitudes of the static and rotating fields reach the required ratio.

cond-mat.soft↗

arXiv2014

Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking

We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.

hep-th↗

arXiv2014

The Numerically Optimized Regulator and the Functional Renormalization Group

We aim to optimize the functional form of the compactly supported smooth (CSS) regulator within the functional renormalization group (RG), in the framework of bosonized two-dimensional Quantum Electrodynamics (QED_2) and of the three-dimensional O(N=1) scalar field theory in the local potential approximation (LPA). The principle of minimal sensitivity (PMS) is used for the optimization of the CSS regulator, recovering all the major types of regulators in appropriate limits. Within the investigated class of functional forms, a thorough investigation of the CSS regulator, optimized with two different normalizations within the PMS method, confirms that the functional form of a regulator first proposed by Litim is optimal within the LPA. However, Litim's exact form leads to a kink in the regulator function. A form of the CSS regulator, numerically close to Litim's limit while maintaining infinite differentiability, remains compatible with the gradient expansion to all orders. A smooth analytic behaviour of the regulator is ensured by a small, but finite value of the exponential fall-off parameter in the CSS regulator. Consequently, a compactly supported regulator, in a parameter regime close to Litim's optimized form, but regularized with an exponential factor, appears to have favorable properties and could be used to address the scheme dependence of the functional renormalization group, at least within the the approximations employed in the studies reported here.

hep-th↗

arXiv2014

Spontaneous symmetry breaking and optimization of functional renormalization group

The requirement for the absence of spontaneous symmetry breaking in the d=1 dimension has been used to optimize the regulator dependence of functional renormalization group equations in the framework of the sine-Gordon scalar field theory. Results obtained by the optimization of this kind were compared to those of the Litim-Pawlowski and the principle of minimal sensitivity optimization scenarios. The optimal parameters of the compactly supported smooth (CSS) regulator, which recovers all major types of regulators in appropriate limits, have been determined beyond the local potential approximation, and the Litim limit of the CSS was found to be the optimal choice.

hep-th↗