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Włodzimierz Wójcik

Publications and source records attributed to Włodzimierz Wójcik.

13 recordsLinked to original sources
arXiv2026

Examining the possibility of a thick crust in the compact stellar object HESS J1731-347

A relativistic mean-field model with a crossing term of isovector-scalar and isoscalar mesons, the Cracow crossing terms (CCT) model, has previously been shown to be capable of explaining the light and compact object HESS J1731-347 [11]. Here, the model is supplemented with a correct treatment of the phase transition. Applying the thermodynamically consistent Gibbs conditions shows that a mixed-phase system occurs in the core of the neutron star over a wide range of densities, extending up to the neutron star crust, leading to an intriguing stellar structure with a thick and massive crust.

nucl-th↗
arXiv2026

A nonstandard statistics for strongly correlated systems: Two simple examples

We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, $i.e.$, that of fermions with exclusion of doubly occupancy of quasimomentum states $\{\bf k\}$ with opposite spins ($\uparrow\downarrow$). The second is that of statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_B T/|t|$, where $t<0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ($n\to1$). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.

cond-mat.str-el↗
arXiv2023

Relativistic mean field model for ultra-compact low mass neutron star of HESS J1731-347

The recent observation of the object HESS J1731-347 suggests the existence of a very light and very compact neutron star being a challenge for commonly used equation of state for dense matter. In this work we present a relativistic mean field model enriched with meson crossing terms among isovector and isoscalar mesons. Such interactions particularly dominate the behavior of the symmetry energy and accounts for small size of compact star radius. The proposed model fulfill the recent constraints concerning the symmetry energy slope and state-of-the-art compact stars constraints derived from the NICER measurements of PSR J0030+0451 and PSR J0740+6620 pulsars as well as from the GW170817 event and its associated electromagnetic counterparts AT2017gfo/GRB170817A.

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arXiv2021

The role of the electric Bond number in the stability of pasta phases

The stability of pasta phases in cylindrical and spherical Wigner-Seitz (W-S) cells is examined. The electric Bond number is introduced as the ratio of electric and surface energies. In the case of a charged rod in vacuum, other kinds of instabilities appear in addition to the well known Plateau- Rayleigh mode. For the case of a rod confined in a W-S cell the variety of unstable modes is reduced. It comes from the virial theorem, which bounds the value of the Bond number from above and reduces the role played by electric forces. A similar analysis is done for the spherical W-S cell, where it appears that the inclusion of the virial theorem stabilizes all of the modes.

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arXiv2019

Influence of the interactions of scalar mesons on the behavior of the symmetry energy

Symmetry energy behavior of scalar mesons interactions is analyzed within the framework of the standard relativistic mean field model. Whereas the presence of the $δ$ meson itself makes the symmetry energy stiffer, the crossing term $δ\textrm{-}σ$ allows its slope to decrease to the suggested experimental value. Moreover, such controlling of the symmetry energy does not significantly affect the stiffness of the equation of state and acceptable neutron star masses result. Interestingly, for the most plausible value of the symmetry energy slope, the phase transition occurs in the neutron star core.

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arXiv2018

Shape stability of pasta phases: Lasagna case

The stability of periodically placed slabs occurring in neutron stars (lasagna phase) is examined by exact geometrical methods for the first time. It appears that the slabs are stable against any shape perturbation modes for the whole range of volume fraction occupied by the slab. The calculations are done in the framework of the liquid drop model and obtained results are universal - they do not depend on model parameters like surface tension or charge density. The results shows that the transition to other pasta shapes requires crossing the finite energy barrier

astro-ph.HE↗
arXiv2017

Topological analysis of nuclear pasta phases

In this paper the analysis of the result of numerical simulations of pasta phases using algebraic topology methods is presented. These considerations suggest that some phases can be further split into (sub)phases and therefore should be more refined in numerical simulations. The results presented in the paper can also be used to relate the Euler characteristic from numerical simulations to the geometry of the phases. The Betti numbers are used as they provide finer characterization of the phases. It is also shown that different boundary conditions give different outcomes.

astro-ph.HE↗
arXiv2015

Exact solution of equations for proton localization in neutron star matter

The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner- Seitz approximation of spherically symmetric cell. The analysis of three different nuclear models suggests that the proton localization is likely to take place in the interior of neutron star.

nucl-th↗
arXiv2014

Extended Hubbard model with renormalized Wannier wave functions in the correlated state III: Statistically consistent Gutzwiller approximation and the metallization of atomic solid hydrogen

We extend our previous approach (Eur. Phys. J. B, \textbf{74}, 63(2010)) to modeling correlated electronic states and the metal-insulator transition by applying the so-called \emph{statistically consistent Gutzwiller approximation} (SGA) to carry out self-consistent calculations of the renormalized single-particle Wannier functions in the correlated state. The transition to the Mott-Hubbard insulating state at temperature T=0 is of weak first order even if antiferromagnetism is disregarded. The magnitude of the introduced self-consistent magnetic correlation field is calculated and shown to lead to a small magnetic moment in the magnetically uniform state. Realistic value of the applied magnetic field has a minor influence on the metallic-state characteristics near the Mott-Hubbard lcalization threshold. The whole analysis has been carried out for an extended Hubbard model on a simple cubic (SC) lattice and the evolution of physical properties is analyzed as a function of the lattice parameter for the renormalized 1s-type Wannier functions. Quantum critical scaling of the selected physical properties is analyzed as a function of the lattice constant $R\rightarrow R_c=4.1 a_0$, where $R_c$ is the critical value for metal-insulator transition and $a_0=0.53 Å$ is the Bohr radius. A critical pressure for metallization of solid atomic hydrogen is estimated and is $\sim 10^2 GPa$.

cond-mat.str-el↗
arXiv2009

Extended Hubbard model with renormalized Wannier wave functions in the correlated state II: Quantum critical scaling of the wave function near the Mott-Hubbard transition

We present a model example of a quantum critical behavior of renormalized single-particle Wannier function composed of Slater s-orbitals and represented in an adjustable Gaussian STO-7G basis, which is calculated for cubic lattices in the Gutzwiller correlated state near the metal-insulator transition (MIT). The discussion is carried out within the extended Hubbard model and the method of approach proposed earlier [cf. Eur. Phys. J. B {\bf 66}, 385 (2008)]. The component atomic-wave-function size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice parameter $R$ as $[(R-R_{c})/R_{c}]^{s}$ with $s$ in the interval $[0.9,1.0]$. Such scaling law is interpreted as evidence of a dominant role of the interparticle Coulomb repulsion, which for $R>R_c$ is of intersite character. Relation of the insulator-metal transition lattice-parameter value $R=R_{c}$ to the original {\em Mott criterion} is also obtained. The method feasibility is tested by comparing our results with the exact approach for the Hubbard chain, for which the Mott-Hubbard transition is absent. In view of unique features of our results, an extensive discussion in qualitative terms is also provided.

cond-mat.str-el↗
arXiv2008

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models

The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the parameters of the Hubbard model (the hopping \textit{t} and the magnitude of the intraatomic interaction \textit{U}) are determined explicitly in the correlated state for the electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular planar lattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolution of the electronic properties as a function of interatomic distance $R$ is obtained. The model parameters in most cases do not scale linearly with the lattice spacing and hence, their solution as a function of microscopic parameters reflects only qualitatively the system evolution. Also, the atomic energy changes with $R$ and therefore should be included in the model analysis. The solutions in one dimension (\textit{D} = 1) can be analyzed both rigorously (by making use of the Lieb--Wu solution) and compared with the approximate Gutzwiller treatment. In higher dimensions (\textit{D} = 2, 3) only the latter approach is possible to implement within the scheme. The renormalized single particle wave functions are almost independent of the choice of the scheme selected to diagonalize the Hamiltonian in the Fock space in D=1 case. The method can be extended to other approximation schemes as stressed at the end.

cond-mat.str-el↗
arXiv2007

Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximation, with Adjustable Single-Particle Wave Function for the Hubbard Chain

The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adjustment of the single-particle wave functions in the correlated state (EDABI method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controllable parameter - the interatomic distance.

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