Zero Density Research Articles

Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego , ; G. M. Buendía , ]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick , ]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point. Published by the American Physical Society 2024

Reduction for one-loop tensor Feynman integrals in the relativistic quantum field theories at finite temperature and/or finite density

The Passarino-Veltman reduction is a systematic procedure based on the Lorentz covariance, which can efficiently reduce the one-loop tensor Feynman integrals in the relativistic quantum field theories (QFTs) at zero temperature and zero density. However, the Lorentz covariance is explicitly broken when either of the temperature and density is finite, due to a rest reference frame of the many-body system in which the temperature and density are measured, rendering the Passarino-Veltman reduction not applicable anymore to reduce the one-loop tensor Feynman integrals therein. In this paper, we report a Passarino-Veltman reduction which can efficiently simplify the one-loop tensor Feynman integrals in the relativistic QFTs at finite temperature and/or finite density. The Passarino-Veltman reduction can analyze the one-loop tensor Feynman integrals in a wide range of physical systems described by the relativistic QFTs at finite temperature and/or finite density, such as quark-gluon plasma in nuclear physics. Published by the American Physical Society 2024

On some local properties of sequences of big Galois representations

In this article, we prove that for a convergent sequence of residually absolutely irreducible representations of the absolute Galois group of a number field F with coefficients in a domain, which admits a finite monomorphism from a power series ring over a p-adic integer ring, the set of places of F where some of the representations ramifies has density zero. Using this, we extend a result of Das–Rajan to such convergent sequences. We also establish a strong multiplicity one theorem for big Galois representations.

A Density Theorem for Dedekind Zeta Functions

We apply a recent general zero density theorem of us (valid for a large class of complex functions) to improve earlier density theorems of Heath-Brown and Paul–Sankaranarayanan for Dedekind zeta functions attached to a number field 𝐾 of degree 𝑛 with 𝑛 > 2.

Distribution in homology classes and discrete fractal dimension

In this note, we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.

Zeros of higher derivatives of Riemann zeta function

In this article, we extend the result of Conrey [4, Theorem 2] to shorter intervals for higher-order derivatives of the zeta function. That is we study the mean value of the product of two finite order derivatives of the zeta function multiplied by a mollifier in short intervals. In this process, we obtain better mollifier length in some short intervals compared to the length of mollifier implied by Conrey's result. These finer studies allow us to refine the error term of some classical results of Levinson and Montgomery [13], Ki and Lee [11] on zero density estimates of ζ(k). Further, we showed that almost all non-trivial zeros of Matsumoto-Tanigawa's ηk-function cluster near the critical line.

A two-capillary viscometer for temperatures up to 473 K and pressures up to 100 MPa—operation and verification at low pressure

In this paper, we described the design and construction of a new two-capillary viscometer with several novel technical solutions for viscosity and density measurements. Our design, which is based on the low-pressure principle, featured numerous improvements in hardware and procedure that allowed the greatly extended range of pressure. The new design adopted a (2 × 2) capillary configuration, utilizing different combinations of four capillaries to enable viscosity measurements with a wide range of flow rates, temperatures, and pressures. The design temperature range is 213 K–473 K, and the pressure range is up to 100 MPa. The viscometer was specifically designed for measuring the viscosity of pure CO2 and CO2-rich mixtures, addressing the scarcity of data in conditions relevant to carbon capture, transport, and storage. Our facility is capable of viscosity measurements in different thermodynamic states; gaseous, liquid, supercritical, and critical regions. A commercial densimeter is integrated to measure density under the same temperatures and pressures. We aimed for a total uncertainty target of better than 0.03%. The performance of the viscometer was validated by measurements with pure CO2 at 298.15 K and zero density. We observed a deviation of less than 0.03% between the reference viscosity of CO2 of this work and accurately calculated data using ab initio quantum mechanics with a standard uncertainty of 0.2%. Our primary focus in this paper was to provide a detailed description of the design and construction of the apparatus, emphasizing improvements and introducing new solutions to other research groups in constructing similar instruments suitable for low- and high-pressure viscosity measurements with high accuracy.

A weighted one-level density of the non-trivial zeros of the Riemann zeta-function

A weighted one-level density of the non-trivial zeros of the Riemann zeta-function

Log-free zero density estimates for automorphic L-functions

We prove a log-free zero density estimate for automorphic L-functions defined over a number field k. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree n over k (for any n) that an effective Chebotarev density theorem and a bound on ℓ-torsion in class groups hold for almost all fields in the family.

Zeros of Rankin–Selberg L-functions in families

Let $\mathfrak {F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm {GL}_n$ with unitary central character over a number field $F$ . We prove the first unconditional zero density estimate for the set $\mathcal {S}=\{L(s,\pi \times \pi ')\colon \pi \in \mathfrak {F}_n\}$ of Rankin–Selberg $L$ -functions, where $\pi '\in \mathfrak {F}_{n'}$ is fixed. We use this density estimate to establish: (i) a hybrid-aspect subconvexity bound at $s=\frac {1}{2}$ for almost all $L(s,\pi \times \pi ')\in \mathcal {S}$ ; (ii) a strong on-average form of effective multiplicity one for almost all $\pi \in \mathfrak {F}_n$ ; and (iii) a positive level of distribution for $L(s,\pi \times \widetilde {\pi })$ , in the sense of Bombieri–Vinogradov, for each $\pi \in \mathfrak {F}_n$ .

The degree of commutativity of wreath products with infinite cyclic top group

The degree of commutativity of a finite group is the probability that two uniformly and randomly chosen elements commute. This notion extends naturally to finitely generated groups G: the degree of commutativity dcS(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{dc}\\,}}_S(G)$$\\end{document}, with respect to a given finite generating set S, results from considering the fractions of commuting pairs of elements in increasing balls around 1G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1_G$$\\end{document} in the Cayley graph . We focus on restricted wreath products of the form G=H≀⟨t⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G = H \\hspace{1.111pt}{\\wr }\\hspace{1.111pt}\\langle \\hspace{1.111pt}t \\rangle $$\\end{document}, where H≠1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \ e 1$$\\end{document} is finitely generated and the top group ⟨t⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\hspace{1.111pt}t \\rangle $$\\end{document} is infinite cyclic. In accordance with a more general conjecture, we show that dcS(G)=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{dc}\\,}}_S(G) = 0$$\\end{document} for such groups G, regardless of the choice of S. This extends results of Cox who considered lamplighter groups with respect to certain kinds of generating sets. We also derive a generalisation of Cox’s main auxiliary result: in ‘reasonably large’ homomorphic images of wreath products G as above, the image of the base group has density zero, with respect to certain types of generating sets.

Generalized skyrmion crystals with applications to neutron stars

In this article we study properties of isospin asymmetric nuclear matter in the generalized L0246-Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found skyrmion multiwall crystal. We obtain, for the first time, an equation of state from the Skyrme model which interpolates between infinite isospin asymmetric nuclear matter and finite isospin symmetric atomic nuclei. This enables us to describe neutron stars with crusts within the Skyrme framework. Furthermore, we observe that the symmetry energy tends to a constant value at zero density, which can be identified with the asymmetry coefficient in the semiempirical mass formula for atomic nuclei. The symmetry energy also reveals a cusp in its structure below the nuclear saturation point n0 at n*∼3n0/4. This cusp density point n* can be interpreted as the nuclear density whereby the infinite crystalline multiwall configuration undergoes a phase transition to a finite isolated multiwall configuration. Both of these observations are observed to be generic features of skyrmion crystals that tend asymptotically to somewhat isolated skyrmion configurations in the zero density limit. We find that the resulting neutron stars from our study agree quite well with recent NICER/LIGO observational data. Published by the American Physical Society 2024

One-level density of zeros of Dirichlet L-functions over function fields

TextWe compute the one-level density of zeros of order ℓ Dirichlet L-functions over function fields Fq[t] for ℓ=3,4 in the Kummer setting (q≡1(modℓ)) and for ℓ=3,4,6 in the non-Kummer setting (q≢1(modℓ)). In each case, we obtain a main term predicted by Random Matrix Theory (RMT) and lower order terms not predicted by RMT. We also confirm the symmetry type of the families is unitary, supporting Katz and Sarnak's philosophy. VideoFor a video summary of this paper, please visit https://youtu.be/0tGmXHvVKF0.

Zeros of dirichlet L‐functions near the critical line

AbstractWe prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line.

On integers of the form [formula omitted

Let r1,…,rt be positive integers and let R2(r1,…,rt) be the set of positive odd integers that can be represented as p+2k1r1+⋯+2ktrt, where p is a prime and k1,…,kt are positive integers. It is easy to see that if r1−1+⋯+rt−1<1, then the set R2(r1,…,rt) has asymptotic density zero. In this paper, we prove that if r1−1+⋯+rt−1≥1, then the set R2(r1,…,rt) has a positive lower asymptotic density. Several conjectures and open problems are posed for further research.

Remark on a General Zero Density Theorem

Recently [3] we proved a general zero density theorem for a large class of functions which included among others the Riemann zeta function, Dedekind zeta functions, Dirichlet 𝐿-functions. The goal of the present work is a (slight) improvement of this general theorem which might lead to stronger results in some applications.

Møller energy momentum distribution for higher dimensional Morris Thorne wormhole

In this study, Møller energy momentum distribution is investigated for the higher dimensional Morris Thorne wormhole (MTW) in general relativity theory (GR) and results are given for the MTW in (4+1) and (5+1) dimensions. In addition, using the MTW, Møller energy and momentum distributions were investigated for 4-dimensional Morris Thorne wormhole, Hyperbolic Morris Thorne wormhole, Zero Tidal wormhole, Zero Density wormhole, Visser–Kar–Dadhich wormhole and (2+1) dimensional Morris Thorne wormhole. Except for the Zero Tidal wormhole model, we obtained the Møller energy distribution as well defined and non-zero in all other wormhole models. Besides, our results are in agreement with Aygün and Yılmaz and support Lesnner’s idea for Møller energy momentum definition.

HL ideals and Sacks indestructible ultrafilters

We study ultrafilters on countable sets and reaping families which are indestructible by Sacks forcing. We deal with the combinatorial characterization of such families and we prove that every reaping family of size smaller than the continuum is Sacks indestructible. We prove that complements of many definable ideals are Sacks reaping indestructible, with one notable exception, the complement of the ideal Z of sets of asymptotic density zero. We investigate the existence of Sacks indestructible ultrafilters and prove that every Sacks indestructible ultrafilter is a Z-ultrafilter.

On the type of the meromorphic function of finite order

Let $f(z)$ be a meromorphic function on the complex plane of finite order $\rho&gt;0$. Let $\rho(r)$ be a proximate order in the sense of Boutroux such that $\limsup\limits_{r\to\infty}\rho(r)=\rho$, $\liminf\limits_{r\to\infty}\rho(r)=\alpha&gt;0$. If $[\alpha]&lt;\alpha\leqslant\rho&lt;[\alpha]+1$ then the types of $T(r,f)$ and $|N|(r,f)$ coincide with respect to $\rho(r)$. If there are integers between $\alpha$ and $\rho$, then the resulting criterion is formulated in terms of the upper density of zeros and poles of the function $f$ and their argument symmetry.

Sifting for small primes from an arithmetic progression

In this work and its sister paper (Friedlander and Iwaniec (2023)), we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic progression. Using sieve machinery in both papers, we are able to dispense with the log-free zero density bounds and the repulsion property of exceptional zeros, two deep innovations begun by Linnik and relied on in earlier proofs.