arXiv subjects

Marc Winstel

Publications and source records attributed to Marc Winstel.

15 recordsLinked to original sources

arXiv2026

Coin selection by Random Draw according to the Boltzmann distribution

Coin selection refers to the problem of choosing a set of tokens to fund a transaction in token-based payment systems such as, e.g., cryptocurrencies or central bank digital currencies (CBDCs). In this paper, we propose the Boltzmann Draw that is a probabilistic algorithm inspired by the principles of statistical physics. The algorithm relies on drawing tokens according to the Boltzmann distribution, serving as an extension and improvement of the Random Draw method. Numerical results demonstrate the effectiveness of our method in bounding the number of selected input tokens as well as reducing dust generation and limiting the token pool size in the wallet. Moreover, the probabilistic algorithm can be implemented efficiently, improves performance and respects privacy requirements - properties of significant relevance for current token-based technologies. We compare the Boltzmann draw to both the standard Random Draw and the Greedy algorithm. We argue that the former is superior to the latter in the sense of the above objectives. Our findings are relevant for token-based technologies, and are also of interest for CBDCs, which as a legal tender possibly needs to handle large transaction volumes at a high frequency.

cs.CR↗

arXiv2025

Objectives and Design Principles in Offline Payments with Central Bank Digital Currency (CBDC)

In this work, fundamental design principles for a central bank digital currency (CBDC) with an offline functionality and corresponding counter measures are discussed. We identify three major objectives for any such CBDC proposal:(i) Access Control Security - protection of a user's funds against unauthorized access by other users; (ii) Security against Depositor's Misbehavior - preservation of the integrity of an environment (potentially the wallet) against misbehavior of its owner (for example, double-spending), and (iii) Privacy by Design - ensuring privacy is embedded into the system architecture. Our central conclusion is the alignment of the objectives to concrete design elements as countermeasures, whereas certain objectives and countermeasures have no or minimal interferences with each other. For example, we work out that the integrity of a user's wallet and, accordingly, the prevention of double-spending race attacks should be addressed through the adoption and integration of \textit{secure hardware} within a CBDC system.

cs.CR↗

arXiv2024

Dilepton production from moaton quasiparticles

The phase diagram of QCD may contain a moat regime in a large region of temperature $T$ and chemical potential $\mu\neq0$. A moat regime is characterized by quasiparticle moatons (pions) whose energy is minimal at nonzero spatial momentum. At $\mu\neq 0$, higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.

hep-ph↗

arXiv2024

Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime

This work investigates the phase structure of the non-renormalizable (3+1)-dimensional Nambu-Jona-Lasinio (NJL) model with particular focus on inhomogeneous phases (IPs), where the chiral condensate is non-uniform in space, and the closely related moat regimes, where mesonic dispersion relations favor non-vanishing momenta. We use the mean-field approximation and consider five different regularization schemes including three lattice discretizations. The results within the different regularization schemes are systematically analyzed in order to study the dependence of the IP on the choice of regulatization scheme and regulator value. The IP exhibits a drastic dependence on the chosen regularization scheme rendering any physical interpretation of results on inhomogeneous phases in this model doubtful. In contrast, we find only a mild scheme dependence of the moat regime suggesting that its existence is a consequence of the action of the NJL model and its symmetries and, thus, that it might also exist in QCD.

hep-ph↗

arXiv2024

Revisiting the spatially inhomogeneous condensates in the $(1 + 1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the $(1 + 1)$-dimensional chiral Gross-Neveu model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results arXiv:hep-th/0008175, arXiv:0807.2571, arXiv:0909.3714, arXiv:1810.03921, arXiv:2203.08503. The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-$N$ limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic $1$-particle irreducible two-point vertex function of the chiral Gross-Neveu model and the spinodal line of the Gross-Neveu model.

hep-th↗

arXiv2024

Lattice study of disordering of inhomogeneous condensates and the Quantum Pion Liquid in effective $O(N)$ model

In this talk, we study a scalar $O(N)$ model with a so-called moat regime -- a regime with negative bosonic wave function renormalization -- using lattice field theory. For negative bare wave function renormalization, inhomogeneous condensates are solutions of the classical equations of motions. Using hybrid Monte Carlo simulations we demonstrate how bosonic quantum fluctuations disorder the inhomogeneous condensate. Instead, one finds a so-called Quantum Pion Liquid, where bosonic correlation functions are spatially oscillating, but also exponentially decaying.

hep-lat↗

arXiv2024

Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density

In this work, we demonstrate that the mixing of scalar and vector condensates produces spatially oscillating, but exponentially damped correlation functions in fermionic theories at finite density and temperature. We find a regime exhibiting this oscillatory behavior in a Gross-Neveu-type model that also features vector interactions within the mean-field approximation. The existence of this regime aligns with expectations based on symmetry arguments, that are also applicable to QCD at finite baryon density. We compute the phase diagram including both homogeneous phases and regions with spatially oscillating, exponentially damped correlation functions at finite temperature and chemical potential for different strengths of the vector coupling. Furthermore, we find that inhomogeneous condensates are disfavored compared to homogeneous ones akin to previous findings without vector interactions. We show that our results are valid for a broad class of $\left(2+1\right)$-dimensional models with local four-fermion interactions.

hep-ph↗

arXiv2023

Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models

We show the absence of an instability of homogeneous (chiral) condensates against spatially inhomogeneous perturbations for various 2+1-dimensional four-fermion and Yukawa models. All models are studied at non-zero baryon chemical potential, while some of them are also subjected to chiral and isospin chemical potential. The considered theories contain up to 16 Lorentz-(pseudo)scalar fermionic interaction channels. We prove the stability of homogeneous condensates by analyzing the bosonic two-point function, which can be expressed in a purely analytical form at zero temperature. Our analysis is presented in a general manner for all of the different discussed models. We argue that the absence of an inhomogeneous chiral phase (where the chiral condensate is spatially non-uniform) follows from this lack of instability. Furthermore, the existence of a moat regime, where the bosonic wave function renormalization is negative, in these models is ruled out.

hep-ph↗

arXiv2022

Inhomogeneous phases in the 3+1-dimensional Nambu-Jona-Lasinio model and their dependence on the regularization scheme

In this work we study the $3+1$-dimensional Nambu-Jona-Lasinio (NJL) model in the mean field-approximation. We carry out calculations using five different regularization schemes (two continuum and three lattice regularization schemes) with particular focus on inhomogeneous phases and condensates. The regularization schemes lead to drastically different inhomogeneous regions. We provide evidence that inhomogeneous condensates appear for all regularization schemes almost exclusively at values of the chemical potential and with wave numbers, which are of the order of or even larger than the corresponding regulators. This can be interpreted as indication that inhomogeneous phases in the $3+1$-dimensional NJL model are rather artifacts of the regularization and not a consequence of the NJL Lagrangian and its symmetries.

hep-lat↗

arXiv2022

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

In this work, inhomogeneous chiral phases are studied in a variety of Four-Fermion and Yukawa models in $2+1$ dimensions at zero and non-zero temperature and chemical potentials. Employing the mean-field approximation, we do not find indications for an inhomogeneous phase in any of the studied models. We show that the homogeneous phases are stable against inhomogeneous perturbations. At zero temperature, full analytic results are presented.

hep-ph↗

arXiv2021

Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit

We study the $\mu$-$\mu_{45}$-$T$ phase diagram of the $2+1$-dimensional Gross-Neveu model, where $\mu$ denotes the ordinary chemical potential, $\mu_{45}$ the chiral chemical potential and $T$ the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.

hep-lat↗

arXiv2021

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1 + 1)$-dimensional Gross-Neveu model in the mean-field approximation

The phase diagram of the $(1 + 1)$-dimensional Gross-Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-field approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the $\mathbb{Z}_2$ symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that confirms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross-Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-field approximation, which is extracted analytically from the bosonic two-point function. We find regions -- a so-called moat regime -- where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.

hep-ph↗

arXiv2021

Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance

In this work, the phase diagram of the $2+1$-dimensional Gross-Neveu model is investigated with baryon chemical potential as well as chiral chemical potential in the mean-field approximation. We study the theory using two lattice discretizations, which are both based on naive fermions. An inhomogeneous chiral phase is observed only for one of the two discretizations. Our results suggest that this phase disappears in the continuum limit.

hep-lat↗

arXiv2020

Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model

The phase diagram of the Gross-Neveu model in $2+1$ space-time dimensions at non-zero temperature and chemical potential is studied in the limit of infinitely many flavors, focusing on the possible existence of inhomogeneous phases, where the order parameter $σ$ is non-uniform in space. To this end, we analyze the stability of the energetically favored homogeneous configuration $σ(\textbf{x}) = \barσ= \textrm{const}$ with respect to small inhomogeneous fluctuations, employing lattice field theory with two different lattice discretizations as well as a continuum approach with Pauli-Villars regularization. Within lattice field theory, we also perform a full minimization of the effective action, allowing for arbitrary 1-dimensional modulations of the order parameter. For all methods special attention is paid to the role of cutoff effects. For one of the two lattice discretizations, no inhomogeneous phase was found. For the other lattice discretization and within the continuum approach with a finite Pauli-Villars cutoff parameter $Λ$, we find a region in the phase diagram where an inhomogeneous order parameter is favored. This inhomogeneous region shrinks, however, when $a$ is decreased or $Λ$ is increased, and finally diappears for all non-zero temperatures when the cutoff is removed completely. For vanishing temperature, we find hints for a degeneracy of homogeneous and inhomogeneous solutions, in agreement with earlier findings.

hep-lat↗

arXiv2020

Lattice investigation of an inhomogeneous phase of the 2+1-dimensional Gross-Neveu model in the limit of infinitely many flavors

We investigate the phase structure of the 2+1-dimensional Gross-Neveu model in the large-Nf limit, where Nf denotes the number of fermion flavors. We discuss two different fermion representations and their implication on the interpretation of a discrete symmetry of the action. We present numerical results, which indicate the existence of an inhomogeneous phase similar as in the 1+1-dimensional Gross-Neveu model.

hep-lat↗