arXiv subjects

Samuel Kováčik

Publications and source records attributed to Samuel Kováčik.

At least 19 recordsLinked to original sources

arXiv2026

White paper: 1-10 Hz matter-wave interferometer to test the spin entanglement witness for quantum gravity

In this white paper, we highlight the importance of the ($1-10~{\rm Hz}$) frequency range for laboratory tests of the quantum nature of gravity using the quantum gravity-induced entanglement of masses (QGEM) protocol. QGEM requires matter-wave interferometers with masses ($m\sim10^{-15}-10^{-14}~{\rm kg}$), brought within separations ($d\sim30-50~μ{\rm m}$), while maintaining spatial superpositions of ($1-20~μ{\rm m}$) and coherence for ($τ\sim 0.1 - 1~{\rm s}$). These requirements make low-frequency environmental noise a central experimental challenge and place QGEM in a regime closely related to the low-frequency goals of the Einstein Telescope (ET) and the Cosmic Explorer (CE). In particular, QGEM is sensitive to relative acceleration noise (RAN) and to gravity-gradient noise (GGN) generated by seismic and other environmental mass-density fluctuations. For representative parameters $m=10^{-14}~{\rm kg}$, $Δx=10~μ{\rm m}$, and $τ=1~{\rm s}$, the differential acceleration-noise amplitude spectral density must be suppressed well below the $10^{-15}~{\rm m\,s^{-2}/\sqrt{Hz}}$ level to keep acceleration-induced dephasing below the relevant experimental scale. Achieving this level of low-frequency noise suppression is therefore a key requirement for QGEM and closely parallels the seismic and gravity-gradient noise challenges that ET and CE address.

quant-ph↗

arXiv2026

Asymmetric phase transitions in random noncommutative geometries

In this paper, we study the asymmetric phases of the quartic type (0, 1) and (1, 0) Dirac en- sembles via three approaches: the Riemann-Hilbert approach, bootstrapping with positivity, and Hamiltonian Monte Carlo (HMC) simulations. The focus of this work is on asymmetric solutions to the Schwinger-Dyson and saddle point equations of these models, whose solution spaces prove deeply intricate. Via the Riemann-Hilbert approach, we are able to give explicit formulae for the eigenvalue distributions and free energy of various solutions. Using Hamiltonian Monte Carlo simulations, we are able to reconstruct the phase structure. Lastly, using bootstrapping with positivity, we are able to reconstruct the eigenvalue distribution of these models from their bootstrapped moments. All three methods show excellent agreement for a large matrix size.

math-ph↗

arXiv2026

Numerical Study of Scalar Field Theory on the Fuzzy Onion

We study the behaviour of the scalar field theory on the fuzzy onion model -- a three-dimensional matrix model consisting of concentric fuzzy spheres of gradually increasing radii. We use a numerical method of Hamiltonian Monte Carlo simulations to study the phase structure of this theory. We identify the field phases, investigate and describe a phenomenon of dynamical phase transitions and attempt to reconstruct phase transition lines. We compare the results with the well-studied phase structure of the fuzzy sphere. Finally, we identify two boundaries on the phase transitions of the theory, a uniform phase boundary and a critical boundary between the disordered and non-uniform phase.

hep-th↗

arXiv2026

Eigenvalue-cluster Algorithm for Matrix Monte Carlo

Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the simulation may become stuck in a vacuous state, and probing the relevant parts of the configuration space might be difficult. Here, we propose an algorithm that moves around a cluster of eigenvalues and show that it converges to the true vacuum state.

hep-lat↗

arXiv2025

Eigenvalue distribution from bootstrap estimates

The bootstrap method has proven useful for a wide range of matrix models. Here, we show that the computed momenta can be used to reconstruct the underlying eigenvalue probability distribution, which in turn allows us to compute the free energy of the model, a necessary quantity for identifying the thermodynamically preferred solution. We verify the method on the well-studied quartic potential model and then apply it to a recently analysed asymmetric multi-trace model. We consider an extended class of possible solutions and demonstrate that free-energy analysis reliably selects the correct one, making it an essential tool for studying models with a complex solution structure.

hep-th↗

arXiv2025

Hydrogen Atom in a Fuzzy Spherical Cavity

The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in three-dimensional space -- like scalar fields or wavefunctions -- are expressed in terms of Hermitian matrices of a certain structure. Relevant equations are then matrix equations, and some problems, such as searching for the energy spectrum for fixed quantum numbers $(l,m)$, can be expressed as an eigenvalue problem. We show how this simple approach can reproduce the results of other studies analyzing the hydrogen atom in a spherical cavity. We also test the effect of the short-distance quantum structure of the space on these solutions -- not looking for the phenomenological consequences, as the scale of quantum space is many orders below the order of the Bohr radius, but to understand the effect of quantum space in general. We observe a set of solutions without a classical counterpart which have been suggested also in a former theoretical study.

hep-th↗

arXiv2024

Phenomenology of the dispersion law in three-dimensional quantum space

The concept of a quantum structure underlying space has been proposed for quite some time, yet it has largely eluded direct observation. There is a prevailing notion that the minuscule effects stemming from quantum space could, under certain astronomical conditions, accumulate to an observable magnitude. Typically, these effects are perturbative, limited to the first one or two orders. This study presents a full dispersion law derived from a three-dimensional quantum space model. Our primary focus is investigating the in-vacuo dispersion phenomenon and the threshold anomaly. Furthermore, we briefly explore the implications of additional spatial dimensions within this framework and suggest a way of distinguishing between various theories that agree in the leading order approximation.

gr-qc↗

arXiv2024

The Fuzzy Onion: An Initial Study

In our previous contribution, we introduced a matrix formulation of a three-dimensional quantum space named the fuzzy onion. The novel part of the construction is the radial derivative term, which has been defined to recover the correct continuum limit. Here, we describe a numerical simulation of the scalar field theory in this space and test some physical properties of the model with emphasis on the interaction between neighbouring layers.

hep-th↗

arXiv2024

Expanding Microscopic Black Holes

Two interesting hypotheses about black holes have been proposed. The older one states that microscopic black holes can be accountable for the observed dark matter density. The newer one states that black holes are coupled to the expansion of the universe. Here, we combine those ideas and investigate the behaviour of expanding microscopic black holes. We observe two temperatures at which the radiation balances the expansion. While one of the balance points might be important in the analysis of primordial scenarios, the other would lead to a strong diffuse gamma radiation background, which is contradicted by the lack of observations. This establishes another indirect evidence disfavouring the hypothesis of cosmological coupling of black holes.

gr-qc↗

arXiv2024

Fuzzy Onion as a Matrix Model

We propose a matrix model realisation of a three-dimensional quantum space. It has an onion-like structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the fuzzy sphere. The radial part is constructed using operators that relate matrices of various sizes using the matrix harmonic expansion. As an example of this approach, we produce a numerical simulation of a scalar quantum field theory, the classical heat transfer, study the quantum mechanical hydrogen atom, and consider some analytical aspects of the scalar field theory on this space.

hep-th↗

arXiv2023

Phase transitions in a $Φ^4$ matrix model on a curved noncommutative space

In this contribution, we summarize our recent studies of the phase structure of the Grosse-Wulkenhaar model and its connection to renormalizability. Its action contains a special term that couples the field to the curvature of the noncommutative background space. We first analyze the numerically obtained phase diagram of the model and its three phases: the ordered, the disordered, and the noncommutative stripe phase. Afterward, we discuss the analytical derivation of the effective action and the ordered-to-stripe transition line, and how the obtained expression successfully explains the curvature-induced shift of the triple point compared to the model without curvature. This shift also causes the removal of the stripe phase and makes the model renormalizable.

hep-th↗

arXiv2022

Microscopic black holes as probes for quantum gravity

One of the main goals of contemporary theoretical physics is to find the quantum theory of gravity. There are various working hypotheses, mostly operating in the regime of high-energy physics well above the reach of particle accelerators. So far, strong experimental or observational evidence to guide the theory is missing. A possible consequence of quantum gravity and quantum spacetime that is often discussed is the vacuum dispersion effect. In this paper, we consider a different line of quantum space phenomenology, the behaviour of microscopic black holes. Even though their exact nature is unknown, some of their features are very model-independent, allowing us to draw conclusions about their role in the current cosmological models.

gr-qc↗

arXiv2022

Eigenvalue-flipping Algorithm for Matrix Monte Carlo

Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.

hep-lat↗

arXiv2022

The nonperturbative phase diagram of the bosonic BMN matrix model

We study the thermal phase transition of the bosonic BMN model which is a mass deformed version of the bosonic part of the BFSS model. Our results connect the massless region of the phase diagram described by the bosonic BFSS model with the large-mass region, where the model is analytically solvable. We observe that at finite value of the matrix size $N$, the critical region is smeared over a small temperature range. The model has a single critical temperature, which arises as the large $N$ limit of two apparent transitions at finite $N$. We emphasise the vital role played by finite $N$ corrections in the confined phase and illustrate this with a novel treatment of the noninteracting Gaussian model.

hep-th↗

arXiv2021

Hawking-Radiation Recoil of Microscopic Black Holes

Hawking radiation would make microscopic black holes evaporate rapidly, which excludes them from many astrophysical considerations. However, it has been argued that the quantum nature of space would alter this behaviour: the temperature of a Planck-size black hole vanishes, and what is left behind is a Planck-mass remnant with the cross-section of $\approx 10^{-70}\mbox{m}^2$, which makes a direct observation nearly impossible. Such black hole remnants have been identified as possible dark matter candidates. Here, we argue that the final stage of evaporation has a recoil effect that gives them a velocity up to $\approx 10^{-1} c$. This would lead to a disagreement with the cold dark matter cosmological model unless the primordial black hole formation ceased shortly after the inflation era.

gr-qc↗

arXiv2020

The Confining Transition in the Bosonic BMN Matrix Model

We study the confining/deconfining phase transition in the mass deformed Yang-Mills matrix model which is obtained by the dimensional reduction of the bosonic sector of the four-dimensional maximally supersymmetric Yang-Mills theory compactified on the three sphere, i.e. the bosonic BMN model. The $1/D$ (with $D$ the number of matrices) expansion suggests that the model may have two closely separated transitions. However, using a second order lattice formulation of the model we find that for the small value of the mass parameter, $μ=2$, those two apparent critical temperatures merge at large $N$, leaving only a single weakly first-order phase transition, in agreement with recent numerical results for $μ=0$ (the bosonic BFSS model).

hep-th↗

arXiv2018

A Computer Test of Holographic Flavour Dynamics II

We study the second derivative of the free energy with respect to the fundamental mass (the mass susceptibility) for the Berkooz-Douglas model as a function of temperature and at zero mass. The model is believed to be holographically dual to a D0/D4 intersection. We perform a lattice simulation of the system at finite temperature and find excellent agreement with predictions from the gravity dual.

hep-th↗

arXiv2018

The non-perturbative phase diagram of the BMN matrix model

We study the maximally supersymmetric plane wave matrix model (the BMN model) at finite temperature, $T$, and locate the high temperature phase boundary in the $(μ,T)$ plane, where $μ$ is the mass parameter. We find the first transition, as the system is cooled from high temperatures, is from an approximately $SO(9)$ symmetric phase to one where three matrices expand to form fuzzy spheres. For $μ> 3.0$ there is a second distinct transition at a lower temperature. The two transitions approach one another at smaller $μ$ and merge in the vicinity of $μ=3.0$. The resulting single transition curve then approaches the gauge/gravity prediction as $μ$ is further decreased. We find a rough estimate of the transition, for all $μ$, is given by a Padé resummation of the large-$μ$, 3-loop perturbative, predictions. We find evidence that the transition at small $μ$ is to an M5-brane phase of the theory.

hep-th↗