abstract

In this paper, we investigate the thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in contact with a heat bath. Using the canonical ensemble, we determine the properties for both relativistic and nonrelativistic cases through the Euler–MacLaurin formula in the high-temperature regime. In particular, the main properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. Once these properties are obtained, we analyze via 2D graphs the behavior of the properties as a function of temperature \(T\), where we note that the Helmholtz free energy decreases with \(T\) and \(\omega _\theta \), and increases with \(\omega \), \(\Tilde {\omega }\), \(\omega _\eta \), where \(\omega \) is the frequency of the oscillator, \(\Tilde {\omega }\) is a type of cyclotron frequency, and \(\omega _\theta \) and \(\omega _\eta \) are the noncommutative frequencies of position and momentum. For the entropy, we note an increase with \(T\) and \(\omega _\theta \), and a decrease with \(\omega \), \(\Tilde {\omega }\), \(\omega _\eta \). Now, for the mean energy, we note that such property increases linearly with \(T\), and their values for the relativistic case are twice that of the nonrelativistic case. As a direct consequence of this, the value of the heat capacity for the relativistic case is also twice that of the nonrelativistic case, and both are constants, thus satisfying the Dulong–Petit law. Lastly, we also note that the electric field does not influence the properties in any way.

abstract

Detecting beyond the Standard Model (BSM) signals in high-energy particle collisions presents significant challenges due to complex data and the need to differentiate rare signal events from the Standard Model (SM) backgrounds. This study investigates the efficacy of deep learning models, specifically Deep Neural Networks (DNNs) and Graph Neural Networks (GNNs), in classifying particle collision events as either BSM signal or background. The research utilized a dataset comprising 214,000 SM background and 10,755 BSM events. To address class imbalance, an undersampling method was employed, resulting in balanced classes. Three models were developed and compared: a DNN and two GNN variants with different graph construction methods. All models demonstrated high performance, achieving Area Under the Receiver Operating Characteristic curve (AUC) values exceeding \(94\%\). While the DNN model slightly outperformed GNNs across various metrics, both GNN approaches showed comparable results despite different graph structures. The GNNs’ ability to explicitly capture inter-particle relationships within events highlights their potential for BSM signal detection.

abstract

In this note, we outline how a modest violation in the conservation of mass during the merger of two PBHs affects the PBH mass spectrum that we previously obtained using a Boltzmann equation model for the evolution of the mass spectrum with no mass loss. We find that if the initial cosmological redshift is of the order of 10\(^{12}\), then the fraction of primordial holes with masses greater than \(10^{3}\) solar masses appears to be close to what is required to provide the seeds for galaxies. In addition, we note that as a result of rapid collisions and strong coupling to electromagnetic radiation for temperatures \(\gt \) GeV, there will be an effective low-mass cutoff in the mass spectrum for PBH masses less than a certain PBH mass less than \(0.1M_{\odot }\). We also point out that this cutoff in the mass spectrum below \(\sim 0.1 M_\odot \) can be confirmed by combining future microlensing observations from the Roman Space Telescope and the Vera C. Rubin Observatory with astrometric observations.

abstract

In this paper, we study an ensemble of random matrices called the Elliptic Volatility Model, which arises in finance as models of stock returns. This model consists of a product of independent matrices \(X = {\mit \Sigma } Z\), where \(Z\) is a \(T\) by \(S\) matrix of i.i.d. light-tailed variables with mean 0 and variance 1, and \({\mit \Sigma }\) is a diagonal matrix. In this paper, we take the randomness of \({\mit \Sigma }\) to be i.i.d. heavy-tailed. We obtain an explicit formula for the empirical spectral distribution of \(X^*X\) in the particular case when the elements of \({\mit \Sigma }\) are distributed as Student’s \(t\) with parameter 3.