Related papers: Concerning the differentiability of the energy fun…
The conjecture, that the finite volume corrections to the thermodynamic functions can be correctly reproduced by using the thermodynamic limit with low particle momenta cutoff is examined in a very transparent example of an ideal boson gas…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…
Quantized deep neural networks (QDNNs) are necessary for low-power, high throughput, and embedded applications. Previous studies mostly focused on developing optimization methods for the quantization of given models. However, quantization…
Recently, the bound state solutions of a confined Klein-Gordon particle under the mixed scalar-vector generalized symmetric Woods-Saxon potential in one spatial dimension have been investigated. The obtained results reveal that in the spin…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
For a many-electron system, whether the particle density $\rho(\mathbf{r})$ and the total current density $\mathbf{j}(\mathbf{r})$ are sufficient to determine the one-body potential $V(\mathbf{r})$ and vector potential…
A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…
In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…
Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which…
The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary…
The processing of quantum information always has a cost in terms of physical resources such as energy or time. Determining the resource requirements is not only an indispensable step in the design of practical devices - the resources need…
We identify the fluctuations of the partition function of the continuous random energy model on a Galton-Watson tree in the so-called weak correlation regime. Namely, when the ``speed functions'', that describe the time-inhomogeneous…
The variational argument is presented to establish the attainability of homogeneity of degree one in the number of particles for any functional $F[n, f]$ that depends on both the state variable $f$ and the particle count $n$. Euler's…
Machine learning potentials have become increasingly successful in atomistic simulations. Many of these potentials are based on an atomistic representation in a local environment, but an efficient description of non-local interactions that…
A central challenge of applying near-term quantum optimization algorithms to industrially relevant problems is the need to incorporate complex constraints. In general, such constraints cannot be easily encoded in the circuit, and the…
We consider the problem of deciding whether an $n$-qubit unitary (or $n$-bit Boolean function) is $\varepsilon_1$-close to some $k$-junta or $\varepsilon_2$-far from every $k$-junta, where $k$-junta unitaries act non-trivially on at most…
The free energy principle (FEP), as an encompassing framework and a unified brain theory, has been widely applied to account for various problems in fields such as cognitive science, neuroscience, social interaction, and hermeneutics. As a…
Energy conditions are attempts to summarise the properties of realistic descriptions of matter via constraints on the energy-momentum tensor. This is, for example, useful when one wants to understand the types of spacetime geometry that can…