Related papers: The Riemannium
We continue our investigation of the distribution of the fractional parts of $a \gamma$, where $a$ is a fixed non-zero real number and $\gamma$ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We…
A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is…
These expository lectures focus on the distribution of zeros of the Riemann zeta function. The topics include the prime number theorem, the Riemann hypothesis, mean value theorems, and random matrix models.
Prime numbers are the building blocks of our arithmetic, however, their distribution still poses fundamental questions. Bernhard Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
We discuss the energy distribution of free-electron Fermi-gas, a problem with a textbook solution of Gaussian energy fluctuations in the limit of a large system. We find that for a small system, characterized solely by its heat capacity…
We investigate the simultaneous distribution of the fractional parts of $\{\alpha_1 \gamma, \alpha_2\gamma, \cdots, \alpha_n\gamma\}$, where $n\geq 2$, $\alpha_1$, $\alpha_2$, $\ldots$, $\alpha_n$ are fixed, distinct positive real numbers…
We study a system of self-gravitating massive fermions in the framework of the general-relativistic Thomas-Fermi model. We postulate the free energy functional and show that its extremization is equivalent to solving the Einstein's field…
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to…
The statistical mechanics characterization of a finite subsystem embedded in an infinite system is a fundamental question of quantum physics. Nevertheless, a full closed form { for all required entropic measures} does not exist in the…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for…
Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We…
A quantum-field approach for describing many-particle Fermi systems at finite temperatures and with spontaneously broken symmetry has been proposed. A generalized model of self-consistent field (SCF), which allows one to describe the states…
We introduce a general, simple and effective method of evaluating the zero point energy of a quantum field under the influence of arbitrary boundary conditions imposed on the field on flat surfaces perpendicular to a chosen spatial…
The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the…
The Riemann hypothesis states that all nontrivial zeros of the zeta function lie on the critical line $\Re(s)=1/2$. Hilbert and P\'olya suggested a possible approach to prove it, based on spectral theory. Within this context, some authors…
Isospin e ffects on multifragmentation properties were studied thanks to nuclear collisions between di fferent isotopes of xenon beams and tin targets. It is shown that, in central collisions leading to multifragmentation, the mean number…