Related papers: Distribution of the Riemann zeros represented by t…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
We present a theoretical interpretation of a recent experiment presented in ref. \cite{Zwierlein06} on the density profile of Fermi gases with unbalanced spin populations. We show that in the regime of strong interaction, the boundaries of…
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for…
We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one dimensional configurations. The ground state properties are determined within local density approximation, starting from the exact…
We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density…
The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the…
We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution; this subsequently allows us to formally derive an integral expression for the Li coefficients associated with…
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…
The Riemann Hypothesis states that the Riemann zeta function $\zeta(z)$ admits a set of ``non-trivial'' zeros that are complex numbers supposed to have real part $1/2$. Their distribution on the complex plane is thought to be the key to…
We introduce the quadratic Fermi algebra, which is a Lie algebra, and show that the vacuum distributions of the associated Hamiltonians define the fermionic Meixner probability distributions. In order to emphasize the difference with the…
Friedel oscillations appear in density of Fermi gases due to Pauli exclusion principle and translational symmetry breaking nearby a defect or impurity. In confined Fermi gases, this symmetry breaking occurs also near to boundaries. Here,…
In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors…
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.
We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of…
A one dimensional Fermi mixture with delta--interaction is investigated in the limit of extreme imbalance. In particular we consider the cases of only one or two minority Fermions which interact with the Fermi-sea of the majority Fermions.…
A Fermi gas of non-interacting electrons, or ultra-cold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The Euler characteristic $\chi_F$ of the Fermi sea serves to…
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…
We introduce an exactly solvable model of a fermi gas in one dimension and compute the momentum distribution exactly. This is based on a generalisation of the ideas of bosonization in one dimension. It is shown that in the RPA limit(the…
We review recent progress in the theory of neutron matter with particular emphasis on its superfluid properties. Results of quantum Monte Carlo calculations of simple and realistic models of uniform superfluid neutron gas are discussed…
The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi von Weizs\"acker-like theory for the…