相关论文: Distribution of the Riemann zeros represented by t…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully…
We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution is used to calculate the many-body wave function of the system. Then we evaluate…
The ideal (i.e. noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold…
We present the partition function of a most generic $U(N)$ single plaquette model in terms of representations of unitary group. Extremising the partition function in large N limit we obtain a relation between eigenvalues of unitary matrices…
We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased Reptation Monte Carlo for various densities and extrapolate the momentum distribution, and the kinetic and potential energies to…
A detailed calculation of the coherent and incoherent dynamic structure functions of the free Fermi gas, starting from their expressions in terms of the one- and semi-diagonal two-body density matrices, is derived and discussed. Their…
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas -- the Gaudin-Yang model -- and its generalisations…
We investigate within density functional theory various physical properties of the zero-temperature unitary Fermi gas which critically depend on the presence of a dispersive gradient term in the equation of state. First, we consider the…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
We evaluate the scattering functions of a gas of spin-polarized, non-interacting fermions confined in a quasi-onedimensional harmonic trap at zero temperature. The main focus is on the inelastic scattering spectrum and on the angular…
We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N…
We study a Fermi gas with strong, tunable interactions dispersively coupled to a high-finesse cavity. Upon probing the system along the cavity axis, we observe a strong optomechanical Kerr nonlinearity originating from the density response…
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…
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 demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic…
In this work, we prove the equivalence between the zero distributions of the Riemann zeta function {\zeta}(s) and a two-dimensional (2D) Ising model with a mixture of ferromagnetic and randomly distributed competing interactions. At first,…
The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in…
Using Landau theory of Fermi liquids we calculate the dynamic response of both a polarized and unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation…