Related papers: On free fermions and plane partitions
A method of building and investigation of the Fermi surfaces for three-dimensional crystals subjected to a uniform magnetic field is presented. The Hamiltonian of a charged particle in the crystal is treated in the framework of the…
Quantum field theoretic treatments of fermion oscillations are typically restricted to calculations in Fock space. In this letter we extend the oscillation formulae to include more general quasi-free states, and also consider the case when…
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
We show that the sum of two free random variables can have a free Poisson law without any of them having a free Poisson law.
We give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two classes of lattice models: the classical…
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
We present a SU(2)_L * SU(2)_R * U(1) left-right symmetric model for elementary particles and their connection with the fermion mass spectrum. New mirror fermions and a minimal set of Higgs particles are proposed. The model can accommodate…
Lateral effects are analyzed in the antibunching of a beam of free non-interacting fermions. The emission of particles from a source is dynamically described in a 3D full quantum field-theoretical framework. The size of the source and the…
We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the…
In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 satisfy the so-called free fermion condition. This both implies that all these…
In this paper we discuss a left-right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group $SU(2)_L\otimes SU(2)_R\otimes U(1)$. New mirror fermions and…
We discuss systematically the fermion mass and mixing matrices in a generic \linebreak field-theoretical flipped $SU(5)$ model, with particular applications to neutrino and baryon number-changing physics. We demonstrate that the different…
In this paper we return to the question of the modular properties of a generalised Gibbs ensemble of a single free fermion. We extend our previous proposals to a GGE containing an arbitrary number of conserved charges and provide a physical…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…
We extend the free convolution of Brown measures of $R$-diagonal elements introduced by K\"{o}sters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional powers. We then show how this fractional free convolution…
We derive accurately the fermion resonance propagator by means of Dyson summation of the self-energy contribution. It turns out that the relativistic fermion resonance differs essentially from its boson analog.
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
In this paper we study analytical solutions for fermion localization in Randall-Sundrum (RS) models. We show that there exist special couplings between scalar fields and fermions giving us discrete massive localizable modes. Besides this we…
We study a model of strongly correlated spinless fermions on a kagome lattice at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian. An effective Hamiltonian in the desired strong correlation regime is derived, from…