相关论文: A multispecies Calogero-Sutherland model
A system of three-species fermions in one spatial dimension (1D) with a contact three-body interaction is known to display a scale anomaly. This anomaly is identical to that of a two-dimensional (2D) system of two-species fermions. The…
We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of…
We consider a system of $N$ individuals consisting of $S$ species that interact pairwise: $x_m+x_\ell \rightarrow 2x_m\,\,$ with arbitrary probabilities $p_m^\ell $. With no spatial structure, the master equation yields a simple set of rate…
We discuss the connection between the random matrix approach to disordered wires and the Calogero-Sutherland models. We show that different choices of random matrix ensembles correspond to different classes of CS models. In particular, the…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the…
The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
We study the Cauchy theory for a multi-species mixture, where the different species can have different masses, in a perturbative setting on the $3$-dimensional torus. The ultimate aim of this work is to obtain existence, uniqueness and…
We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated…
The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square interactions. At interaction strength $\lambda=2$, the CSM exhibits a deep connection to anyon…
We study and predict the interfacial tension, solubility parameters and Flory-Huggins parameters of binary mixtures as functions of pressure and temperature, using multiscale numerical simulation. A mesoscopic approach is proposed for…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
We study a Lagrangian with a cubic Galileon term and a standard scalar-field kinetic contribution with two exponential potentials. In this model the Galileon field generates scaling solutions in which the density of the scalar field $\phi$…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
We consider the large-$N$ Sutherland model in the Hamiltonian collective-field approach based on the $1/N$ expansion. The Bogomol'nyi limit appears and the corresponding solutions are given by static-soliton configurations. They exist only…
We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an…
We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the…
We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a…
Coupled, multi-field models of inflation can provide several attractive features unavailable in the case of a single inflaton field. These models have a rich dynamical structure resulting from the interaction of the fields and their…