相关论文: Local exclusion principle for identical particles …
In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb-Thirring…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
We introduce a rigorous approach to the many-body spectral theory of extended anyons, i.e. quantum particles confined to two dimensions that interact via attached magnetic fluxes of finite extent. Our main results are many-body magnetic…
After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional…
We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
We calculate the partition function of a gas of particles obeying Haldane exclusion statistics, using a definition of a Hilbert space having a `fractional dimension' and constructing appropriate coherent states. The fractional dimension is…
We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a…
We derive a Pauli exclusion principle for extended fermion-based anyons of any positive radius and any non-trivial statistics parameter. That is, we consider 2D fermionic particles coupled to magnetic flux tubes of non-zero radius, and…
We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $\alpha \in [0,1]$ ranging from bosons ($\alpha=0$) to fermions ($\alpha=1$). We prove a…
The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on $N$ strands. Allowing for arbitrary rank…
A general method for extending a non-dissipative nonlinear Schr\"odinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is…
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These…
We study Coulomb gases in any dimension $d \geq 2$ and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes…
The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary…
We examine when it is possible to locally extract energy from a bipartite quantum system in the presence of strong coupling and entanglement, a task which is expected to be restricted by entanglement in the low-energy eigenstates. We fully…
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the…
The purpose of the present paper is to establish appropriate cut-off resolvent estimates for the Dirichlet Laplacian on exterior domains. The geometrical assumptions on domains are rather general, for example, non-trapping condition is not…