T. H. Hansson, S. B. Isakov, J. M. Leinaas, U. Lindstrom
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of Haldane's exclusion statistics.
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In this paper we discuss limitions appearing while using Boolean Logic in Non-Constructive Mathematics (NCM) as a mathematical foundation for Quantum Mechanics. These limitations naturally vanish using Constructive Mathematics (CM) and Topos Theory which is one of its models. The line of reasoning is in agreement with recent theoretical work on Quantum Logic, and focusses on the pivotal role of the excluded middle law, and this will be addressed in more detail in our discussion.
Motivated by Haldane's exclusion statistics, we construct creation and annihilation operators for $g$-ons using a bosonic algebra. We find that $g$-ons appear due to the breaking of a descrete symmetry of the original bosonic system. This symmetry is intimately related to the braid group and we demonstrate a link between exclusion statistics and fractional statistics.
We examine the notion of Haldane's dimension and the corresponding statistics in a probabilistic spirit. Motivated by the example of dimensional-regularization we define the dimension of a space as the trace of a diagonal `unit operator', where the diagonal matrix elements are not, in general, unity but are probabilities to place the system into a given state. These probabilities are uniquely defined by the rules of Haldane's statistics. We calculate the second virial coefficient for our system and demonstrate agreement with Murthy and Shankar's calculation. The partition function for an ideal…
The development of mathematically complete and consistent models solving the so-called "measurement problem", strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical Reduction Models posses the unique characteristic to be experimentally testable. In the first part of the paper an upper limit on the reduction rate parameter of such models will be obtained, based on the analysis of the X-ray spectrum emitted by an isolated slab of germanium and measured by the IGEX experiment. The second part of the paper is devoted to present…
I show that if the total energy of a system of interacting particles may be written as a sum of quasiparticle energies, then the system of quasiparticles can be viewed in general as an ideal gas with fractional exclusion statistics (FES). The general method for calculating the FES parameters is also provided. The interacting particle system cannot be described as an ideal gas of Bose and Fermi quasiparticles except in trivial situations.
A local exclusion principle is observed for identical particles obeying intermediate/fractional exchange statistics in one and two dimensions, leading to bounds for the kinetic energy in terms of the density. This has implications for models of Lieb-Liniger and Calogero-Sutherland type, and implies a non-trivial lower bound for the energy of the anyon gas whenever the statistics parameter is an odd numerator fraction. We discuss whether this is actually a necessary requirement.
Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical particles in the lowest Landau level, and vortices in the Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical} statistical mechanics is shown to be a nontrivial classical limit of Haldane's exclusion statistics.
We show that the $N$-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the $N$-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrop…
Exclusion Statistics as a Thermodynamic Resource in Quantum Heat Engines
本文发现量子热机的最大功率受限于载流子统计，玻色子工作介质比费米子具有更高的通用极限，并通过Haldane分数排斥统计实现连续调控，揭示排斥统计是一种可独立调谐的热力学资源。
It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old …
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