相关论文: Exclusion Statistics in Classical Mechanics
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
We derive the Hamiltonian formulation of classical mechanics directly, without reference to Lagrangian mechanics. We start from the definition of states in terms of labels used to identify them, and show how, under a deterministic and…
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…
The discussion of Fractional dimensional Hilbert spaces in the context of Haldane exclusion statistics is extended from the case \cite{IG} of $g=1/p$ for the statistical parameter to the case of rational $g=q/p$ with $q,p$-coprime positive…
We present, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum. We concentrate on the essential aspects of any reduction procedure, both in the algebraic…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
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',…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for…
We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic…
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…