The partition function for an anyon-like oscillator

Comment on "Partition function of anyon gas"

An Arithmetic Formula for the Partition Function

Although there is a vast literature on the properties of p(n), typically motivated by work of Ramanujan, some of the simplest questions remain open. For example, little is known about p(n) modulo 2 and 3. Most results concerning the congruence properties of p(n) have been proved using properties of (1.1). Theorems typically depend on q-series identities, the theory of modular equations, or the ...

The Partition Function for the Anharmonic Oscillator in the Strong-Coupling Regime

We consider a single anharmonic oscillator with frequency ω and coupling constant λ respectively, in the strong-coupling regime. We are assuming that the system is in thermal equilibrium with a reservoir at temperature β−1. Using the strong-coupling perturbative expansion, we obtain the partition function for the oscillator in the regime λ >> ω, up to the order 1 √ λ . To obtain this result, we...

Schwinger’s Formula and the Partition Function for the Bosonic and Fermionic Harmonic Oscillator

We use Schwinger’s formula, introduced by himself in the early fifties to compute effective actions for QED, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillator. * e-mail: farina@vms1. nce.ufrj.br 1 The computation of the partition function of the usual harmonic oscillator is probably one of the most elementary exe...

Using the Adaptive Frequency Nonlinear Oscillator for Earning an Energy Efficient Motion Pattern in a Leg- Like Stretchable Pendulum by Exploiting the Resonant Mode

In this paper we investigate a biological framework to generate and adapt a motion pattern so that can be energy efficient. In fact, the motion pattern in legged animals and human emerges among interaction between a central pattern generator neural network called CPG and the musculoskeletal system. Here, we model this neuro - musculoskeletal system by means of a leg - like mechanical system cal...