Equivalence of the grand canonical partition functions of particles with different statistics

Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach

The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field s…

Partition functions and thermodynamic properties of paraboson and parafermion systems

New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for such systems. We analyze and discuss the average number of particles on an orbital, and the average number of particles in the system. For some special cases (identical orbital energies, or equidistant orbital energies) we can simplify the grand partition functions and describe thermodynamic properties in more detail. Some specific properties are also illust…

Finite Quantum Grand Canonical Ensemble and Temperature from Single Electron Statistics in a Mesoscopic Device

I present a theoretical model of a quantum statistical ensemble for which, unlike in conventional physics, the total number of particles is extremely small. The thermodynamical quantities are calculated by taking a small $N$ by virtue of the orthodicity of canonical ensemble. The finite quantum grand partition function of a Fermi-Dirac system is calculated. The model is applied to a quantum dot coupled with a small two dimensional electron system. Such system consists of an alternatively single and double occupied electron system confined in a quantum dot, which exhanges one electron with a sm…

Schwarzschild black hole as a grand canonical ensemble

For long black holes have been considered as endowed with a definite temperature. Yet when the Schwarzschild black hole is treated as a canonical ensemble three problems arise: incompatibility with the Hawking radiation, divergence of the partition function, and a formally negative mean-square fluctuation of the energy. We solve all three problems by considering the Schwarzschild black hole as a grand canonical ensemble, with the Hamiltonian (the ADM mass) and the horizon surface area, separately, as observable parameters. The horizon area simulates the number of particles in statistical mecha…

Can We Distinguish Between the Grand Canonical and the Canonical Ensemble in a BEC Experiment?

It is well known that at the thermodynamic limit there are no observable differences in the results obtained by grand canonical and canonical descriptions of a many-body system. In the present paper, we test the validity of this statement for finite systems using as an example an ensemble of bosons trapped in a 1D harmonic potential well. We have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein …

粒子数守恒量子信号处理用于热性质：正则系综估计与巨正则重构

Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction

提出一个端到端量子模拟框架，结合粒子数守恒Trotter化与广义量子信号处理，估计正则热性质，并通过经典重加权实现巨正则重构，在特定温度区间优于经典Lanczos方法，数值验证于二维Hubbard模型。