arXiv 1809.044722018-09-12cond-mat.stat-mech

Occupation numbers in a quantum canonical ensemble: a projection operator approach

Wim Magnus, Fons Brosens

备注：: 23 pages, 8 figures
DOI：: 10.1016/j.physa.2018.11.056

英文摘要：

Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is 1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and 2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Unified framework for generalized quantum statistics: canonical partition function, maximum occupation number, and permutation phase of wave function

Beyond Bose and Fermi statistics, there still exist various kinds of generalized quantum statistics. Two ways to approach generalized quantum statistics: (1) in quantum mechanics, generalize the permutation symmetry of the wave function and (2) in statistical mechanics, generalize the maximum occupation number of quantum statistics. The connection between these two approaches, however, is obscure. In this paper, we suggest a unified framework to describe various kinds of generalized quantum statistics. We first provide a general formula of canonical partition functions of ideal $N$-particle ga…

2020-03-04cond-mat.stat-mech

Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap

We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an exp…

2018-11-28cond-mat.quant-gascond-mat.stat-mech

Projection operator approach to master equations for coarse grained occupation numbers in non-ideal quantum gases

We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These sums correspond to "grains" in momentum space. This equation of motion is supposed to involve only a moderate number of dynamical variables and/or exhibit a sufficiently simple structure such that neither its construction nor its analyzation/solution requires substantial numerical effort. To this we end compute, by means of a projection operator technique, …

2010-04-29cond-mat.quant-gascond-mat.stat-mech

Exact canonical occupation numbers in a Fermi gas with finite level spacing and a q-analog of Fermi-Dirac distribution

We consider equilibrium level occupation numbers in a Fermi gas with a fixed number of particles, n, and finite level spacing. Using the method of generating functions and the cumulant expansion we derive a recurrence relation for canonical partition function and an explicit formula for occupation numbers in terms of single-particle partition function at n different temperatures. We apply this result to a model with equidistant non-degenerate spectrum and obtain close-form expressions in terms of q-polynomials and Rogers-Ramanujan partial theta function. Deviations from the standard Fermi-Dira…

2011-10-28cond-mat.mes-hallcond-mat.stat-mechmath-ph

On the theory of ideal Bose-gas at a finite particle number

The ideal Bose-gas with finite number $N$ of particles is investigated. The exact expressions for the partition functions and occupation numbers in the grand canonical, canonical and microcanonical ensembles are found. The asymp\-totic expressions (in the case $N\gg1$) for the partition functions and occupation numbers in the canonical and microcanonical ensembles are evaluated. It is shown that the chemical potential $μ$ of the ideal Bose-gas can lie in the range $-\infty<μ<\infty$ oppositely to the widely adopted opinion that the value of this potential is negative.

2020-11-09cond-mat.stat-mech

The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains

We introduce the exit time finite state projection (ETFSP) scheme, a truncation-based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of time-homogeneous continuous-time Markov chains. We prove that: (i) the computed approximations bound the measures from below; (ii) the total variation distances between the approximations and the measures decrease monotonically as states are added to the truncation; and (iii) the scheme converges, in the sense that…

2019-01-25cond-mat.stat-mechmath.OCmath.PR

更多相关论文收起更多论文

Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non…

2020-08-08cond-mat.quant-gascond-mat.stat-mech

囚禁理想玻色气体和相互作用玻色气体的正则统计

Canonical Statistics of Trapped Ideal and Interacting Bose Gases

本文用正则系综方法研究了谐振势阱中相互作用和非相互作用玻色气体的平均基态占据数和凝聚态涨落。为了得到平均基态占据数和凝聚态涨落，直接从系统的配分函数出发，给出了凝聚态概率分布函数的解析描述.对于理想玻色气体，概率分布函数被发现是一个高斯的情况下的谐波陷阱。对于相互作用玻色气体，基于最低阶微扰法和Bogoliubov理论，采用统一的方法计算了凝聚态涨落。结果表明，基于最低阶微扰理论的凝聚态涨落遵循$<delta^{2}N_{\bf 0}>\sim N$定律，而基于Bogoliubov理论的凝聚态涨落遵循$N^{4/3}$定律.

2001-11-08cond-mat.softcond-mat.stat-mech

有限费米系统中占据数的分布及相互作用在混沌和热化中的作用

Distribution of occupation numbers in finite Fermi-systems and role of interaction in chaos and thermalization

本文提出了一种计算有限相互作用费米系统中单粒子占据数的新方法。它比正则分布方法更精确，并给出了大粒子数极限下的Fermi-Dirac分布。结果表明，统计效应的相互作用被吸收的有效温度的增加。量子混沌和统计平衡的标准被认为是。所有结果都通过两体随机相互作用模型的数值实验得到了证实。

1996-10-24cond-mat.stat-mechnucl-thquant-ph

Quantum canonical ensemble: a projection operator approach

Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary $N$ since, unlike the case of the grand-canonical ensemble, traces in the $N$-particle Hilbert space fail to factorize into simple traces over single-particle states. In this paper we introduce a projection operator that enables a constraint-free computation of the partition function and its derived quanti…

2016-12-22cond-mat.stat-mechquant-ph

总动量固定的正则系综中的玻色-爱因斯坦凝聚

Bose-Einstein condensation in canonical ensemble with fixed total momentum

该研究针对总动量与粒子数均固定的无相互作用三维玻色气体，通过鞍点法推导大N极限下的解析近似，预测了凝聚体碎裂现象，揭示了伽利略不变性破缺，拓展了运动量子系统的有限温度理论。

2024-06-13cond-mat.quant-gascond-mat.stat-mech

无序玻色谐振器中的通用熵占据统计

Universal entropic occupation statistics in disordered bosonic resonators

University of California San Diego（加州大学圣地亚哥分校）

该研究分析可编程微腔中巨正则光子气体的玻色态计数，得出无序玻色谐振器的通用熵占据统计规律，关联光子热力学与度量数论，并提出相关实验测试方案。

2026-08-11cond-mat.quant-gascond-mat.stat-mechmath-ph

玻色气体正则系综的随机场方程

Stochastic field equation for the canonical ensemble of a Bose gas

提出了一个新的保范玻色场随机发展方程。系综平均值是正则系综中的量子期望值。这个数值上非常稳定的方程抑制了高能量波动指数，防止截止问题的发生。我们提出了三维模拟的理想气体在各种陷阱的潜力集中在基态占领数和空间关联函数的温度范围很广，高于和低于临界温度。虽然严格有效的非相互作用玻色子，我们认为，弱相互作用玻色气体也可以服从这种方法，在通常的平均场近似。

2008-09-05cond-mat.othercond-mat.stat-mech

二阶量子化约化Bloch方程与配对哈密顿量的精确解

Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian

在这篇文章中，我们提出了一组层次Bloch方程的约化密度算子的正则或巨正则系综在占领数表示。它们为研究某些模型系统的平衡态量子统计力学提供了方便的工具。作为它们的应用的一个例子，我们解决的模型系统的方程与配对的哈密顿量。借助于它的辛群对称性，我们得到了不同阶的统计约化密度矩阵。作为解的特例，我们还得到了超导体基态的约化密度矩阵。

2003-11-12cond-mat.stat-mech

实时量子多体动力学的非马尔可夫特性与不可逆性

Non-Markovian character and irreversibility of real-time quantum many-body dynamics

本研究针对核动力学中传统量子动理学的马尔可夫局限，探索正则波函数/自然轨道在多体计算中的应用，揭示超流TDDFT的非马尔可夫特性与不可逆性表征方法。

2024-06-20cond-mat.stat-mechnucl-th

Multiple Exclusion Statistics

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 states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function $\mathcal{G}(n)$ is introduced to account for the dep…

2019-06-10cond-mat.stat-mech

不同维囚禁玻色-爱因斯坦凝聚体的几率分布和粒子数涨落

Probability Distributions and Particle Number Fluctuations of Trapped Bose-Einstein Condensates in Different Dimensions

利用正则系综方法研究了一维、二维和三维服从玻色-爱因斯坦统计的有限系统的解析概率分布。本文从系统的正则配分函数出发，提供了一种统一的方法来研究凝聚体在不同约束和不同维数下的几率分布。基于概率分布函数，可以直接得到凝聚体的平均基态占据数和粒子数涨落。研究发现，玻色气体中粒子数的涨落与束缚势的类型和系统的维数密切相关。

2001-11-10cond-mat.softcond-mat.stat-mech

正则系综中量子蒙特卡罗模拟的循环更新

Loop updates for quantum Monte Carlo simulations in the canonical ensemble

提出了一种新的量子蒙特卡罗模拟的非定域更新方案，该方案保持了粒子数和其他对称性。它允许精确的对称投影和直接评估的等时格林函数和其他观测的正则系综。该方法适用于光晶格中的玻色子原子、原子核中的中子对和超小超导晶粒中的电子对。

2005-08-12cond-mat.stat-mechcond-mat.supr-connucl-th