scholarly journals Grand canonical partition function of a serial metallic island system

2022 ◽  
Vol 2022 (1) ◽  
pp. 013101
Author(s):  
Pipat Harata ◽  
Prathan Srivilai
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Electron Number ◽  
Canonical Partition Function ◽  
Grand Canonical Partition Function ◽  
Large Channel ◽  
Phase Fields ◽  
Island System ◽  
Average Electron ◽  
Grand Canonical

Abstract We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path probability given in an analytically known effective action functional. Using the result, we also propose a calculation of the average electron number of the serial island system in terms of the expectation value of winding numbers. Finally, as an example, we describe the Coulomb blockade effect in the two-island system by the average electron number and propose a method to construct the quantum stability diagram.

scholarly journals A HETEROGENEOUS ZERO-RANGE PROCESS RELATED TO A TWO-DIMENSIONAL WALK MODEL

2012 ◽  
Vol 26 (09) ◽  
pp. 1250044 ◽  
Author(s):  
SEYEDEH RAZIYEH MASHARIAN ◽  
FARHAD H. JAFARPOUR
Keyword(s):  
Partition Function ◽  
Matrix Product ◽  
Two Dimensional ◽  
Canonical Partition Function ◽  
Zero Range Process ◽  
Grand Canonical Partition Function ◽  
Driven Diffusive System ◽  
Zero Range ◽  
Grand Canonical ◽  
Range Process

We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a matrix product formalism and that it is exactly equal to the partition function of a two-dimensional walk model. The canonical partition function of this process is also calculated. Two simple examples are presented in order to confirm the results.

scholarly journals DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

2016 ◽  
Vol 4 (2) ◽  
pp. 179
Author(s):  
R. Yosi Aprian Sari ◽  
W. S. B. Dwandaru
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Canonical Partition Function ◽  
Thermodynamics Properties ◽  
Grand Canonical Partition Function ◽  
Bose Einstein ◽  
Grand Canonical ◽  
Number Of Particles

This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties

Classical Ensembles: Grand and Otherwise

2019 ◽  
pp. 258-265
Author(s):  
Robert H. Swendsen
Keyword(s):  
Partition Function ◽  
Particle Number ◽  
Canonical Ensemble ◽  
Ideal Gas ◽  
Grand Canonical Ensemble ◽  
Physical Situation ◽  
Canonical Partition Function ◽  
Grand Canonical Partition Function ◽  
Grand Canonical ◽  
The Ideal

The chapter introduces the grand canonical ensemble as a means of describing systems that exchange particles with a reservoir. The grand canonical partition function is defined in general and calculated for the ideal gas in particular. Other ensembles are described and their relationship to the grand canonical ensemble is shown. The physical situation described by the grand canonical ensemble is that of a system that can exchange both energy and particles with a reservoir. As usual, we assume that the reservoir is much larger than the system of interest, so that its properties are not signifficantly affected by relatively small changes in its energy or particle number.

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