Relevant bibliographies by topics / Grand partition function

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Academic literature on the topic 'Grand partition function'

Author: Grafiati
Published: 5 June 2025
Last updated: 24 June 2025

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Journal articles on the topic "Grand partition function"

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Kozlovskii, M. P., O. A. Dobush, and R. V. Romanik. "Concerning a Calculation of the Grand Partition Function Of A Fluid Model." Ukrainian Journal of Physics 60, no. 8 (2015): 808–25. http://dx.doi.org/10.15407/ujpe60.08.0808.

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Nagamori, Meguru, Kimihisa Ito, and Motonori Tokuda. "The grand partition function of dilute biregular solutions." Metallurgical and Materials Transactions B 25, no. 5 (1994): 703–11. http://dx.doi.org/10.1007/bf02655178.

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Sari, R. Yosi Aprian, and W. S. B. Dwandaru. "DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES." Jurnal Sains Dasar 4, no. 2 (2016): 179. http://dx.doi.org/10.21831/jsd.v4i2.9096.

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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
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Ciolli, Fabio, and Francesco Fidaleo. "On the Thermodynamics of the q-Particles." Entropy 24, no. 2 (2022): 159. http://dx.doi.org/10.3390/e24020159.

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Since the grand partition function Zq for the so-called q-particles (i.e., quons), q∈(−1,1), cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q=0, and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q∈[−1,1]. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., q=0) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor 1/n! in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons q∈(0,1).
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Bialas, P., Z. Burda, and D. A. Johnston. "Partition function zeros of zeta-urns." Condensed Matter Physics 27, no. 3 (2024): 33601. http://dx.doi.org/10.5488/cmp.27.33601.

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We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for finite-size systems and test scaling relations describing the accumulation of zeros near the critical point against theoretical predictions for both the first and higher order transition regimes.
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Harata, Pipat, and Prathan Srivilai. "Grand canonical partition function of a serial metallic island system." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 013101. http://dx.doi.org/10.1088/1742-5468/ac3e6c.

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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.
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Barbour, I. M., and E. G. Klepfish. "Grand-canonical partition function of a two-dimensional Hubbard model." Physical Review B 46, no. 1 (1992): 469–78. http://dx.doi.org/10.1103/physrevb.46.469.

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MASHARIAN, SEYEDEH RAZIYEH, and FARHAD H. JAFARPOUR. "A HETEROGENEOUS ZERO-RANGE PROCESS RELATED TO A TWO-DIMENSIONAL WALK MODEL." International Journal of Modern Physics B 26, no. 09 (2012): 1250044. http://dx.doi.org/10.1142/s0217979212500440.

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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.
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AHMAD, FAROOQ, MANZOOR A. MALIK, and SAJAD MASOOD. "DISTRIBUTION FUNCTION OF GALAXIES FOR TWO-COMPONENT SYSTEMS." International Journal of Modern Physics D 15, no. 08 (2006): 1267–82. http://dx.doi.org/10.1142/s0218271806008875.

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We extend the statistical mechanical theory of cosmological many-body problem to a system consisting of two kinds of galaxies with different masses. The general partition function for such a two-component system, in the grand canonical ensemble, is developed. From this partition function various thermodynamical quantities and distribution functions are evaluated. A quantity bm, called the clustering parameter for the two-component system, which inherently takes into account the ratio of the number of particles (galaxies) of each kind and their masses, emerges directly from the calculations. Various clustering phenomena can be explained on the basis of this parameter. We find these results in agreement with the available N-body simulation results as well as the observational distribution function determined from the 2MASS survey. Besides, our distribution function, for the two-component system, makes these comparisons more objective and easily comprehensible.
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Chaturvedi, S., P. K. Panigrahi, V. Srinivasan, and R. MacKenzie. "Equivalence of the Grand Canonical Partition Functions of Particles with Different Statistics." Modern Physics Letters A 12, no. 15 (1997): 1095–99. http://dx.doi.org/10.1142/s0217732397001114.

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It is shown that the grand partition function of an ideal Bose system with single particle spectrum εi=(2n+k+3/2)ℏω is identical to that of a system of particles with single particle energy εi=(n+1/2)ℏω and obeying a particular kind of statistics based on the permutation group.
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Books on the topic "Grand partition function"

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Horing, Norman J. Morgenstern. Quantum Mechanical Ensemble Averages and Statistical Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0006.

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Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.
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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.
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Book chapters on the topic "Grand partition function"

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Kim, S. Y., and R. J. Creswick. "Zeros of the Grand Partition Function of the Potts Model in a Magnetic Field." In Springer Proceedings in Physics. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-60095-1_19.

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"The Grand Canonical Ensemble and Grand Partition Function." In Statistical Physics. John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781118597507.ch7.

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"Appendix C: The Grand Partition Function: Derivation and Relation to Other Types of Partition Functions." In Equilibria and Kinetics of Biological Macromolecules. John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118733639.app3.

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Swendsen, Robert H. "Classical Ensembles: Grand and Otherwise." In An Introduction to Statistical Mechanics and Thermodynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.003.0020.

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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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Eckle, Hans-Peter. "Equilibrium Statistical Mechanics." In Models of Quantum Matter. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0004.

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Chapter 4 reviews the basic notions of equilibrium statistical mechanics and begins with its fundamental postulate and outlines the structure of the theory using the most important of the various statistical ensembles, the microcanonical, the canonical, and the grand canonical ensemble and their corresponding thermodynamic potential, the internal energy, the Helmholtz free energy, and the grand canonical potential. The notions of temperature, pressure, and chemical potential are obtained and it introduces the laws of thermodynamics, the Gibbs entropy, and the concept of the partition function. It also discusses quantum statistical mechanics using the density matrix and as applied to non-interacting Bosonic and Fermionic quantum gases, the former showing Bose–Einstein condensation. The mean-field theory of interacting magnetic moments and the transfer matrix to exactly solve the Ising model in one dimension serve as applications.
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Tuckerman, Mark E. "Quantum ideal gases: Fermi-Dirac and Bose-Einstein statistics." In Statistical Mechanics: Theory and Molecular Simulation, 2nd ed. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780198825562.003.0011.

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Abstract Chapter 11 presents a statistical mechanical treatment of the quantum ideal gases, i.e., the ideal Boltzmann, fermion, and boson gases. The discussion begins with the microscopic description and the solution of the eigenvalue problem for a quantum ideal gas. It is argued that calculating the partition function is most readily accomplished in the grand canonical ensemble using a second-quantized formulation. When the particles are distinguishable, the equation of state is identical to that of a classical ideal gas. For fermions and bosons, however, the problem of computing thermodynamic properties is significantly more complex and can only be solved exactly in certain limits. Away from these limits approximations are needed and are discussed in detail. The relevant distributions - the Fermi-Dirac and Bose-Einstein distributions are derived. The local density approximation of density functional theory is derived for the ideal electron gas. For the ideal boson gas, the phenomenon of Bose-Einstein condensation is discussed
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Prašmantaitė, Aldona. "Kanonicy regularni od pokuty prowincji litewskiej na ziemiach byłego Wielkiego Księstwa Litewskiego w pierwszych latach po rozbiorach Rzeczypospolitej." In Duchowe korzenie błogosławionego Michała Giedroycia: Zakon Kanoników Regularnych od Pokuty. Ksiegarnia Akademicka Publishing, 2021. http://dx.doi.org/10.12797/9788381385848.03.

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CANONS REGULAR OF PENANCE OF THE LITHUANIAN PROVINCE ON THE TERRITORY OF THE FORMER GRAND DUCHY OF LITHUANIA IN EARLY YEARS AFTER THE PARTITION OF POLISH LITHUANIAN COMMONWEALTH The history of Canons Regular of Penance (Ordo Canonicorum S. Mariae de Metro [or Demetri] de Urbe de Poenitentia Beatorum Martyrum) on the territory of the Grand Duchy of Lithuania began in the end of the 14th century. The king of Poland and Grand Duke of Lithuania Władysław Jagiełło brought Canons of Penance from Cracow to the just christened Lithuania and founded for them two monasteries in the parishes of the diocese of Vilnius. Over centuries, new communities of the convent arose in the Vilnius diocese with their number reaching almost twenty in certain periods. Towards the end of the 17th century, the new Lithuanian Province was established. Partitions of Polish-Lithuanian Commonwealth in the end of the 18th century caused serious transformations within the Catholic Church of the Grand Duchy of Lithuania, which affected Canons Regular, as well. The Vilnius diocese, where the communities of the Lithuanian Province stayed, found itself under power of the Russian Empire. Repressions against the Catholic Church led to cassation of the Canon’s convents of the Lithuanian Province after the November Uprising (1830-31). On the ground of the literature and sources related to the Canons Regular of Penance of the Lithuanian Province, the research concerning their history in the early years after partition has been undertaken. The analysis proved the initial hypothesis that in the early years after partition, Canons Regular of the Lithuanian Province were still vital. Nothing indicated that their end was coming. The rule of the convent strongly emphasized pastoral work. The majority of its members were priests, active in parishes as parish-priests or vicars. Even though the number of vocations started to decrease after the partitions – there were even years when nobody joined the community – the convent functioned successfully enough. According to the rule, the priority was given to pastoral work and all 15 convents had their own parishes in the said period. A typical representative of the convent during the early stage after partitions was middle-aged and ordained, usually a parish priest or his auxiliary in the parish belonging to the convent on a given territory. Usually, a monk appointed to a certain office would hold it for several terms. The presented research demonstrates that the convent of Canons Regular had a relatively big influence upon the spiritual life of the Vilnius diocese during the said period.
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Zinn-Justin, Jean. "Quantum statistical physics: Functional integration formalism." In Quantum Field Theory and Critical Phenomena. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0004.

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The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.
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Conference papers on the topic "Grand partition function"

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IGUCHI, KAZUMOTO. "A THEORY OF INTERACTING MANY-BODY SYSTEMS WITH EXCLUSION STATISTICS: ORIGIN OF EXCLUSION STATISTICS, HALDANE LIQUIDS, SUTHERLAND-WU EQUATIONS, GRAND PARTITION FUNCTION AND LEE-YANG THEOREM." In Proceedings of the Nagoya 1999 International Workshop. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810199_0004.

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MANDAL, SEIKH HANNAN, RATHINDRANATH GHOSH, GOUTAM SANYAL, and DEBASHIS MUKHERJEE. "A FINITE-TEMPERATURE GENERALISATION OF THE COUPLED CLUSTER METHOD: A NON-PERTURBATIVE ACCESS TO GRAND PARTITION FUNCTIONS." In Proceedings of the 11th International Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777843_0044.

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Lee, Chae J., Bernard D. Reger, Matthew C. Tresch, J. Edward Colgate, and Ferdinando A. Mussa-Ivaldi. "Emulation of Biological Motor Primitives in an Artificial System: The Generation of Static Force Fields." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0122.

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Abstract We have used observations of posture and movements in biological limbs to derive a controller for an artificial mechanism. The controller architecture emulates some of the known relations between spinal cord circuitry and the musculoskeletal system of vertebrates and, specifically, of the rat. This work relates to recent experiments suggesting that the neural circuitry of the spinal cord may be partitioned into a small set of functional modules. Activation of these modules, each connected to a set of limb muscles, resulted in force fields that have been measured at the endpoint of a limb. These force fields map each position of the foot into a corresponding static force vector. The force fields have been found to converge toward equilibrium positions located inside the leg’s workspace. The experimental observation that vector fields induced by multiple stimulations add vectorially, suggested that convergent force fields form a system of building blocks (or “primitives”) for the generation of stable postures and movements. To emulate this biological mechanism in the control of an artificial two-joint limb, we established relationships among three hierarchical levels — spinal modules, muscles, and actuators — by deriving the mappings among the respective output fields. These mappings are used in combination with an inverse model of the actuators to calculate the actuator commands that generate a desired force field. We tested the ability of this control system to reproduce the force fields generated by the leg muscles of the rat and a set of force fields with significant geometrical features. Our results show that we can successfully and reliably transfer to our artificial system the features of muscle force fields. In addition, we exploited the same principle of vector summation observed in the biological system to combine these muscle fields into a variety of force field patterns, including the gradients of Gaussian potentials and locally parallel fields. We consider this a first step in the generation of a biomorphic motor control system. This work is supported by ONR grant N00014-95-1-0571 and NIH grant MH48185.
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