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Journal articles on the topic 'Grand partition function'

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Published: 5 June 2025

Last updated: 24 June 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kuriyama, A., J. da Providencia, C. Providencia, Y. Tsue, and M. Yamamura. "Thermal Effect in Lipkin Model. II: Grand Partition Function and Mean Field Approximation." Progress of Theoretical Physics 95, no. 2 (1996): 339–51. http://dx.doi.org/10.1143/ptp.95.339.

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12

Matsumoto, Akira. "Critical Properties of Isobaric Processes of Lennard-Jones Gases." Zeitschrift für Naturforschung A 60, no. 1-2 (2005): 23–28. http://dx.doi.org/10.1515/zna-2005-1-204.

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The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T-P grand canonical ensemble Y(T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y(T,P,N) by the Legendre transformation G(T,P,N) = −kT logY(T,P,N). The volume, enthalpy, entropy, and heat capacity are analytically expressed as functions of the intensive variables temperature and pressure. Some critical thermodynamic quantities for Xe are calculated and drawn. At the critical point the heat capacity diverges to infinity, while the Gibbs free energy, volume, enthalpy, and entropy are continuous. This suggests that a second-order phase transition may occur at the critical point.

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13

Bornyakov, V. G., D. Boyda, V. Goy, et al. "Restoring canonical partition functions from imaginary chemical potential." EPJ Web of Conferences 175 (2018): 07027. http://dx.doi.org/10.1051/epjconf/201817507027.

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Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Zn(T) are coefficients of this expansion. Using various methods we study properties of Zn(T). At the last step we perform cubic spline for temperature dependence of Zn(T) at fixed n and compute baryon number susceptibility χB/T2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 163 × 4 lattice with mπ/mρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line Tc(µ2B) = Tc(C−ĸµ2B/T2c) with ĸ = −0.0453 ± 0.0099.

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14

PINTASSILGO, PEDRO, and MARKO LINDROOS. "COALITION FORMATION IN STRADDLING STOCK FISHERIES: A PARTITION FUNCTION APPROACH." International Game Theory Review 10, no. 03 (2008): 303–17. http://dx.doi.org/10.1142/s0219198908001959.

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In this paper the management of straddling fish stocks is approached through a coalition game in partition function form. A two-stage game is applied, assuming ex ante symmetric players and the classical Gordon-Schaefer bioeconomic model. It is shown that the game is characterized by positive externalities — the merger of coalitions increases the payoffs of players who belong to other coalitions. A key result is that, apart from the case of two players, the grand coalition is not a Nash equilibrium outcome. Furthermore, in the case of three or more players the only Nash equilibrium coalition structure is the one formed by singletons. The results indicate that the prospects of cooperation in straddling stock fisheries are low if players can free ride cooperative agreements. Thus, in order to protect cooperation, under the aegis of regional fishery management organizations, unregulated fishing must be prevented.

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15

Mandal, Sheikh Hannan, Rathindranath Ghosh, and Debashis Mukherjee. "A non-perturbative cumulant expansion method for the grand partition function of quantum systems." Chemical Physics Letters 335, no. 3-4 (2001): 281–88. http://dx.doi.org/10.1016/s0009-2614(01)00026-4.

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16

FORRESTER, P. J., and M. L. ROSINBERG. "CONFORMAL INVARIANCE IN ONE-DIMENSION AND A TWO-COMPONENT LOG-GAS." International Journal of Modern Physics B 04, no. 05 (1990): 943–52. http://dx.doi.org/10.1142/s0217979290000450.

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Conformal invariance in one-dimension implies the correlation functions must be constant. It is demonstrated by an exact solution that all the correlations between like species in a two-component lattice gas with the logarithmic potential have the conformal invariance property at the metal- insulator transition. A further exactly solvable isotherm of the model system is studied and the corresponding density of zeros for the grand partition function is obtained explicitly. A phase transition along this isotherm can be induced by appropriate choice of the parameters.

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17

RISCHKE, D. H., та W. GREINER. "A FUNCTIONAL INTEGRAL APPROACH TO THE THERMODYNAMICS OF THE σ-ω MODEL". International Journal of Modern Physics E 03, № 04 (1994): 1157–94. http://dx.doi.org/10.1142/s0218301394000358.

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We study the σ-ω model for nuclear matter at finite temperature and density in the functional integral approach. Particular emphasis is put on the treatment of the degrees of freedom of the massive vector meson. Various ways to calculate the grand partition function for free massive vector particles are presented. Then we show how field theories of two mutually interacting fields can be alternatively formulated in terms of a theory containing one free field and a nonlocal self-interaction of the other field. For a perturbative expansion in powers of the coupling constant and in the mean-field approximation, this formulation gives the same results as the standard treatment, e.g., the loop-expansion scheme of the effective potential. However, in contrast to the latter, the mean-field approximation is now obtained in a very simple and physically obvious way which closely resembles the analogous derivation for statistical-mechanical systems. We apply our alternative formulation to the case of scalar and massive vector particles interacting with another field. Combining both cases and taking the nucleon field as the interaction partner, we finally arrive at the grand partition function for the σ-ω model in mean-field approximation.

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18

Ciolli, Fabio, Francesco Fidaleo, and Chiara Marullo. "On the Thermodynamics of Particles Obeying Monotone Statistics." Entropy 25, no. 2 (2023): 216. http://dx.doi.org/10.3390/e25020216.

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The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called block-monotone, based on a partial order arising from the natural one on the spectrum of a positive Hamiltonian with compact resolvent. The block-monotone scheme is never comparable with the weak monotone one and is reduced to the usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian are non-degenerate. Through a detailed analysis of a model based on the quantum harmonic oscillator, we can see that: (a) the computation of the grand-partition function does not require the Gibbs correction factor n! (connected with the indistinguishability of particles) in the various terms of its expansion with respect to the activity; and (b) the decimation of terms contributing to the grand-partition function leads to a kind of “exclusion principle” analogous to the Pauli exclusion principle enjoined by Fermi particles, which is more relevant in the high-density regime and becomes negligible in the low-density regime, as expected.

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19

ANTONOV, DMITRI. "ENSEMBLE OF VORTEX LOOPS IN THE ABELIAN-PROJECTED SU(3)-GLUODYNAMICS." Modern Physics Letters A 14, no. 26 (1999): 1829–39. http://dx.doi.org/10.1142/s0217732399001917.

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Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case is the presence of two interacting gases of vortex loops. Two alternative representations for the partition function of such a grand canonical ensemble are derived, and one of them, which is a representation in terms of the integrals over vortex loops, is employed for the evaluation of the correlators of both kinds of loops in the low-energy limit.

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20

Lee, S. J., and A. Z. Mekjian. "Development of particle multiplicity distributions using a general form of the grand canonical partition function." Nuclear Physics A 730, no. 3-4 (2004): 514–47. http://dx.doi.org/10.1016/j.nuclphysa.2003.11.008.

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21

Kuriyama, A., J. d. Providencia, Y. Tsue, and M. Yamamura. "Pairing Model and Mixed State Representation. II: Grand Partition Function and Its Mean Field Approximation." Progress of Theoretical Physics 107, no. 1 (2002): 43–63. http://dx.doi.org/10.1143/ptp.107.43.

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22

Seikh, Hannan Mandal. "Calculation of grand partition function (gpf) of the symmetric and asymmetric double well potential by using path-integral based thermal cluster cumulant (PI-TCC) method." Journal of Indian Chemical Society Vol. 91, Mar 2014 (2014): 465–82. https://doi.org/10.5281/zenodo.5717629.

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Department of Chemistry, Rishi Bankim Chandra College, Naihati-743 165, North 24-Parganas, West Bengal, India <em>E-mail</em> : hanrkm1@yahoo.co.in <em>Manuscript received 01 April 2013, accepted 04 June 2013</em> In this paper, the grand partition function of symmetric and asymmetric double well potential is calculated by using Path-Integral based Thermal Cluster Cumulant (PI-TCC) method developed by us. This method like Feynman path-integral representation treats the cyclical path x(\(\tau\)) as a Fourier series with a sum of a classical centroid point, x<sub>0</sub> and a fluctuation variable, y(\(\tau\)). Then, y(\(\tau\)) is treated as a field variable. The contribution of the fluctuation component of the grand partition function (gpf) around x<sub>0</sub> is related to the y-average with respect to the y-dependent optimized Gaussian path-integral measure of an evolution operator, <em>U<sub>I</sub></em> (\(\tau\)) which satisfy an equation of motion in imaginary-time around x<sub>0</sub> . In the PI-representation, U<sub>I</sub> (\(\tau\)) is generically T-ordered product of y(\(\tau\))-variables. So, the y-average of <em>U<sub>I</sub></em> (\(\tau\)), denoted as <em>U<sub>I</sub></em> (\(\tau\)) y , is computed by utilising the concept of a Wick-like reordering theorem that needs the new concept of y-normal ordering and y-contraction. Then, the quantity <em>U<sub>I</sub></em> (\(\tau\)) y is computed nonperturbatively by using a y-normal ordered exponential cluster cumulant ansatz for <em>UI</em> (\(\tau\)) involving both the operator cumulant with y variables and the number cumulant. Now, <em>U<sub>I</sub></em> (\(\tau\)) y becomes exponential of only the number cumulant simply because by definition y-average of y-normal ordered product of operators vanishes. Finally, the grand partition function (gpf) is computed by integration over the <em>x</em><sub>0</sub> variables in the range for which the integrand almost vanishes at <em>–x<sub>0</sub></em> and at <em>+x<sub>0</sub></em> .

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23

Yukhnovskii, I. R. "The functional of the grand partition function for the investigation of the liquid-gas critical point." Physica A: Statistical Mechanics and its Applications 168, no. 3 (1990): 999–1020. http://dx.doi.org/10.1016/0378-4371(90)90268-w.

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24

SWAMY, P. NARAYANA. "THERMODYNAMICS OF q-MODIFIED BOSONS." International Journal of Modern Physics B 10, no. 06 (1996): 683–99. http://dx.doi.org/10.1142/s0217979296000283.

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Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

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25

Patsahan and Mryglod. "Functional representation for the grand partition function of a multicomponent system of charged particles: Correlation functions of the reference system." Condensed Matter Physics 9, no. 4 (2006): 659. http://dx.doi.org/10.5488/cmp.9.4.659.

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26

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." International Journal of Modern Physics B 17, no. 28 (2003): 5367–77. http://dx.doi.org/10.1142/s021797920302048x.

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We present here a succinct account of the finite-temperature generalisation of the coupled cluster (CC) method. It requires the concept of thermal normal ordered products whose Boltzmann trace is zero. The basic idea is to express the Boltzmann operator as a normal ordered exponential containing cluster operators and a number, and express the free energy as a logarithm of a suitable Boltzmann trace, where only the number part in the ordered exponential survives. The free energy is manifestly extensive. Free energies of Lipkin model and anharmonic oscillators obtained from the grand partition function are discussed as example applications.

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27

CORGINI, M., and D. P. SANKOVICH. "STUDY OF A NON-INTERACTING BOSON GAS." International Journal of Modern Physics B 16, no. 03 (2002): 497–509. http://dx.doi.org/10.1142/s0217979202009329.

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For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operators [Formula: see text] upper bounds on the thermal averages [Formula: see text] are obtained. These bounds lead to the proof of Bose–Einstein condensation for finite values of the inverse temperature β and for chemical potential μ=0. Finally for μ<0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.

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28

TAO, R., A. WIDOM, Z. C. TAO, and HOCK-KEE SIM. "THERMODYNAMIC STABILITY OF THE TWO-DIMENSIONAL JELLIUM MODEL IN A STRONG MAGNETIC FIELD." International Journal of Modern Physics B 03, no. 01 (1989): 129–34. http://dx.doi.org/10.1142/s0217979289000129.

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It is shown that two-dimensional jellium in a strong magnetic field is thermodynamically unstable. At filling factor v < 1, it produces a negative pressue and a negative compressibility, violating the second law of thermodynamics. The grand canonical partition function is convergent, but is not equivalent to the canonical ensemble. After Maxwell construction, the v < 1 state is a non-uniform phase-coexistent state. The application of this finding to the theoretical study of the fractional quantum Hall effect is also discussed.

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29

Seikh, Hannan Mandal. "A nonperturbative quantum transition state theory of reaction dynamics using Path-integral Thermal Cluster Cumulant (PI-TCC) method." Journal of Indian Chemical Society Vol. 92, Sep 2015 (2015): 1419–26. https://doi.org/10.5281/zenodo.5701783.

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Department of Chemistry, Rishi Bankim Chandra College, Naihati-743 165, North 24-Parganas, West Bengal, India <em>E-mail</em> : hanrkm1@yahoo.co.in <em>Manuscript received 05 December 2014, accepted 05 February 2015</em> In this particle, a nonperturbative path-integral quantum transition state (PI-QTST) theory is proposed for estimating quantum effect in reaction dynamics in which the rate of the reaction is successfully modelled as the crossing of quantum particle over the free barrier of the double-well potential. It is well known that the rate essentially depends on the centroid density ρ(x<sub>0</sub>*) at the top of the barrier x<sub>0</sub>* dividing the two well representing the two stable configurations and x is defined along the reaction coordinate in one dimension. In path-integral approach to quantum transition state theory (PI-QTST), the quantum effect is estimated by calculating the ratio of the quantum grand partition function constrained to x<sub>0</sub>*, Z<sub>q</sub> (x<sub>0</sub>*) to its classical counterpart Z<sub>cl</sub>(x<sub>0</sub>*) and is called quantum correction factor, Γ. The quantum grand partition function Zq (x<sub>0</sub>*) is computed by using our non-perturbative Path-integral based Thermal Cluster Cumulant (PI-TCC) method. It is also shown that the value of quantum correction factor, Γ tends to unity as the temperature goes high indicating the validity of the theory.

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30

Brambilla, M., A. Giovannini, and R. Ugoccioni. "Maps of zeros of the grand canonical partition function in a statistical model of high energy collisions." Journal of Physics G: Nuclear and Particle Physics 32, no. 6 (2006): 859–70. http://dx.doi.org/10.1088/0954-3899/32/6/009.

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31

Mandal, Sheikh Hannan, Rathindranath Ghosh, Goutam Sanyal, and Debashis Mukherjee. "A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems." Chemical Physics Letters 352, no. 1-2 (2002): 63–69. http://dx.doi.org/10.1016/s0009-2614(01)01424-5.

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32

Saryal, Sushant, and Deepak Dhar. "Exact results for interacting hard rigid rotors on a d-dimensional lattice." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 4 (2022): 043204. http://dx.doi.org/10.1088/1742-5468/ac6038.

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Abstract We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is situated asymmetrically on the object, we show that there is a range of lattice spacings a, where in any orientation, a particle can overlap with at most one of its neighbors. In this range, the entropy of the system of particles can be expressed exactly in terms of the grand partition function of coverings of the base lattice by dimers at a finite negative activity. The exact entropy in this range is fully determined by the second virial coefficient. Calculation of the partition function is also shown to be reducible to that of the same model with discretized orientations. We determine the exact functional form of the probability distribution function of orientations at a site. This depends on the density of dimers for the given activity in the dimer problem, which we determine by summing the corresponding Mayer series numerically. These results are verified by numerical simulations.

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33

Tawfik, Abdel. "Phase Space and Dynamical Fluctuations of Kaon-to-Pion Ratios." Progress of Theoretical Physics 126, no. 2 (2011): 279–92. http://dx.doi.org/10.1143/ptp.126.279.

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Abstract The dynamical fluctuations of kaon-to-pion ratios have been studied over a wide range of center-of-mass energies √s. On the basis of changing phase space volume which apparently is the consequence of phase transition from hadrons to quark-gluon plasma at large √s, the single-particle distribution function f is assumed to be rather modified. Varying f and phase space volume are implemented in the grand-canonical partition function, especially at large √s, so that the hadron resonance gas model, when taking into account the experimental acceptance and quark phase space occupation factor, turns to be able to reproduce the dynamical fluctuations of kaon-to-pion ratios over the entire range of √s.

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34

Kozlovskii, M., and O. Dobush. "Representation of the grand partition function of the cell model: The state equation in the mean-field approximation." Journal of Molecular Liquids 215 (March 2016): 58–68. http://dx.doi.org/10.1016/j.molliq.2015.12.018.

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35

Patsagan, O. V., and I. R. Yukhnovskii. "Functional of the grand partition function in the method of collective variables with distinguished reference system. Multicomponent system." Theoretical and Mathematical Physics 83, no. 1 (1990): 387–95. http://dx.doi.org/10.1007/bf01019137.

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36

Ou, Meng-Jun, and Ji-Xuan Hou. "Harmonically confined Bose–Einstein condensation on the surface of a cylinder." Modern Physics Letters B 35, no. 17 (2021): 2150285. http://dx.doi.org/10.1142/s0217984921502857.

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It is well known that Bose–Einstein condensation cannot occur in a free two-dimensional (2D) system. Recently, several studies have showed that BEC can occur on the surface of a sphere. We investigate BEC on the surface of cylinder on both sides of which atoms are confined in a one-dimensional (1D) harmonic potential. In this work, only the non-interacting Bose gas is considered. We determine the critical temperature and the condensate fraction in the geometry using the semi-classical approximation. Moreover, the thermodynamic properties of ideal bosons are also studied using the grand canonical partition function.

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37

Chebotarev, Ivan, Vladislav Guskov, Stanislav Ogarkov, and Matthew Bernard. "S-Matrix of Nonlocal Scalar Quantum Field Theory in Basis Functions Representation." Particles 2, no. 1 (2019): 103–39. http://dx.doi.org/10.3390/particles2010009.

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Nonlocal quantum theory of a one-component scalar field in D-dimensional Euclidean spacetime is studied in representations of S -matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant g in the form of an infrared smooth function of argument x for space without boundary. Nonlocality is given by the evolution of a Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter l. By representation of the S -matrix in terms of abstract functional integral over a primary scalar field, the S form of a grand canonical partition function is found. By expression of S -matrix in terms of the partition function, representation for S in terms of basis functions is obtained. Derivations are given for a discrete case where basis functions are Hermite functions, and for a continuous case where basis functions are trigonometric functions. The obtained expressions for the S -matrix are investigated within the framework of variational principle based on Jensen inequality. Through the latter, the majorant of S (more precisely, of - ln S ) is constructed. Equations with separable kernels satisfied by variational function q are found and solved, yielding results for both polynomial theory φ 4 (with suggestions for φ 6 ) and nonpolynomial sine-Gordon theory. A new definition of the S -matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are obtained and numerically illustrated, with plots of variational functions q and corresponding majorants for the S -matrices of the theory. For simplicity of numerical calculation, the D = 1 case is considered, and propagator for free theory G is in the form of Gaussian function typically in the Virton–Quark model, although the obtained analytical inferences are not, in principle, limited to these particular choices. Formulation for nonlocal QFT in momentum k space of extra dimensions with subsequent compactification into physical spacetime is discussed, alongside the compactification process.

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Paul, Chandrima. "Integrability of type 0A matrix model in the presence of D-brane." International Journal of Modern Physics A 34, no. 03n04 (2019): 1950020. http://dx.doi.org/10.1142/s0217751x19500209.

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We consider type 0A matrix model in the presence of spacelike D-brane which is localized in matter direction at any arbitrary point. In string theory, the boundary state, which in matrix model corresponds to the Laplace transform of the macroscopic loop operator, is known to obey the operator constraints corresponding to open string boundary condition. When we analyze MQM as well as the respective collective field theory and compare it with dual string theory, it appears that consistency of the theory requires a condition equivalent to a constraint on the matter part that needed to be imposed in the matrix model. We identified this condition and observed that this results in constraining the macroscopic loop operator so that it projects the Hilbert space generated by the operator to its physical sector at the point of insertion while keeping the bulk matrix model unaffected, thereby describing a situation parallel to string theory. We analyzed the theory with uncompactified time and have shown explicitly that the matrix model predictions are in good agreement with the relevant string theory. Next, we considered the theory with compactified time, analyzed MQM on a circle in the presence of D-brane. We evaluated the partition function along with the constrained macroscopic loop operator in the grand canonical ensemble and showed the free energy corresponds to that of a deformed Fermi surface. We have also shown that the path integral in the presence of D-brane can be expressed as the Fredholm determinant. We have studied the fermionic scattering in a semiclassical regime. Finally, we considered the compactified theory in the presence of the D-brane with tachyonic background. We evaluated the free energy in the grand canonical ensemble. We have shown the integrable structure of the respective partition function and it corresponds to the tau function of Toda hierarchy. We have also analyzed the dispersionless limit.

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39

MABIALA, J., A. BONASERA, H. ZHENG, et al. "CRITICAL SCALING OF TWO-COMPONENT SYSTEMS FROM QUANTUM FLUCTUATIONS." International Journal of Modern Physics E 22, no. 12 (2013): 1350090. http://dx.doi.org/10.1142/s0218301313500900.

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The thermodynamics of excited nuclear systems allows the exploration of a phase transition in a two-component quantum mixture. Temperatures and densities are derived from quantum fluctuations of fermions. The pressures are determined from the grand partition function of Fisher's model. Critical scaling of observables is found for the first time for fragmenting systems which differ in neutron to proton concentrations thus constraining the equation of state (EOS) of asymmetric nuclear material. The derived critical exponent, β = 0.35 ±0.01, belongs to the liquid–gas universality class. The critical compressibility factor Pc/ρcTc increases with increasing neutron concentration, which could be due to finite-size and/or Coulomb effects.

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40

Nagamori, Meguru. "Second nearest-neighbor interactions in ternary regular solutions." Canadian Journal of Chemistry 70, no. 10 (1992): 2569–73. http://dx.doi.org/10.1139/v92-326.

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The concept of classical regular solutions has been expanded by considering both first and second nearest-neighbor interactions between randomly distributed molecules. While the present model requires an ideal entropy of mixing, as does the classic regularity model, its heat of mixing is expressed by a more flexible equation which attributes the second-order terms of the Margules formalism to first nearest-neighbor interactions, and the third-order terms to second nearest-neighbor interactions. The activity–composition relations have been expressed by a single equation of the grand partition function, which converges to that of the classical regularity with decreasing contributions from second nearest-neighbor molecules.

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41

Joyce, G. S. "On the icosahedral equation and the locus of zeros for the grand partition function of the hard-hexagon model." Journal of Physics A: Mathematical and General 22, no. 6 (1989): L237—L242. http://dx.doi.org/10.1088/0305-4470/22/6/009.

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42

Salmhofer, Manfred. "Functional Integral and Stochastic Representations for Ensembles of Identical Bosons on a Lattice." Communications in Mathematical Physics 385, no. 2 (2021): 1163–211. http://dx.doi.org/10.1007/s00220-021-04010-4.

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AbstractRegularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is proven for various discretized actions. The focus is on the integral representation for the partition function and expectation values in the canonical ensemble. The connection to the grand-canonical integral is exhibited and some important differences are discussed. Uniform bounds for covariances are proven, which simplify the analysis of the time-continuum limit and can also be used to analyze the thermodynamic limit. The relation to a stochastic representation by an ensemble of interacting random walks is made explicit, and its modifications in presence of a condensate are discussed.

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43

HAN, FUXIANG, MINGHAO LEI, and E. WU. "SIMULTANEOUS ONSET OF CONDENSATION OF MOLECULES AND ATOMS IN AN ATTRACTIVE FERMI GAS OF ATOMS." Modern Physics Letters B 21, no. 01 (2007): 51–58. http://dx.doi.org/10.1142/s0217984907012396.

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The self-consistent equations for the order parameters of Bose–Einstein condensation (BEC) of molecules and Bardeen–Cooper–Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms have been derived within the Hartree–Fock–Bogoliubov approximation from the path integral representation of the grand partition function. We have found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We have also found that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.

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PANZERI, STEFANO. "THE c=1 MATRIX MODEL FORMULATION OF TWO-DIMENSIONAL YANG-MILLS THEORIES." Modern Physics Letters A 08, no. 33 (1993): 3201–14. http://dx.doi.org/10.1142/s0217732393002130.

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We find the exact matrix model description of two-dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary semisimple compact gauge group. This matrix model is the singlet sector of a c=1 matrix model where the matrix field is in the fundamental representation of the gauge group. We also prove that the basic constituents of the theory are Sutherland fermions in the zero coupling limit, and this leads to an interesting connection between two-dimensional gauge theories and one-dimensional integrable systems. In particular we derive for all the classical groups the exact grand canonical partition function of the free fermion system corresponding to a two-dimensional gauge theory on a torus.

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Senay, Mustafa, and Salih Kibaroglu. "Thermosize effects in a q-deformed fermion gas model." Modern Physics Letters B 32, no. 20 (2018): 1850230. http://dx.doi.org/10.1142/s0217984918502305.

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We study the the high-temperature thermodynamic properties of the q-deformed fermion gas model by taking into account of the size effect of the gas particles. Starting from the logarithm of the grand partition function of the model, we calculate several thermodynamic functions of the model such as internal energy, entropy, and Helmholtz free energy by means of the deformation parameter q. Furthermore, the influences of the fermionic q-deformation on the thermosize effect in the confined deformed quantum gas systems such as the Seebeck-like and Peltier-like thermosize effects are discussed. Especially, we focus on the absorbed or released heat of the model in the Peltier-like thermosize effect. In the light of the results obtained in this work, we can conclude that the present q-deformed fermion model can be used to desing the new types of the micro-/nano-scaled quantum heat engines.

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Abraham, E., I. M. Barbour, P. H. Cullen, E. G. Klepfish, E. R. Pike, and Sarben Sarkar. "Monte Carlo finite-size analysis of Yang-Lee zeros of the grand canonical partition function for a 2D Hubbard model." Physica C: Superconductivity 235-240 (December 1994): 2425–26. http://dx.doi.org/10.1016/0921-4534(94)92433-3.

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47

Desgranges, Caroline, and Jerome Delhommelle. "Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. III. Impact of combining rules on mixtures properties." Journal of Chemical Physics 140, no. 10 (2014): 104109. http://dx.doi.org/10.1063/1.4867498.

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48

Fang, Ren-Hong, Ren-Da Dong, De-Fu Hou, and Bao-Dong Sun. "Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field." Chinese Physics Letters 38, no. 9 (2021): 091201. http://dx.doi.org/10.1088/0256-307x/38/9/091201.

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We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel–Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable b = 2eB/T 2. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass correction to chiral separation effect is discussed. For massless chiral fermions, our results recover the chiral magnetic effect for right- and left-handed fermions, as well as chiral separation effect.

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MATERDEY, TOMAS B. "GRAND CANONICAL MIXED-STATE WIGNER FUNCTION IN A MAGNETIC FIELD: de HAAS–van ALPHEN OSCILLATIONS." International Journal of Modern Physics B 21, no. 06 (2007): 829–55. http://dx.doi.org/10.1142/s0217979207036680.

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Kohn proved in 1961 that interactions between electrons did not change the de Haas–van Alphen (dHvA) oscillation frequency for single electrons in the nondegenerate ground-state [Phys. Rev.123(4), 1242 (1961)]. It was proved recently that the pure-state Wigner function for an electron in a magnetic field carries this quantum and physical oscillation, and a quantum dielectric function, so the conductance can be calculated from the Wigner function [Int. J. Mod. Phys. B17(25), 4555 (2003)], [Int. j. Mod. Phys. B17(26), 4683 (2003)]. We present the first complete proof that at a finite temperature, the mixed-state Wigner function also shows dHvA oscillations with the same frequency. The Wigner function is a fundamental quantity, the fact that it carries observable physical information shows a great potential in the design of new quantum materials at the nanoscale. The definition of the mixed-state Wigner function involves a grand canonical partition function (GCPF). Although dHvA is a well-known phenomenon, we present the first complete proof of it happening in degenerate mixed-states, based on a GCPF, which requires reconciliation between the dHvA experimental condition of a fixed number of particles and the GCPF's sum over number of particles. The GCPF is applied to one of the two spin species, while both the spin and spin-magnetic moment interaction are considered. We show that the contour integration in ω(ε) leads to a non-oscillatory term that is much larger than an oscillatory term, in the dHvA experimental conditions of high fields and low temperatures. This dominance of the non-oscillatory term explains the constancy of the chemical potential, allowing it to reduce to the Fermi energy in the limit of zero temperature. The obtained mixed-state Wigner function shows a fundamental period of oscillation with respect to B-1 that reduces to the Onsager's period for dHvA oscillations. This indicates that in mixed-states, dHvA oscillations depend on electrons of one spin species, this means the population of electrons of each spin species oscillates with the magnetic field. The temperature dependence in the Wigner function will allow a combination of phase-space and thermodynamics information for mesoscopic structures, and the study of phase-space density holes such as BGK modes in the quantum domain.

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BARRY, J. H., and N. S. SULLIVAN. "EXACT PHASE DIAGRAMS FOR THE CONDENSATION OF A KAGOMÉ LATTICE GAS WITH THREE-PARTICLE INTERACTIONS." International Journal of Modern Physics B 07, no. 15 (1993): 2831–57. http://dx.doi.org/10.1142/s0217979293003061.

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The condensation of a two-dimensional kagomé lattice gas having purely three-particle interactions is first theoretically investigated. The Hamiltonian Hℓg=−∈3Σ<i, j, k> ninjnk, where ∈3>0 is the strength. parameter of the short-range attractive triplet interaction, the sum is taken over all elementary triangles of the kagomé lattice, and nℓ=0, 1 is an idempotent site-occupation number. The method initially involves transforming the lattice-gas model into a generalized kagomé Ising model having both pair and triplet interactions as well as a magnetic field. Since the canonical partition function of a generalized kagomé Ising model is equivalent (aside from known prefactors) to the canonical partition function of a standard honeycomb Ising model in a magnetic field, one can deduce the exact liquid-vapor phase diagrams of the triplet-interaction kagomé lattice gas from its grand canonical partition function. As results, the liquid-vapor phase boundary (reduced chemical potential μ/∈3 vs reduced temperature T/Tc) is found to be curvilinear with a positive slope, originating at zero temperature with μ/∈3=−2/3 and analytic at its terminating critical point whose coordinates are T/Tc=1, μc/∈3=−0.64469…, where ∈3/kBTc=3.96992…. The companion coexistence curve (particle number density ρ vs. reduced temperature T/Tc) exhibits an asymmetric rounded shape with a positive-slope curvilinear diameter, and the value of the critical density ρc=0.58931…. At criticality, the expression for the coexistence curve superposes a pair of branch point singularities resulting in an infinite (vertical) slope at the critical point (T/Tc=ρ/ρc=1). The case of a kagomé lattice gas having mixed attractive pair interactions and very weak repulsive triplet interactions (Axilrod-Teller) is next considered. Perturbation analyses upon exact expressions relating to the phase diagrams reveal, over chosen ranges of reduced temperatures, that the phase boundary and the diameter of the two-phase coexistence region each have a negative slope due to the repulsive three-particle interactions.

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