Complex pole approach in thermodynamic description of fluid mixtures with small number of molecules

Aslyamov, Timur; Dinariev, O. Yu.

doi:10.1016/j.physleta.2014.10.014

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…In spite of long history of these problems major results were obtained for idealized smooth surfaces of the solid. However, real surfaces are usually rough, so influence of geometry on adsorption and other thermodynamic processes is actively investigated in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

Khlyupin

Aslyamov

2017

J Stat Phys

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Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarsegrained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations shows good qualitative agreement with the theory predictions. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.

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Section: Introductionmentioning

confidence: 99%

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

Khlyupin

Aslyamov

2017

J Stat Phys

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“…Refs. [32][33][34][35][36][37]. Dynamical phase transitions in the thermodynamic limit can be detected using transfer matrix approach 38 .…”

Section: Introductionmentioning

confidence: 99%

Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain

et al. 2016

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Quantum dynamics of magnetic order in a chiral multiferroic chain is studied. We consider two different scenarios: Ultrashort terahertz (THz) excitations or a sudden electric field quench. Performing analytical and numerical exact diagonalization calculations we trace the pulse induced spin dynamics and extract quantities that are relevant to quantum information processing. In particular, we analyze the dynamics of the system chirality, the von Neumann entropy, the pairwise and the many body entanglement. If the characteristic frequencies of the generated states are non-commensurate then a partial loss of pair concurrence occurs. Increasing the system size this effect becomes even more pronounced. Many particle entanglement and chirality are robust and persist in the incommensurate phase. To analyze the dynamical quantum transitions for the quenched and pulsed dynamics we combined the Weierstrass factorization technique for entire functions and Lanczos exact diagonalization method. For a small system we obtained analytical results including the rate function of Loschmidt echo. Exact numerical calculations for a system up to 40 spins confirm phase transition. Quenchinduced dynamical transitions have been extensively studied recently. Here we show that related dynamical transitions can be achieved and controlled by appropriate electric field pulses.

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“…Therefore, Information about the the partition function zeros distribution of an finite number of molecules is crucial to calculate singularities at thermodynamic limit. Considering the finite (small) systems, the thermodynamic properties strongly depend on used statistical ensemble [3][4][5][6]. Hence, constant number of molecules at canonical ensemble is described by Fisher zeros in the plane of complex temperature [7], which exhibit more complicated limit behaviour than Lee-Yang zeros [8].…”

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confidence: 99%

“…Thus, expression (13) with equation ( 14) allows to calculate the p.f. in NPT-ensemble for any λ and for finite number of molecules N (it is useful for application to small systems [5]). Obtained partition function ( 13) is similar to the ones of Potts and hard hexagons models in terms of transfer matrix [20].…”

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confidence: 99%

Zeros of partition functions in the NPT ensemble

Aslyamov

Akhatov

2019

Phys. Rev. E

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Lee-Yang and Fisher zeros are crucial for study of phase transitions in the grand canonical and the canonical ensembles, respectively. However, these powerful methods do not cover the isothermalisobaric ensemble (NPT-ensemble), which reflects the conditions of many experiments. In this letter we present a new theory of the phase transitions in terms of the zeros of the NPT-ensemble partition functions in the complex plane. Proposed theory provides an approach to calculate all the partition function zeros in the NPT-ensemble, which form certain curves in the thermodynamic limit. To verify the theory we considered the Tonks gas and van der Waals fluid in the NPT-ensemble. In the case of Tonks gas, similarly to Lee-Yang circle theorem, we obtained an exact equation for the zeros limit curve. Also we derived the approximated limit curve equation for van der Waals fluid in terms of Szego curve. This curve fits numerically calculated zeros and correctly describes how the phenomenon of phase transition depends on the temperature.

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Complex pole approach in thermodynamic description of fluid mixtures with small number of molecules

Cited by 4 publications

References 22 publications

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain

Zeros of partition functions in the NPT ensemble

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