Statistical description of the system electrons on the liquid helium surface

Lev, B. I.; Ostroukh, V.P.; Tymchyshyn, V.B.; Zagorodny, A. G.

doi:10.1140/epjb/e2014-50303-2

Cited by 4 publications

(15 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(73) can also be obtained from the corresponding linear approximation of boundary conditions in Eq. (29). So, the expression forφ (e)(1) j has the form:…”

Section: Critical Parameters Of the Phase Transition To A Spatially Pmentioning

confidence: 99%

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

Lytvynenko¹,

Slyusarenko²

2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The theory of quasi-neutral equilibrium states of charges above liquid dielectric surface is built. This theory is based on first principles of quantum statistics for systems, comprising many identical particles. The proposed approach is concerned with applying the variational principle, modified for the considered systems, and the Thomas-Fermi model. In terms of the developed theory a self-consistency equations are obtained. These equations provide the relation between the main parameters, describing the system: the potential of static electric field, the distribution function of charges and the surface profile of liquid dielectric. The equations are used to study the phase transition in the system to a spatially periodic state. The proposed method can be applied to analyzing the properties of the phase transition in the system to a spatially periodic states of wave type. Using the analytical and numerical methods, we make a detailed research of the dependence of critical parameters of such phase transition on the thickness of liquid dielectric film. Some stability criteria of the new asymmetric phase of the studied system are discussed.

show abstract

“…(73) can also be obtained from the corresponding linear approximation of boundary conditions in Eq. (29). So, the expression forφ (e)(1) j has the form:…”

Section: Critical Parameters Of the Phase Transition To A Spatially Pmentioning

confidence: 99%

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

Lytvynenko¹,

Slyusarenko²

2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…There are two parts of potential energy for electrons on the liquid helium surface [27,[32][33][34]: Coulomb interaction and capillary interaction. For Coulomb interaction we can find a shortcut -it was shown in [35] that this part approximately does not depend on localization distance s. Besides, one may think on approximate expression for Coulomb interaction from example II B (27). It does not contain s, and the same behavior we may expect from Coulomb interaction for 2D lattice.…”

Section: Electrons On the Liquid-helium Surface And Their Localizmentioning

confidence: 85%

“…As mentioned previously, we are interested in twodimensional case as well. One may check, that there exists some sort of analogy of (16) for two dimensions [35]. Difference will appeare in changing summations and…”

Section: Particles Arranged In a Latticementioning

confidence: 99%

“…In this section we aim some general consideration of inhomogeneous system of interacting particles [35,42]. Nor system, neither interaction potential will be specified to keep generosity and extendability.…”

Section: Statistical Description Of Interacting Particles Systemmentioning

confidence: 99%

“…The second system is "electrons on the liquid-helium surface" [23][24][25][26]. It may undergo Wigner crystallization [27][28][29][30][31][32][33] and transition between triangular and square lattices [34,35]. Moreover, homogeneous distribution of electron density is not always stable, and there are critical parameters when spatial structures, especially periodic deformations and multi-electron dimples, are formed [36].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Potential Energy Analysis for a System of Interacting Particles Arranged in a Bravais Lattice

2017

View full text Add to dashboard Cite

We propose a method of free energy calculation for a system of interacting particles arranged in a Bravais lattice. It will be shown how to treat divergences for infinite unbounded systems with "catastrophic" potentials like Coulomb and compare two of them. Besides, we show that current method may be used not only for essentially classical systems, but for some quantum as well. Two systems are considered: grains in dusty plasma and electrons on the liquid-helium surface. For dusty-plasma parameters of grain's lattice are calculated by numerical solution of obtained equations. Electrons on the liquid-helium surface are analyzed to get localization distance. Besides, conditions for existence of electron lattice are found.

show abstract

Free energy analysis for a system of interacting particles arranged in Bravais lattice

Lev¹,

Tymchyshyn²,

Zagorodny³

2015

Preprint

View full text Add to dashboard Cite

Statistical description of the system electrons on the liquid helium surface

Cited by 4 publications

References 40 publications

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

Potential Energy Analysis for a System of Interacting Particles Arranged in a Bravais Lattice

Free energy analysis for a system of interacting particles arranged in Bravais lattice

Contact Info

Product

Resources

About