The equilibrium pair-correlation function and static dielectric response function are calculated ... more The equilibrium pair-correlation function and static dielectric response function are calculated for the one-component two-dimensional plasma in the convolution (Totsuji-Ichimaru) approximation. The long-wavelength (k-->0) compressibility sum rule is exactly satisfied for arbitrary values of the plasma parameter gamma. For gamma0) behavior of the pair-correlation function g(r) while for gamma>=2, it does not. As gamma-->4 the isothermal compressibility tends to zero as it should. The correlation energy is also calculated for this model and compared with the results for other approximation schemes and the Monte Carlo results.
The properties of a classical many-particle system interacting through a scalar field (a scalar p... more The properties of a classical many-particle system interacting through a scalar field (a scalar plasma) are studied. A relativistic Hartree approximation is applied to equilibrium to evaluate thermodynamic characteristics such as the energy, entropy, and equation of state. A gas-liquid phase transition appears at moderate densities. There is no collapse for an attractive interaction: The system can accomodate any density. Stability against small perturbation and the behavior of collective excitations are analyzed through the linear-response function.
Research results are summarized for work on (I) plasma theoretical problems related to the TORMAC... more Research results are summarized for work on (I) plasma theoretical problems related to the TORMAC geometry; (II) hydrogen plasma spectroscopy; (III) an electron collisional cross-section computer code and calculations. In Section (I) the following problems are discussed: (1) MHD equilibrium and stability; (2) sheath structure; (3) particle motion in the sheath and particle escape; (4) microinstabilities in the sheath; (5) general principles and scaling. Section (II) deals with the interpretation of experimental results on polarization and spectra of hydrogenic lines from the TORMAC experiment and presents a new and complete theory for the emission of hydrogenic spectra from turbulent plasmas. Section (III) presents results for inelastic scattering of electrons on molecular Hydrogen.
The implications of the Zeldovich model (baryons interacting through a massive vector field) for ... more The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.
The authors analyze the effects of electrodynamic retardation on the collective modes in an unmag... more The authors analyze the effects of electrodynamic retardation on the collective modes in an unmagnetized infinite superlattice modeled as an array of parallel two-dimensional plasma layers embedded in a dielectric substrate. The present work concentrates for the most part on correlated semiconductor superlattices, although the model is equally well suited to metallic superlattices consisting of an alternating array of thin metal layers and thick insulator slabs (e.g., 50 Å Al layers and 500 Å Al2O3 slabs). The analysis is based on the transverse magnetic (TM) and transverse electric (TE) dispersion relations recently formulated by the authors in the retarded quasilocalized charge approximation (RQLCA) [K. I. Golden, G. Kalman, L. Miao, and R. R. Snapp, Phys. Rev. B 55, 16 349 (1997)]. In the nonretarded limit, the QLCA mode structure consists of (i) an isolated in-phase plasmon mode, (ii) a band of gapped plasmons, (iii) an in-phase acoustic shear mode, and (iv) a band of gapped shear modes. This paper presents numerical and approximate analytical solutions of the long-wavelength RQLCA dispersion relations for the collective modes (i)-(iv) all the way down to very small wave numbers where retardation effects can be especially pronounced. Additionally, this work presents insightful approximate analytical formulas for the electromagnetic mode frequencies and gap widths, which add to the literature on the infinite sequences of TM- and TE-polarized electromagnetic bands. Some noteworthy effects that emerge from this study are as follows: (a) The appearance of ultralow frequency shear modes arising from the combined effect of retardation and strong coulomb interactions; the quasilocalization basis of the theory suggests that these modes can propagate when the two-dimensional plasma layers are in a crystalline phase. (b) A negative random-phase approximation shift in the bulk-plasma frequency induced by electrodynamic retardation; this effect can be appreciable in insulator/metal superlattices.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasm... more Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasmas in the strong coupling regime. The starting point is an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the dynamic correlation function, which is allowed to depend on time and both particle coordinates separately. The time evolution of the correlation function is determined from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. We study the equations in the linear limit and derive a nonlocal equation for the fluid displacement field. Comparisons to first-principles molecular dynamics simulations reveal an excellent quality of our approach thereby overcoming the limitations of the broadly used STLS scheme.
ABSTRACT We present the latest results of our systematic studies of the solid—liquid phase transi... more ABSTRACT We present the latest results of our systematic studies of the solid—liquid phase transition in 2D classical many‐particle systems interacting with the Yukawa potential. Our previous work [1] is extended by applying the molecular dynamic simulations to systems with up to 1.6 million particles in the computational box (for κ = 2 case). Equilibrium simulations are performed for different coupling parameters in the vicinity of the expected melting transition (Γmκ = 2 ≈ 415) and a wide range of observables are averaged over uncorrelated samples of the micro‐canonical ensemble generated by the simulations.
ABSTRACT The roton minimum is a deep minimum in the collective excitation spectrum of the liquid,... more ABSTRACT The roton minimum is a deep minimum in the collective excitation spectrum of the liquid, forming around fairly high k-values. We have discovered, through MD simulations, that this appears to be a general feature of strongly coupled liquids and is ubiquitous in 2D and 3D Yukawa liquids. We suggest that the physical origin of the roton minimum has to be sought in the quasi-localization of particles in a strongly correlated liquid and in the ensuing formation of local microcrystals whose averaged frequency dispersion would show roton minimum-like feature. Focusing on the phonon dispersion in a 2D crystal lattice, the position of the roton minimum is coincident with that of the closest point on the Brillouin zone boundary. To show how this leads to the development of the roton minimum, we have constructed a model for the dynamical structure function S(k,φ) of a 2D lattice system. By using the classical fluctuation dissipation theorem we obtain S(k,φ) through a lattice model for the density response function χ(k,φ), where the liquid behavior is emulated by a phenomenological collision frequency. The liquid dispersion relation is calculated through angular averaging. We examine its behavior in the vicinity of the Brillouin zone boundaries, and compare the results with MD simulations.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We compute linear and quadratic static density response functions of three-dimensional Yukawa liq... more We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.
In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present he... more In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present here our results of theoretical calculations accompanied by and Molecular Dynamics simulation findings on the ground state configuration and on the collective modes mode spectrum of a system of magnetic dipoles, interacting via the magnetic dipole pair-dipole potential, fixed on two-dimensional (2D) lattice sites. In
The equilibrium pair-correlation function and static dielectric response function are calculated ... more The equilibrium pair-correlation function and static dielectric response function are calculated for the one-component two-dimensional plasma in the convolution (Totsuji-Ichimaru) approximation. The long-wavelength (k-->0) compressibility sum rule is exactly satisfied for arbitrary values of the plasma parameter gamma. For gamma0) behavior of the pair-correlation function g(r) while for gamma>=2, it does not. As gamma-->4 the isothermal compressibility tends to zero as it should. The correlation energy is also calculated for this model and compared with the results for other approximation schemes and the Monte Carlo results.
The properties of a classical many-particle system interacting through a scalar field (a scalar p... more The properties of a classical many-particle system interacting through a scalar field (a scalar plasma) are studied. A relativistic Hartree approximation is applied to equilibrium to evaluate thermodynamic characteristics such as the energy, entropy, and equation of state. A gas-liquid phase transition appears at moderate densities. There is no collapse for an attractive interaction: The system can accomodate any density. Stability against small perturbation and the behavior of collective excitations are analyzed through the linear-response function.
Research results are summarized for work on (I) plasma theoretical problems related to the TORMAC... more Research results are summarized for work on (I) plasma theoretical problems related to the TORMAC geometry; (II) hydrogen plasma spectroscopy; (III) an electron collisional cross-section computer code and calculations. In Section (I) the following problems are discussed: (1) MHD equilibrium and stability; (2) sheath structure; (3) particle motion in the sheath and particle escape; (4) microinstabilities in the sheath; (5) general principles and scaling. Section (II) deals with the interpretation of experimental results on polarization and spectra of hydrogenic lines from the TORMAC experiment and presents a new and complete theory for the emission of hydrogenic spectra from turbulent plasmas. Section (III) presents results for inelastic scattering of electrons on molecular Hydrogen.
The implications of the Zeldovich model (baryons interacting through a massive vector field) for ... more The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.
The authors analyze the effects of electrodynamic retardation on the collective modes in an unmag... more The authors analyze the effects of electrodynamic retardation on the collective modes in an unmagnetized infinite superlattice modeled as an array of parallel two-dimensional plasma layers embedded in a dielectric substrate. The present work concentrates for the most part on correlated semiconductor superlattices, although the model is equally well suited to metallic superlattices consisting of an alternating array of thin metal layers and thick insulator slabs (e.g., 50 Å Al layers and 500 Å Al2O3 slabs). The analysis is based on the transverse magnetic (TM) and transverse electric (TE) dispersion relations recently formulated by the authors in the retarded quasilocalized charge approximation (RQLCA) [K. I. Golden, G. Kalman, L. Miao, and R. R. Snapp, Phys. Rev. B 55, 16 349 (1997)]. In the nonretarded limit, the QLCA mode structure consists of (i) an isolated in-phase plasmon mode, (ii) a band of gapped plasmons, (iii) an in-phase acoustic shear mode, and (iv) a band of gapped shear modes. This paper presents numerical and approximate analytical solutions of the long-wavelength RQLCA dispersion relations for the collective modes (i)-(iv) all the way down to very small wave numbers where retardation effects can be especially pronounced. Additionally, this work presents insightful approximate analytical formulas for the electromagnetic mode frequencies and gap widths, which add to the literature on the infinite sequences of TM- and TE-polarized electromagnetic bands. Some noteworthy effects that emerge from this study are as follows: (a) The appearance of ultralow frequency shear modes arising from the combined effect of retardation and strong coulomb interactions; the quasilocalization basis of the theory suggests that these modes can propagate when the two-dimensional plasma layers are in a crystalline phase. (b) A negative random-phase approximation shift in the bulk-plasma frequency induced by electrodynamic retardation; this effect can be appreciable in insulator/metal superlattices.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasm... more Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasmas in the strong coupling regime. The starting point is an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the dynamic correlation function, which is allowed to depend on time and both particle coordinates separately. The time evolution of the correlation function is determined from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. We study the equations in the linear limit and derive a nonlocal equation for the fluid displacement field. Comparisons to first-principles molecular dynamics simulations reveal an excellent quality of our approach thereby overcoming the limitations of the broadly used STLS scheme.
ABSTRACT We present the latest results of our systematic studies of the solid—liquid phase transi... more ABSTRACT We present the latest results of our systematic studies of the solid—liquid phase transition in 2D classical many‐particle systems interacting with the Yukawa potential. Our previous work [1] is extended by applying the molecular dynamic simulations to systems with up to 1.6 million particles in the computational box (for κ = 2 case). Equilibrium simulations are performed for different coupling parameters in the vicinity of the expected melting transition (Γmκ = 2 ≈ 415) and a wide range of observables are averaged over uncorrelated samples of the micro‐canonical ensemble generated by the simulations.
ABSTRACT The roton minimum is a deep minimum in the collective excitation spectrum of the liquid,... more ABSTRACT The roton minimum is a deep minimum in the collective excitation spectrum of the liquid, forming around fairly high k-values. We have discovered, through MD simulations, that this appears to be a general feature of strongly coupled liquids and is ubiquitous in 2D and 3D Yukawa liquids. We suggest that the physical origin of the roton minimum has to be sought in the quasi-localization of particles in a strongly correlated liquid and in the ensuing formation of local microcrystals whose averaged frequency dispersion would show roton minimum-like feature. Focusing on the phonon dispersion in a 2D crystal lattice, the position of the roton minimum is coincident with that of the closest point on the Brillouin zone boundary. To show how this leads to the development of the roton minimum, we have constructed a model for the dynamical structure function S(k,φ) of a 2D lattice system. By using the classical fluctuation dissipation theorem we obtain S(k,φ) through a lattice model for the density response function χ(k,φ), where the liquid behavior is emulated by a phenomenological collision frequency. The liquid dispersion relation is calculated through angular averaging. We examine its behavior in the vicinity of the Brillouin zone boundaries, and compare the results with MD simulations.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We compute linear and quadratic static density response functions of three-dimensional Yukawa liq... more We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.
In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present he... more In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present here our results of theoretical calculations accompanied by and Molecular Dynamics simulation findings on the ground state configuration and on the collective modes mode spectrum of a system of magnetic dipoles, interacting via the magnetic dipole pair-dipole potential, fixed on two-dimensional (2D) lattice sites. In
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