The e − e , e − i, i − i and charge-charge static structure factors are calculated for alkali and... more The e − e , e − i, i − i and charge-charge static structure factors are calculated for alkali and Be 2+ plasmas using the method described by Gregori et al. in [1]. The dynamic structure factors for alkali plasmas are calculated using the method of moments [2], [3]. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the ion structure [4].
We study the effective interactions and the mass action constants for pair and triple association... more We study the effective interactions and the mass action constants for pair and triple associations in classical and quantum plasmas. Avoiding double counting, we derive new expressions for the mass action constants. The calculations resulted in values that were substantially smaller than the standard ones in relevant temperature ranges by up to 50 percent. On this basis, we determine the pressure of H, He and Li plasmas and the osmotic coefficient of electrolytes with higher charges such as, e.g., seawater. Classical and quantum Coulomb systems show strong similarities. The contributions in low orders with respect to the interaction e2 are suppressed by thermal and screening effects. The contributions of weakly bound states, near the continuum edge, to the mass action constants are reduced, replacing the exponential functions with cropped exponentials. The new mass action constants are consistent with well-known extended limiting cases of screening effects. We analyze classical exam...
This paper investigates the density expansion of the thermodynamic properties of a two component ... more This paper investigates the density expansion of the thermodynamic properties of a two component plasma under the influence of a weak constant uniform magnetic field. We start with the fugacity expansion for the Helmholtz free energy. The leading terms with respect to the density are calculated by a perturbation expansion with respect to the magnetic field. We find a new magnetic virial function for a low density plasma which is exact in quadratic order with respect to the magnetic field. Using these results we compute the magnetization and the magnetic susceptibility.
Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting b... more Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves ͑initial shock͒ and isentropes ͑subsequent shocks͒. For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.
Agent-based modeling is a powerful methodology to describe the occurence of complex behavior in b... more Agent-based modeling is a powerful methodology to describe the occurence of complex behavior in biological systems. The interaction of a large number of individuals (agents) may for example lead to the emergence of new forms of collective motion. In this paper, we investigate a particle-based approach to the coherent motion of a swarm with parabolic (i.e. harmonic) interactions between the agents. It is based on generalized Langevin equations for the particle agents, which take into account (i) energetic conditions for active motion, (ii) linear attractive forces between each two agents. The complex collective motion observed can be explained as the result of these different influences: the active motion of the agents, which is driven by the energy-take up, would eventually lead to a spatial dispersion of the swarm, while the mutual interaction of the agents results in a tendency of spatial concentration. In addition to particlebased computer simulations, we also provide a mathematical framework for investigating the collective dynamics.
This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pres... more This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between 10 −1 and 10 2 Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter Γ 3 and degeneracy parameter n e Λ 3 10. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Padé approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.
The problem of anomalous diffusion in momentum space is considered for plasmalike systems on the ... more The problem of anomalous diffusion in momentum space is considered for plasmalike systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker–Planck equation for description of diffusion (in momentum space) of particles (ions, grains, etc.) in a stochastic system of light particles (electrons or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation due to the small characteristic momentum transfer. The cases of an exponentially decreasing (including a Boltzmann-like) kernel in the PTF in momentum space, as well as more general kernels, which create anomalous diffusion in velocity space due to the long tail in the PTF, are considered. Effective friction and diffusion coefficients fo...
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Journal of Physics A: Mathematical and General, 2003
Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct p... more Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct path integral Monte Carlo methods. The phase boundary of the electron-hole liquid in germanium is calculated and is found to agree reasonably well with the known experimental results. Analogous behaviour is found for high-density hydrogen. For a temperature of T = 10 000 K it is shown that the internal energy is lowered due to droplet formation for densities between 10 23 cm −3 and 10 24 cm −3 .
The e − e , e − i, i − i and charge-charge static structure factors have been calculated for Alka... more The e − e , e − i, i − i and charge-charge static structure factors have been calculated for Alkali and Be 2+ plasmas using Gregori's method [14]. The dynamic structure factors for Alkali plasmas have been calculated using Adamjans' et al method [52], [53]. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on a base of Bogoljubow method, has been used taking into account not only the quantum-mechanical effects but also the ion structure [13].
The semiclassical dynamics of a charged particle moving in a two-component plasma is considered u... more The semiclassical dynamics of a charged particle moving in a two-component plasma is considered using a corrected Kelbg pseudopotential. We employ the classical Nevanlinna-type theory of frequency moments to determine the velocity and force autocorrelation functions. The constructed expressions preserve the exact short and long-time behavior of the autocorrelators. The short-time behavior is characterized by two parameters which are expressable through the plasma static correlation functions. The long-time behavior is determined by the self-diffusion coefficient. The theoretical predictions are compared with the results of semiclassical molecular dynamics simulation.
The distribution of the electric microfield at a charged particle moving in a two-component plasm... more The distribution of the electric microfield at a charged particle moving in a two-component plasma is calculated. The theoretical approximations are obtained via the parameter integration technique and using the screened pair approximation for the generalized radial distribution function. It is shown that the two-component plasma microfield distribution shows a larger probability of high microfield values than the corresponding distribution of the commonly used OCP model. The theory is checked by quasiclassical molecular-dynamics simulations. For the simulations a corrected Kelbg pseudopotential has been used.
Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct p... more Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct path integral Monte Carlo methods. The phase boundary of the electron-hole liquid in germanium is calculated and is found to agree reasonably well with the known experimental results. Analogous behaviour is found for high-density hydrogen. For a temperature of T = 10 000 K it is shown that the internal energy is lowered due to droplet formation for densities between 10 23 cm −3 and 10 24 cm −3 .
The quantum statistical treatment of the Rutherford model, considering matter as a system of poin... more The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei), is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe, are discussed. Beyond this, the modern state of art is presented and new results are given which explain why bound states according to a discrete part of the spectra occur only in a valley in the temperature‐density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture ...
The first part of the paper briefly reviews and explains basic ideas of the theory of Gaussian fl... more The first part of the paper briefly reviews and explains basic ideas of the theory of Gaussian fluctuations and their relaxation developed in 1931 by Lars Onsager in the context of a general theory of irreversible processes. Motivated by Onsager's approach, we extend the theory to fluctuations including Lévy processes. We assume that deviations from Gaussian distributions, which are often observed in non-equilibrium systems, may be described by convoluted Gauss-Lévy distributions and their relation to stationary states by generalized Smoluchowski equations. The central part of the distributions we study here is determined by the Gaussian core with the wings decaying according to a power law characteristic for a Lévy-type contribution to statistics. Furthermore, we develop a generalization of Onsager's theory of linear relaxation processes to those which include statistically independent Gaussian fluctuations and (non-equilibrium) Lévy noises. We apply the generalized version of the fluctuation-dissipation theorem (FDT) to analyze regime of the linear response of the non-equilibrium system driven by Lévy (Cauchy) white noise and subject to thermal (Gaussian) fluctuations. In the last part, applications to non-Maxwellian velocity fluctuations and their relaxations are investigated.
We consider finite systems of interacting Brownian particles including active friction in the fra... more We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for 1−d systems of masses connected by Toda springs which are imbedded into a heat bath. Including negative friction we find N + 1 attractors of motion including an attractor describing dissipative solitons. Noise leads to transition between the deterministic attractors. In the case of two-dynamical motion of interacting particles angular momenta are generated and left/right rotations of pairs and swarms are found.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021
For universality in the approach, it is customary to appropriately rescale problems to a single o... more For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible...
We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice c... more We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a hole, is created in the other. The atoms of each of the backbone lattices interact with anharmonic (short range) Morse potentials whereas the charges interact via (long range) Coulomb potentials. Computer simulations are provided of the possibilities o↵ered by varying interlayer separation, strength of the Coulomb force between the charges and the diverse dynamical role played by excited solitons supersonically moving along crystallographic axes in one of the layers. Optimal conditions are identified for the occurrence of electron-hole pairs and for the more significant case of a boson-like electron-hole-soliton coupled compound, a new form of quasiparticle moving along the coupled bilayer system with no need of applying an external electric field.
The e − e , e − i, i − i and charge-charge static structure factors are calculated for alkali and... more The e − e , e − i, i − i and charge-charge static structure factors are calculated for alkali and Be 2+ plasmas using the method described by Gregori et al. in [1]. The dynamic structure factors for alkali plasmas are calculated using the method of moments [2], [3]. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the ion structure [4].
We study the effective interactions and the mass action constants for pair and triple association... more We study the effective interactions and the mass action constants for pair and triple associations in classical and quantum plasmas. Avoiding double counting, we derive new expressions for the mass action constants. The calculations resulted in values that were substantially smaller than the standard ones in relevant temperature ranges by up to 50 percent. On this basis, we determine the pressure of H, He and Li plasmas and the osmotic coefficient of electrolytes with higher charges such as, e.g., seawater. Classical and quantum Coulomb systems show strong similarities. The contributions in low orders with respect to the interaction e2 are suppressed by thermal and screening effects. The contributions of weakly bound states, near the continuum edge, to the mass action constants are reduced, replacing the exponential functions with cropped exponentials. The new mass action constants are consistent with well-known extended limiting cases of screening effects. We analyze classical exam...
This paper investigates the density expansion of the thermodynamic properties of a two component ... more This paper investigates the density expansion of the thermodynamic properties of a two component plasma under the influence of a weak constant uniform magnetic field. We start with the fugacity expansion for the Helmholtz free energy. The leading terms with respect to the density are calculated by a perturbation expansion with respect to the magnetic field. We find a new magnetic virial function for a low density plasma which is exact in quadratic order with respect to the magnetic field. Using these results we compute the magnetization and the magnetic susceptibility.
Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting b... more Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves ͑initial shock͒ and isentropes ͑subsequent shocks͒. For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.
Agent-based modeling is a powerful methodology to describe the occurence of complex behavior in b... more Agent-based modeling is a powerful methodology to describe the occurence of complex behavior in biological systems. The interaction of a large number of individuals (agents) may for example lead to the emergence of new forms of collective motion. In this paper, we investigate a particle-based approach to the coherent motion of a swarm with parabolic (i.e. harmonic) interactions between the agents. It is based on generalized Langevin equations for the particle agents, which take into account (i) energetic conditions for active motion, (ii) linear attractive forces between each two agents. The complex collective motion observed can be explained as the result of these different influences: the active motion of the agents, which is driven by the energy-take up, would eventually lead to a spatial dispersion of the swarm, while the mutual interaction of the agents results in a tendency of spatial concentration. In addition to particlebased computer simulations, we also provide a mathematical framework for investigating the collective dynamics.
This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pres... more This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between 10 −1 and 10 2 Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter Γ 3 and degeneracy parameter n e Λ 3 10. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Padé approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.
The problem of anomalous diffusion in momentum space is considered for plasmalike systems on the ... more The problem of anomalous diffusion in momentum space is considered for plasmalike systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker–Planck equation for description of diffusion (in momentum space) of particles (ions, grains, etc.) in a stochastic system of light particles (electrons or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation due to the small characteristic momentum transfer. The cases of an exponentially decreasing (including a Boltzmann-like) kernel in the PTF in momentum space, as well as more general kernels, which create anomalous diffusion in velocity space due to the long tail in the PTF, are considered. Effective friction and diffusion coefficients fo...
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Journal of Physics A: Mathematical and General, 2003
Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct p... more Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct path integral Monte Carlo methods. The phase boundary of the electron-hole liquid in germanium is calculated and is found to agree reasonably well with the known experimental results. Analogous behaviour is found for high-density hydrogen. For a temperature of T = 10 000 K it is shown that the internal energy is lowered due to droplet formation for densities between 10 23 cm −3 and 10 24 cm −3 .
The e − e , e − i, i − i and charge-charge static structure factors have been calculated for Alka... more The e − e , e − i, i − i and charge-charge static structure factors have been calculated for Alkali and Be 2+ plasmas using Gregori's method [14]. The dynamic structure factors for Alkali plasmas have been calculated using Adamjans' et al method [52], [53]. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on a base of Bogoljubow method, has been used taking into account not only the quantum-mechanical effects but also the ion structure [13].
The semiclassical dynamics of a charged particle moving in a two-component plasma is considered u... more The semiclassical dynamics of a charged particle moving in a two-component plasma is considered using a corrected Kelbg pseudopotential. We employ the classical Nevanlinna-type theory of frequency moments to determine the velocity and force autocorrelation functions. The constructed expressions preserve the exact short and long-time behavior of the autocorrelators. The short-time behavior is characterized by two parameters which are expressable through the plasma static correlation functions. The long-time behavior is determined by the self-diffusion coefficient. The theoretical predictions are compared with the results of semiclassical molecular dynamics simulation.
The distribution of the electric microfield at a charged particle moving in a two-component plasm... more The distribution of the electric microfield at a charged particle moving in a two-component plasma is calculated. The theoretical approximations are obtained via the parameter integration technique and using the screened pair approximation for the generalized radial distribution function. It is shown that the two-component plasma microfield distribution shows a larger probability of high microfield values than the corresponding distribution of the commonly used OCP model. The theory is checked by quasiclassical molecular-dynamics simulations. For the simulations a corrected Kelbg pseudopotential has been used.
Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct p... more Plasma phase transitions in dense hydrogen and electron-hole plasmas are investigated by direct path integral Monte Carlo methods. The phase boundary of the electron-hole liquid in germanium is calculated and is found to agree reasonably well with the known experimental results. Analogous behaviour is found for high-density hydrogen. For a temperature of T = 10 000 K it is shown that the internal energy is lowered due to droplet formation for densities between 10 23 cm −3 and 10 24 cm −3 .
The quantum statistical treatment of the Rutherford model, considering matter as a system of poin... more The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei), is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe, are discussed. Beyond this, the modern state of art is presented and new results are given which explain why bound states according to a discrete part of the spectra occur only in a valley in the temperature‐density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture ...
The first part of the paper briefly reviews and explains basic ideas of the theory of Gaussian fl... more The first part of the paper briefly reviews and explains basic ideas of the theory of Gaussian fluctuations and their relaxation developed in 1931 by Lars Onsager in the context of a general theory of irreversible processes. Motivated by Onsager's approach, we extend the theory to fluctuations including Lévy processes. We assume that deviations from Gaussian distributions, which are often observed in non-equilibrium systems, may be described by convoluted Gauss-Lévy distributions and their relation to stationary states by generalized Smoluchowski equations. The central part of the distributions we study here is determined by the Gaussian core with the wings decaying according to a power law characteristic for a Lévy-type contribution to statistics. Furthermore, we develop a generalization of Onsager's theory of linear relaxation processes to those which include statistically independent Gaussian fluctuations and (non-equilibrium) Lévy noises. We apply the generalized version of the fluctuation-dissipation theorem (FDT) to analyze regime of the linear response of the non-equilibrium system driven by Lévy (Cauchy) white noise and subject to thermal (Gaussian) fluctuations. In the last part, applications to non-Maxwellian velocity fluctuations and their relaxations are investigated.
We consider finite systems of interacting Brownian particles including active friction in the fra... more We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for 1−d systems of masses connected by Toda springs which are imbedded into a heat bath. Including negative friction we find N + 1 attractors of motion including an attractor describing dissipative solitons. Noise leads to transition between the deterministic attractors. In the case of two-dynamical motion of interacting particles angular momenta are generated and left/right rotations of pairs and swarms are found.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021
For universality in the approach, it is customary to appropriately rescale problems to a single o... more For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible...
We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice c... more We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a hole, is created in the other. The atoms of each of the backbone lattices interact with anharmonic (short range) Morse potentials whereas the charges interact via (long range) Coulomb potentials. Computer simulations are provided of the possibilities o↵ered by varying interlayer separation, strength of the Coulomb force between the charges and the diverse dynamical role played by excited solitons supersonically moving along crystallographic axes in one of the layers. Optimal conditions are identified for the occurrence of electron-hole pairs and for the more significant case of a boson-like electron-hole-soliton coupled compound, a new form of quasiparticle moving along the coupled bilayer system with no need of applying an external electric field.
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