Molecular dynamics studies of thermal conductivity time correlation functions

The Green–Kubo time correlation function for the thermal conductivity in liquid argon is studied for a thermodynamic state close to the triple point by standard molecular dynamics simulations. The collective heat flux vector has been separated into contributions originated at the kinetic energy, the intermolecular potential and the pair virial function. Furthermore, the Green–Kubo time correlation functions have been broken down into partial n-body terms (n=1,2,3,4). The most important contribution to the thermal conductivity is represented by the auto correlation of the virial term. In contrast to other collective phenomena described by time correlation functions involving n-body terms, the partial Green–Kubo time correlation functions for the thermal conductivity are not affected by exponential long-time tails.     

A class of coupled spaces

The algebraic structure and analytic properties of a class of Einstein spaces whose metrics are coupled by a particular type of algebraic relation are analyzed. Several invariant relations among the geometric properties of these spaces are obtained; in particular, a detailed analysis is made of the transformation of time-like congruences. The particular case in which one of the spaces is planar is used to establish the consequences of the Herglotz-Noether theorem.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 52–57, September, 1970.     

Green–Kubo Expressions for a Granular Gas

The transport coefficients for a gas of smooth, inelastic hard spheres are obtained from the Boltzmann equation in the form of Green–Kubo relations. The associated time correlation functions are not simply those constructed from the fluxes of conserved densities. Instead, fluxes constructed from the reference local homogeneous distribution occur as well. The analysis exposes some complexities to be expected in the application of linear response methods to granular systems.     

Velocity Autocorrelation Functions and Diffusion Coefficient of Dusty Component in Complex Plasmas

The velocity autocorrelation functions of dust particles were calculated by the Langevin dynamics. It was indicated that their oscillations decay more rapidly with increase in the friction parameters. The dependencies of the dust particles diffusion coefficient on the friction coefficient at the different values of various parameters were obtained by the Green‐Kubo relation and mean square displacements. The validity of the Einstein relation at small values of coupling parameter was shown (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Berkovits covariant quantization of GS superstring

We study the covariant quantization of the Green–Schwarz (GS) superstrings proposed recently by Berkovits. In particular, we reformulate the Berkovits approach in a way that clarifies its relation with the GS approach and allows to derive in a straightforward way its extension to curved spacetime background. We explain the procedure working explicitly in the case of the heterotic string.     

125m Te (109.3 keV) stimulated emission and gamma lasers

Summary Proceeding from the drastic discrepancy between experimental data and theory, we show (contrary to other authors) that the relations between the Einstein's coefficients are true for transitions from any of the excited levels and theground state of the quantum system only. The relations connecting those coefficients are derived for transitions betweenany two states; the corresponding cross-sections are calculated and it is shown (contrary to other authors) that the stimulated emission cross-section may be large enough for the creation of gamma lasers. The new relation for Einstein's coefficients (and the corresponding cross-sections) are fundamentally different from those known so far (74 years after Einstein). The results are compared with experiment and the coincidence is very good. These investigations can lead to progress in the study of physical processes in star atmospheres. The author of this paper has agreed to not receive the proofs for correction.     

On linear response theory and area preserving mappings

In this report the linear response theory of Kubo and the verification of the Kubo formula for electrical conduction by experiments and numerical calculations is reviewed. A survey of area reserving mappings is given, emphasizing the significance of these mappings for mechanics and statistical mechanics. The response of area preserving mappings with different statistical properties is calculated. The relation between the response, the statistical properties of the mappings and the fundamental assumptions of linear response theory is discussed.     

Theory of hot-electron quantum diffusion in semiconductors

In the linear response regime close to equilibrium, the fluctuation-dissipation theorem relates linear transport coefficients via the well-known Green–Kubo or Einstein relation. The latter embodies a deep connection between fluctuations causing diffusion and dissipation, which are responsible for a finite mobility. Far from equilibrium, however, the Einstein relation is no longer valid so that both the mobility and diffusivity gain their own physical integrity. Consequently, beyond a linear response, both quantities have to be described by different approaches. Unfortunately, there is a strong imbalance of research activities devoted to the study of both transport mechanisms in semiconductors. On one hand, the rich physics of high-field quantum drift in semiconducting structures has a long history and has reached a high level of sophistication. On the other hand, there are only comparatively few and unsystematic studies that cover quantum diffusion of carriers under high-field conditions. This review aims at reducing this gap by presenting a unified approach to quantum drift and quantum diffusion. Starting from a semi-phenomenological basis, a quantum theory of transport coefficients is developed for one- as well as multi-band models. Physical implications are illustrated by selected applications whereby the quantum character of the approach is emphasized. Furthermore, the basic unified treatment of transport coefficients is extended by accounting for the two-time dependence of one-particle correlation functions in quantum statistics. As an application, a phononless transport mechanism is identified, which solely originates from the double-time nature of the evolution. Finally, additional examples are presented that illustrate the important role played by quantum diffusion in semiconductor physics.     

Sound modes in holographic hydrodynamics for charged AdS black hole

In the previous paper we studied the transport coefficients of quark–gluon plasma in finite temperature and finite density in vector and tensor modes. In this paper, we extend it to the scalar modes. We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.     

Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function h_t(x) with corner initialization. We prove, with one exception, that the limiting distribution function of h_t(x) (suitably centered and normalized) equals a Fredholm determinant previously encountered in random matrix theory. In particular, in the universal regime of large x and large t the limiting distribution is the Fredholm determinant with Airy kernel. In the exceptional case, called the critical regime, the limiting distribution seems not to have previously occurred. The proofs use the dual RSK algorithm, Gessel's theorem, the Borodin–Okounkov identity and a novel, rigorous saddle point analysis. In the fixed x, large t regime, we find a Brownian motion representation. This model is equilvalent to the Seppäläinen–Johansson model. Hence some of our results are not new, but the proofs are.     

A self-consistent approach to the localization-delocalization problem of the quantum Hall effect

I present a semi-phenomenological framework for the calculation of the Kubo conductivities in 2d systems subject to a magnetic field based on the memory function formalism. The notion of a memory oscillation time is introduced and its peculiar role related to the orientation dependent quantities in magnetic fields is discussed. Self-consistency equations are formulated which allow to approach the localization-delocalization transition. I study the Hall conductivity and the longitudinal conductivity in the low temperature limit and find that they are related by a universal relation refered to as stable trajectories in renormalization group approaches on the QHE.     

Asymptotic behaviour and general properties of harmonic generation susceptibilities

We use the Kubo response function formalism to derive the asymptotic behaviour of the harmonic generation susceptibilities to all orders n. The results show a stringent correspondence with the ones previously obtained from the classical anharmonic oscillator model. They are characterized by a dependence and a coefficient proportional to the trace of the (n+1)th derivative of the potential energy on the equilibrium density matrix. Using the above results we derive new Kramers-Kr?nig relations and sum rules for all orders of harmonics susceptibilities. Received 17 April 2000     

On the topological explanation of the integer quantum hall effect

We investigate the static and dynamic Kubo Hall conductivity of a non-interacting electron system in a random potential on a torus. Considering the universal covering space of the torus the Bloch theorem is applied for rational values of the filling factor. The localisation is simulated by the assumption of bound states. The Hall conductivity at zero temperatur is shown to be topologically quantized, if the Fermi energy lies in a spectral gap or in a localisation regime. The relation to previous formulations of the topological approach to the integer quantum Hall effect (QHE) is discussed.     

Interferencing in Coupled Bose–Einstein Condensates

We consider an exactly soluble model of two Bose–Einstein condensates with a Josephson-type of coupling. Its equilibrium states are explicitly found showing condensation and spontaneously broken gauge symmetry. It is proved that the total number and total phase fluctuation operators, as well as the relative number and relative current fluctuation operators form both a quantum canonical pair. The exact relation between the relative current and phase fluctuation operators is established. Also the dynamics of these operators is solved showing the collapse and revival phenomenon.     

Transport Properties of a Modified Lorentz Gas

We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed freely-rotating circular scatterers interacting with point particles via perfectly rough collisions. Upon imposing a temperature and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds for low values of the imposed gradients. Transport in this system is normal, in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are non-trivially coupled, satisfying Onsager's reciprocity relations to within numerical accuracy as well as the Green–Kubo relations. We further show numerically that an applied electric field causes the same currents as the corresponding chemical potential gradient in first order of the applied field. Puzzling discrepancies in higher order effects (Joule heating) are also observed. Finally, the role of entropy production in this purely Hamiltonian system is shortly discussed.     

The analysis of time: Is the relativistic time unique?

Time is analyzed by considering the actual setup of clock system within the four-dimensional framework. We find that both relativistic time and universal time can be embedded in such a symmetry framework. Although Poincaré and Einstein both understood the meaning of Lorentz's local time in terms of sending light signals to calibrate clocks, they differed on a basic point: Einstein believed local time to be the necessary and unique time, while Poincaré admitted flexibility in the definitions of time and regarded local time as only a convention. The results of our analysis shed light on Poincaré's original idea concerning conventions of time and provide the conceptual basis for the formulation of a new four-dimensional symmetry with a universal time. We demonstrate that the one-way speeds of light measured by stable atomic clocks in rockets may not be isotropic, in contrast to the two-way speeds of light. Furthermore, atomic clocks can be used to set up a clock system which reads a universal (but not absolute) time.I dedicate this paper to the memory of my beloved father Hsu Mau-Yuen (1903–1977), whose understanding helped me to choose to work on physical problems. Part of the research was accomplished while I held an NRC Senior Resident Research Associateship.     

Green–Kubo relations for dynamic interfacial excess properties

In this paper we analyze the fluctuations of the in-plane interfacial excess fluxes in multiphase systems, in the context of the extended irreversible thermodynamics formalism. We derive expressions for the time correlation functions of the surface extra stress tensor, the surface mass flux vector, and the surface energy flux vector, and use these expressions to derive Green–Kubo relations for the surface shear viscosity, the surface dilatational viscosity, the surface diffusion coefficient, and the surface thermal conductivity. These Green-Kubo relations can be used to compute these excess transport coefficients using for example molecular dynamics simulations.