Hydrodynamic limit for a system with finite range interactions

We study a system of interacting diffusions. The variables present the amount of charge at various sites of a periodic multidimensional lattice. The equilibrium states of the diffusion are canonical Gibbs measures of a given finite range interaction. Under an appropriate scaling of lattice spacing and time, we derive the hydrodynamic limit for the evolution of the macroscopic charge density.     

Thermodynamic limit for classical systems with Coulomb interactions in a constant external field

We introduce a new method for studying the thermodynamic limit for systems of particles with Coulomb interactions. The method is based on calculating the potential energy of the Coulomb interactions from the electric or magnetic fields in the system rather than from the energy of the individual particle — particle interactions. We are able to include the effects of a constant external field being imposed at the boundary of the system. The difficulties associated with Coulomb potentials being not even weakly tempered are overcome by imposing the boundary condition that at the boundary of the region containing the particles, the electric or magnetic field has normal component equal to that of the applied field. We prove that the thermodynamic free energy density exists and is independent of the sequence of regions used to define the limit. We introduce sequences of regions all of the same shape and show that for these sequences of regions the thermodynamic free energy density is independent of shape. Finally, we prove that the thermodynamic free energy is a convex function of the density of particles and of the applied field.     

Nonlinear diffusion limit for a system with nearest neighbor interactions

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.Work supported by the National Science Foundation under grants no. DMS 8600233 and DMS 8701895     

Critical behavior of isotropic three-dimensional systems with dipole-dipole interactions

The critical behavior of Heisenberg magnets with dipole-dipole interactions near the line of second-order phase transitions directly in three-dimensional space is investigated in terms of a field-theoretic approach. The dependences of critical exponents on the dipole-dipole interaction parameter are derived. Comparison with experimental facts is made.     

Thermodynamic limit of correlation functions in a system of gravitating fermions

We show that the correlation functions in a system of gravitating fermions converge as tempered distributions in the thermodynamic limit, if the system is not at the point of phase-transition. The densities converge to the density of the Thomas-Fermi-theory and are not correlated in the limit.     

Optical response of a diatomic system with allowance for the dipole-dipole interaction

The optical response of a diatomic system excited by monochromatic light is studied. On the basis of a semiclassical approach, the effects of rearrangement of the energy spectrum of the system due to the dipole-dipole interaction and the effects related to variations in the orientation of the atomic dipole moments under the action of microscopic fields are jointly taken into account. The strongest response of the system is shown to occur at dimensional resonance frequencies. The number of observed intensity peaks depends on the position of the observation point with respect to the interatomic axis. The frequencies of the dimensional resonances are compared with other characteristic frequencies of the atomic spectrum.     

Dielectric constant of glasses: evidence for dipole-dipole interactions

The 1 kHz real part chi(') of the dielectric constant of a structural glass (a-SiO(2+x)C(1+y)H(z)) was measured at low temperature T. Reducing the sample thickness h below 100 nm weakens the slope /delta(chi('))/delta (T) for T less than or approximately equal 0.1 K, for all measuring fields E. This contrasts with the predictions of the two-level system (TLS) model but is in agreement with the recently proposed delocalization of excitations derived from a field-induced TLS-TLS interaction mechanism. For small h this interaction is screened, which explains the h effects on chi('). Hence, interactions must play a key role in standard thick samples as soon as T less than or approximately equal 0.1 K.     

Diffusion in a system of impurity centers with dipole-dipole hopping rates

Random walks in disordered media with dipole-dipole transition rates are considered. The long-time asymptotics of the process are investigated on the basis of a new numerical simulation method, which includes periodic continuation of the system without periodic continuation of the initial condition. It is shown that the long-time asymptotics have a diffusive character. The concentration dependence of the diffusion coefficient for simple cubic and face-centered cubic lattices is studied. Zh. éksp. Teor. Fiz. 114, 2166–2181 (December 1998)     

Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions

We demonstrate Rabi oscillations of small numbers of 87Rb atoms between ground and Rydberg states with n< or =43. Coherent population oscillations are observed for single atoms, while the presence of two or more atoms decoheres the oscillations. We show that these observations are consistent with van der Waals interactions of Rydberg atoms.     

Probing nanoscale dipole-dipole interactions by electric force microscopy

We address the issue of dipole-dipole interaction measurements at the nanometer scale. Electric dipoles with tunable effective momentum in the range 10(3)-10(4) D are generated by charge injection in single silicon nanoparticles on a conductive substrate and probed by a spectroscopic electric force microscopy analysis. Weak dipole-dipole force gradients are measured and identified from their quadratic momentum dependence. The results suggest that dipolar interactions associated with atomic-scale charge displacements or molecules can be probed by noncontact atomic force microscopy.     

Modification of scattering lengths via magnetic dipole-dipole interactions

We propose a new mechanism for tuning an atomic s-wave scattering length. The effect is caused by virtual transitions between different Zeeman sublevels via magnetic dipole-dipole interactions. These transitions give rise to an effective potential, which, in contrast to standard magnetic interactions, has an isotropic component and thus affects s-wave collisions.     

BKT phase transition in a 2D system with long-range dipole-dipole interaction

We consider phase transitions in 2D XY-like systems with long-range dipole-dipole interactions and demonstrate that BKT-type phase transition always occurs separating the ordered (ferroelectric) and the disordered (paraelectric) phases. The low-temperature phase corresponds to a thermal state with bound vortex-antivortex pairs characterized by linear attraction at large distances. Using the Maier-Schwabl topological charge model, we show that bound vortex pairs polarize and screen the vortex-antivortex interaction, leaving only the logarithmic attraction at sufficiently large separations between the vortices. At higher temperatures the pairs dissociate and the phase transition similar to BKT occurs, though at a larger temperature than in a system without the dipole-dipole interaction.     

Thermodynamic limit in a charged plasma in equilibrium

We study the existence conditions for the thermodynamic limit in the chain of BBGKY equations for the equilibrium correlation functions of a charged plasma. It is shown that in order for the thermodynamic limit to exist the charge of the plasma cannot increase faster than the surface area of the plasma. When this condition is satisfied the equilibrium correlation functions of the charged plasma are asymptotically identical to the correlation functions of a neutral plasma in a self-consistent electrostatic field, which depends only on the one-particle correlation functions. For a plasma which is uniform everywhere except in a thin surface region, this field is found in explicit form. For a plasma occupying an infinite half-space, the problem is equivalent to a neutral plasma near a charged wall.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, 11–16, February, 1987.     

Critical properties of entanglement in the Dicke model with the dipole-dipole interactions

In this paper, we investigate two aspects of entanglement properties of the ground state for the Dicke model with the dipole-dipole interaction between the atoms in the thermodynamic limit, and observe how they are affected by the quantum phase transition. The appearance of dipole-dipole interactions between the atoms does not change the maximum atom-field entanglement at the critical point, while it changes the maximum atom-atom entanglement at the critical point, and has an important influence on the atom-atom entanglement behavior.     

Hydrodynamical limit for a Hamiltonian system with weak noise

Starting from a general hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prolve that, in the scaling limit, the time conserved quantities, energy, momenta and density, satisfy the Euler equation of conservation laws up to a fixed timet provided that the Euler equation has a smooth solution with a given initial data up to timet. The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.Research partially supported by U.S. National Science Foundation grants DMS 89001682, DMS 920-1222 and a grant from ARO, DAAL03-92-G-0317Research partially supported by U.S. National Science Foundation grants DMS-9101196, DMS-9100383, and PHY-9019433-A01, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship     

Dead-time free measurement of dipole-dipole interactions between electron spins

A four-pulse version of the pulse double electron-electron resonance (DEER) experiment is presented, which is designed for the determination of interradical distances on a nanoscopic length-scale. With the new pulse sequence electron-electron couplings can be studied without dead-time artifacts, so that even broad distributions of electron-electron distances can be characterized. A version of the experiment that uses a pulse train in the detection period exhibits improved signal-to-noise ratio. Tests on two nitroxide biradicals with known length indicate that the accessible range of distances extends from about 1.5 to 8 nm. The four-pulse DEER spectra of an ionic spin probe in an ionomer exhibit features due to probe molecules situated both on the same and on different ion clusters. The former feature provides information on the cluster size and is inaccessible with previous methods.     

Thermodynamic functions for fermions with gravostatic and electrostatic interactions

The energy as function of entropy and the free energy as function of temperature is calculated rigorously for nonrelativistic fermions with interactions. It is shown that in the appropriate thermodynamic limit the corresponding Thomas-Fermi equation becomes exact.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung, Projekt Nr. 1391.On leave of absence from the University of Heidelberg, Germany.     

Thermodynamic arrow for a mixing system

The purpose of this paper is to study the appearance of time asymmetry in dynamical systems. The systems are harmonic oscillators and a certain mixing flow on the torus. The asymmetry is a kind of frictional force, but we emphasize that the boundary conditions, a usual source of asymmetry in studies of this sort, are taken to be time symmetric. For the mixing flow the response of the system, as reflected in its entropy as a function of time, occurs only subsequent to the friction, while for the oscillators the effects are both before and after. Some general discussion also takes up the question of which of the foregoing systems is a better model of the physical world for purposes of correlating arrows of time.Work supported in part by U.S. Army Research Office (Durham, N.C.).