Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature

We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. We provide a mathematically rigorous derivation of their FDT solution (for the high temperature regime) and of certain key properties of this solution, which are in agreement with earlier derivations based on physical grounds. AMS (2000) Subject Classification: Primary: 82C44 Secondary: 82C31, 60H10, 60F15, 60K35     

Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature

We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p−spin disordered mean-field models. We provide a mathematically rigorous derivation of their FDT solution (for the high temperature regime) and of certain key properties of this solution, which are in agreement with earlier derivations based on physical grounds. AMS (2000) Subject Classification: Primary: 82C44, Secondery: 82C31, 60H10, 60F15, 60K35     

Equilibrium Sampling From Nonequilibrium Dynamics

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a nonequilibrium random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual nonequilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths. AMS: 65C05 65C35 80A10     

Canonical Analysis of Condensation in Factorised Steady States

We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a condensation transition but does not shed light on the nature of the condensate. Here, within the canonical ensemble, we analyse the condensation transition and the structure of the condensate, determining the precise shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as L ^1/2 where L is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. Our results are asymptotically exact and can also be interpreted within the framework of sums of random variables. We further analyse two additional cases: one where the condensation transition is somewhat different from the usual second order phase transition and one where there is no true condensation transition but instead a pseudocondensate appears at superextensive densities. PACS numbers: 05.40.-a, 02.50.Ey, 64.60.-i.     

The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model

We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.AMS Subject Classification (2000). 60K35 (82C22, 82C31)This work was partially supported by CNPq     

Determination of the chemical potential and the energy of the ν=1/2 FQHE system for low temperatures

We consider the energy density of a spin polarized ν = 1/2 system for low temperatures. We show that due to the elimination of the magnetic field and the field of the positive background charge in the calculation of the grand canonical potential of Chern-Simons systems through a mean field formalism one gets corrections to the well known equations which determine the chemical potential and the energy from the grand canonical potential. We use these corrected equations to calculate the chemical potential and the energy of the ν = 1/2 system at low temperatures in two different approximations. Received 14 March 2001     

Trapping radioactive atoms for basic and applied research

We report on the trapping of radioactive atoms for a variety of nuclear, atomic, and applied physics investigations. To date we have trapped 5 different radioisotopes of rubidium and cesium (^82–84Rb+^135,137Cs) using a magneto-optical trap (MOT) coupled to a mass separator. By optimizing the efficiency of this system, we have been able to trap as many as 6 million radioactive atoms and detect as few as 100. This technology is being applied in three different areas: (1) the parity-violating, β-decay asymmetry measurement of polarized ⁸²Rb; (2) the study of ultracold fermionic ⁸⁴Rb atoms; and (3) the use of MOTs for the ultrasensitive detection of selected radioactive species. Although all of these projects are in a formative stage of development, we highlight the progress that we have made in: (1) the trapping of ⁸²Rb atoms in double MOT system; (2) the hyperfine structure measurement of the 5P_1/2 and 5P_3/2 levels in ⁸²Rb; (3) the simultaneous trapping of ⁸⁴Rb and ⁸⁷Rb in overlapping MOTs; and (4) the first trapping and isotopic ratio measurement of ¹³⁵Cs and ¹³⁷Cs in a MOT. This revised version was published online in August 2006 with corrections to the Cover Date.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

Manipulation of nanoparticles using dynamic force microscopy: simulation and experiments

82 , M = Sc, Y, La) are discussed. The first ¹³C hyperfine structure has been analyzed in detail and at least seven electronically different groups of carbon atoms could be assigned by simulations of the ESR spectra. The strong similarity of the ¹³C satellite structure suggests the preference of one cage isomer for the scandium group C₈₂ endohedrals. The geometric structure and the electronic structure of all nine fullerene cage isomers of La@C₈₂ were studied by approximate density-functional-based theoretical calculations. A C_3v isomer was found as the most stable one. The manifold of ¹³C hyperfine coupling constants could be interpreted on the basis of the calculated spin density distributions. Received: 15 September 1997/Accepted: 16 October 1997     

On induced CPT-odd Chern-Simons terms in the 3+1 effective action

This paper was originally designated as a Comment on the paper by R. Jackiw and V. A. Kostelecky, Phys. Rev. Lett. 82, 3572 (1999). It gives an example of a fermionic system in which the CPT-odd Chern-Simons terms in the effective action are unambiguously induced by chiral fermions: superfluid ³He-A. In this system the Lorentz and gauge invariances are both violated at high energy, but the behavior of the system beyond the cutoff is known. This allows one to construct a CPT-odd action which combines the conventional 3+1 CS term and the mixed axial-gravitational CS term discussed by G. E. Volovik and A. Vilenkin, http://xxx.lanl.gov/abs/hep-ph/9905460. The influence of the CS term on the dynamics of the effective gauge field has been observed experimentally in rotating ³He-A. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 3–6 (10 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part II: Self-Similar Solutions and Tail Behavior

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].     

Analogies between the (p,t) and the (14C,16O) reaction on semi-magic nuclei

The two-proton pickup (¹⁴C,¹⁶O) reaction was studied for the N=82 target nuclei ₅₈ ¹⁴⁰ Ce₈₂, ₆₀ ¹⁴² Nd₈₂, and ₆₂ ¹⁴⁴ Sm₈₂. We observe dominating g.s. transitions and selective population of the first excited 2⁺ and 3^? states, in analogy to the two-proton pickup (p, t)-reaction on the proton-magic Sn-isotopes.     

Resonance Raman excitation and electronic structure of the single bonded dimers (C ¯60)2 and (C 59N)2

Raman spectra are presented for the single bonded dimeric fullerene (C ₆₀ ^- ) ₂ and compared to optical spectra and Raman spectra of the isostructural and isoelectronic heterofullerene (C₅₉N)₂. The spectra of both materials exhibit strong correlations with respect to splitting, line position, and line intensity. This holds for non resonant excitation with blue and green lasers as well as for the strong resonances observed with red lasers. The latter observation is consistent with a downshift for the electronic transition energies as compared to C₆₀. The absorption edge of thin films of (C₅₉N)₂ was found at 1.4 eV. The three intercage modes were observed at 82, 103, and 111, and at 88, 98, and 106 cm^-1 for (C₅₉N)₂ and (C ₆₀ ^- ) ₂ , respectively. A surprising difference was found for the position of the pentagonal pinch modes in the two materials as they were observed at 1461 and at 1451 cm^-1, for (C₅₉N)₂ and (C ₆₀ ^- ) ₂ , respectively. This is interpreted as a consequence of some characteristic differences in the electronic structure of the two compounds. Received 25 January 2000 and Received in final form 10 April 2000     

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].     

Exact Connections between Current Fluctuations and the Second Class Particle in a Class of Deposition Models

We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers’ and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations. MSC: 60K35, 82C41     

Off-centre charge model of the planar electric double layer for asymmetric 2:1/1:2 valencies

ABSTRACT

Grand canonical Monte Carlo simulation results are reported for the structure and capacitance of a planar electric double layer containing off-centre charged rigid sphere cations and centrally charged rigid sphere anions. The ion species are assigned asymmetric valencies, +2:?1 and +1:?2, respectively, and set in a continuum dielectric medium (solvent) characterised by a single relative permittivity. An off-centre charged ion is obtained by displacing the ionic charge from the centre of the sphere towards its surface, and the physical double layer model is completed by placing the ionic system next to a uniformly charged, non-penetrable, non-polarizable planar electrode. Structural results such as electrode-ion singlet distribution functions, ionic charge density and orientation profiles are complemented by differential capacitance results at electrolyte concentrations of 0.2?mol/dm³ and 1?mol/dm³, respectively, and for various displacements of the cationic charge centre. The effect of asymmetry due to off-centre cations and valency asymmetry on the double layer properties is maximum for divalent counterions and when the cation charge is closest to the hard sphere surface.     

Quantum Noether identities for non-local transformationsin higher-order derivatives theories

Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I_eff^P in quantum canonical NIs instead of the classical I^P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively.Received: 12 February 2002, Revised: 16 June 2003, Published online: 25 August 2003Z.-P. Li: Corresponding authorAddress for correspondence: Department of Applied Physics, Beijing Polytechnic University, Beijing 100022, P.R. China     

The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble

This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a generalized canonical ensemble that satisfies a strong form of equivalence with the microcanonical ensemble that we call universal equivalence. The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. For example, if the microcanonical entropy is C², then universal equivalence of ensembles holds with g taken from a class of quadratic functions, giving rise to a generalized canonical ensemble known in the literature as the Gaussian ensemble. This use of functions g to obtain ensemble equivalence is a counterpart to the use of penalty functions and augmented Lagrangians in global optimization. linebreak Generalizing the paper by Ellis et al. [J. Stat. Phys. 101:999–1064 (2000)], we analyze the equivalence of the microcanonical and generalized canonical ensembles both at the level of equilibrium macrostates and at the thermodynamic level. A neat but not quite precise statement of one of our main results is that the microcanonical and generalized canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the generalized microcanonical entropy s–g is concave. This generalizes the work of Ellis et al., who basically proved that the microcanonical and canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the microcanonical entropy s is concave.     

Site factors in N.M.R. solvent effects

An algorithm was developed enabling implementation of a Nosé—Hoover thermostat within the framework of grand canonical molecular dynamics [Lynch, C. G. and Pettitt, B. M., 1997, J. chem. Phys., 107, 8594]. The proposed algorithm could readily be extended to mixtures of molecular species with different chemical potentials as shown in the paper. This algorithm was first applied to simulate a μVT ensemble of TIP4P water molecules at 298 K by means of a system comprising a number of full particles and a single scaled (fractional) particle, with the scaling factor considered as a dynamic variable in its own right and chemical potential a pre-set parameter. Our finding showed that the scheme with a single fractional particle tended to freeze in metastable states as well as failed to reproduce either the real-life (?24.05 kJmol^?1) or the model-specific chemical potential of water (?23.0kJ mol^?1). In order to overcome the inadequacy of a single fractional particle as a chemical potential ‘probe’ the treatment of Pettitt and co-workers was extended to introduce multiple fractional particles. The extended scheme (with 4 fractional particles) was able to reproduce the actual density of water for the driving chemical potential of -24.0k mo^?1. The actual behaviour of the density as a function of the chemical potential also agreed quite well with both the results of thermo-dynamic integration and the findings of Pettitt and co-workers.     

Self-energy contribution to the ground state hyperfine splitting of Bi82+

The self-energy contribution to the hyperfine splitting of the ground state of Bi⁸²⁺ is calculated for a point nucleus. It is found that the theoretical value of the wavelength of the ground-state hyperfine-splitting transition of ²⁰⁹Bi⁸²⁺ is λ=244(1) nm and is in good agreement with experiment. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 309–310 (10 March 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.