Gibbs-Non-Gibbs Transitions via Large Deviations: Computable Examples

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in (van Enter et al. in Mosc. Math. J. 10:687–711, 2010). These examples include Brownian motion with small variance and related diffusion processes, such as the Ornstein-Uhlenbeck process, as well as birth and death processes. We show for a large class of initial measures and diffusive dynamics both short-time conservation of Gibbsianness and dynamical Gibbs-non-Gibbs transitions.     

Flows in Complex Networks: Theory,Algorithms, and Application to Lennard–Jones Cluster Rearrangement

A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which transitions occur between specific groups of nodes on the network. Sampling tools are built upon the outputs of TPT that allow to generate these reactive trajectories directly, or even transition paths that travel from one group of nodes to the other without making any detour and carry the same probability current as the reactive trajectories. These objects permit to characterize the mechanism of the transitions, for example by quantifying the width of the tubes by which these transitions occur, the location and distribution of their dynamical bottlenecks, etc. These tools are applied to a network modeling the dynamics of the Lennard–Jones cluster with 38 atoms ( \(\mathrm{LJ}_{38}\) ) and used to understand the mechanism by which this cluster rearranges itself between its two most likely states at various temperatures.     

Field Theoretic Formulation of Kinetic Theory: Basic Development

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables ?? the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables ?? and B.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.     

Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables ρ, the number density, and B, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.     

Phase transition in a harmonic oscillator with dynamical traps

We consider the characteristic features of a new class of nonequilibrium phase transitions, namely, transitions due to dynamical traps. We studied an individual oscillator with dynamical traps located in a small neighborhood of the x axis of the phase plane {x, v = dx/dt}. The dynamics of this system is analyzed numerically. The mechanism and conditions of the occurrence of various dynamic states is established. We demonstrate that the dynamics of such an oscillator can be represented by a number of random jump-like transitions between long-lived states. For these states to occur, random forces are necessary with intensity lying within a certain interval. If the intensity of the random forces is high or low, phase transitions due to dynamical traps will not occur.     

Low-frequency critical dynamics in (CnH2n+1NH3)2SnCl6 model biomembrane systems

Nuclear magnetic resonance has been employed as a probe for the collective hydrocarbon chain dynamics in the organic–inorganic model biomembranes (C_nH_2n+1NH₃)₂SnCl₆, undergoing order–disorder and conformational phase transitions. No anomalies were observed in the laboratory-frame spin–lattice relaxation measurements at the order–disorder phase transitions, whereas a discontinuity was manifest at the conformational phase transitions characteristic of a first-order phase transition. On the other hand, our rotating frame spin–lattice relaxation measurements revealed a low-frequency critical collective chain dynamics in the kilohertz regime associated with the order–disorder phase transition.     

Laser-irradiated thermodynamic behaviors of spallation and recombination at solid-state interface

A microscopic insight of interfacial spallation and recombination behaviors at multilayer thin-film interface induced by incident femtosecond pulsed laser is presented in this paper. Such two different aforementioned behaviors are investigated via the thermodynamic trajectories obtained by using standard Lennard-Jones (L-J) molecular dynamics (MD) simulation. Based on the simulation results, the interfacial damages of multilayer thin film are dominated by a critical threshold that induces an extraordinary expansive dynamics and phase transitions leading to the structural softened and tensile spallation at interface. The critical damage threshold is evaluated at around 8.5 J/m² which governs the possible occurrence of two different regimes, i.e. interfacial spallaiton and recombination. In interfacial damage region, quasi-isothermal thermodynamic trajectories can be observed after the interfacial spallation occurs. Moreover, the result of thermodynamic trajectories analyses indicates that, the relaxation of pressure wave may cause the over-heated interfacial zone to reduce volumetric density, thus leading to structural softness and even weaken interfacial structural strength. The crucial effect leading to the phenomenon of low tension spallation is identified.     

Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein–Maxwell field equations for this gas becomes a dynamical system in a 4D phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3D sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H ₀ is negative. If H ₀ is positive the trajectories end up in a curvature singularity that can be, depending on initial conditions, isotropic or anisotropic. In particular, if the initial magnetic field intensity is sufficiently large the collapsing singularity will always be anisotropic and pointing in the same direction of the field.     

Distribution function and electron state density in nonequilibrium plasma created by dye laser

Ultracold nonequilibrium plasma created by a dye laser has been studied by the molecular dynamics method. Electrons and protons in this model of nonequilibrium plasma interacted according to the Coulomb law. In the case of electron-proton interaction and a distance between particles r < a ₀ (Bohr radius), the interaction energy is constant, e ²/a ₀ (e is the charge of electron). An initial proton kinetic energy is set randomly so that the average kinetic energy is 0.01–1 K. Initial full electron energy is also set randomly, but at the same time it is positive; i.e., all the electrons according to our task are located in the continuous spectrum. Average kinetic electron energy per one particle varies from 1 to 50 K. The motion equations in periodical boundary condition for this system have been solved by molecular dynamics method. We have calculated the distribution function in the region near the ionization threshold. The distribution function is being described using electron state density in the nearest neighbor approximation with activity correction.     

Photoinduced dynamics to photoluminescence in Ln3+ (Ln = Ce,Pr) doped β-NaYF4 nanocrystals computed in basis of non-collinear spin DFT with spin-orbit coupling

ABSTRACT

In this work, non-collinear spin DFT + U approaches with spin-orbit coupling (SOC) are applied to Ln³⁺ doped β-NaYF₄ (Ln = Ce, Pr) nanocrystals in Vienna ab initio Simulation Package taking into account unpaired spin configurations using the Perdew–Burke–Ernzerhof functional in a plane wave basis set. The calculated absorption spectra from non-collinear spin DFT + U approaches are compared with that from spin-polarised DFT + U approaches. The spectral difference indicates the importance of spin–flip transitions of Ln³⁺ ions. Suite of codes for nonadiabatic dynamics has been developed for 2-component spinor orbitals. On-the-fly nonadiabatic coupling calculations provide transition probabilities facilitated by nuclear motion. Relaxation rates of electrons and holes are calculated using Redfield theory in the reduced density matrix formalism cast in the basis of non-collinear spin DFT + U with SOC. The emission spectra are calculated using the time-integrated method along the excited state trajectories based on nonadiabatic couplings.     

A study of three-dimensional reaction dynamics by means of quantum trajectories

Equations for quantum trajectories in three dimensions are derived and applied to studying the reaction dynamics of the interaction of the chlorine atom with the hydrogen molecule. The velocities of quantum trajectories are determined from the nonstationary wave function preliminary calculated by integrating the Schrödinger equation using the grid method and an expansion in basis set. An ensemble of 60 quantum trajectories for the initial vibrational state ν ₀ = 0 and rotational states j ₀ = 0 and 4 is obtained. A detailed analysis of one of the reaction trajectories is conducted. The existence of the effect of tunneling in the system is confirmed.     

Differential thermal analysis of the field induced phase transitions of (TMTSF)2ClO4 above 1.2 K

We present some results of a differential thermal analysis of the magnetic field induced phase transitions in the organic conductor (TMTSF)₂ClO₄ above 1.2 K. This study shows that transitions between different spin density wave states are first order and that the total entropy change involved in the two detected transitions (in the temperature range 1.2–2 K) is close to that of the quasi-one-dimensional electron gas. Above 2 and 4.2 K, only a single transition has been detected in our measurements. The entropy of that transition decreases and extrapolates to zero near 5 K. We present some arguments suggesting that if longitudinal nesting (2k_F, 0, 0) is to take place in the semi-metallic SDW phase at high fields it exists only above 2 K or so.     

Intersublevel transitions in self-assembled quantum dots

Intersublevel transitions in semiconductor quantum dots are transitions of a charge carrier between quantum dot confined states. In InAs/GaAs self-assembled quantum dots, optically active intersublevel transitions occur in the mid-infrared spectral range. These transitions can provide a new insight on the physics of semiconductor quantum dots and offer new opportunities to develop mid-infrared devices. A key feature characterizing intersublevel transitions is the coupling of the confined carriers to phonons. We show that the effect of the strong coupling regime for the electron–optical phonon interaction and the formation of mixed electron–phonon quasi-particles called polarons drastically affect and control the dynamical properties of quantum dots. The engineering of quantum dot relaxation rates through phonon coupling opens the route to the realization of new devices like mid-infrared polaron lasers. We finally show that the measurement of intersublevel absorption is not limited to quantum dot ensembles and that the intersublevel ultrasmall absorption of a single quantum dot can be measured with a nanometer scale resolution by using phonon emission as a signature of the absorption. To cite this article: P. Boucaud et al., C. R. Physique 9 (2008).