Decay and diffusion in hierarchical systems

We investigate the combined effects of decay and diffusion in a hierarchically organized system, i.e. in an ultrametric space. The long time asymptotics for the law of disappearance of particles is found and the conditions that the disappearance is diffusion-controlled are determined. The diffusional spreading of particles in the presence of decay is analyzed.     

Nonlinear wave processes in a deformable solid as a hierarchically organized system

Theoretical predictions and experiments demonstrate that solid state mechanics should consider, along with a structurally equilibrium 3D crystalline subsystem, a structurally nonequilibrium planar subsystem as a complex of all surface layers and internal interfaces with broken translation invariance. Primary plastic flow of a loaded solid develops in its structurally nonequilibrium planar subsystem as channeled nonlinear waves of local structural transformations that determine the self-organization law of multiscale plastic flow. These waves initiate mesoscale rotational deformation modes, giving rise to all types of microscale strain-induced defects in the planar subsystem. The strain-induced defects are emitted into the crystalline subsystem as an inhibitor of nonlinear waves of plastic flow in the planar subsystem. Plastic deformation of solids, whatever the loading type, evolves in the field of rotational couple forces. Loss of hierarchical self-consistency by rotational deformation modes culminates in fracture of material as an uncompensated rotational deformation mode on the macroscale.     

Decay rate with coordinate-dependent diffusion coefficients

Using a master equation for the reduced density matrix of open quantum system, the influence of coordinate-dependent microscopical diffusion coefficients on the decay rate from a potential well is studied. For different temperatures, frictions, heights of barrier and ratios of stiffnesses of the potential in the minimum and on the top of the barrier, the quasistationary decay rates are obtained with the sets of coordinate-dependent and -independent microscopical diffusion coefficients, and coordinate-dependent phenomenological diffusion coefficients.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Differences and similarities between self-organizing and organized systems

The energy and dynamic characteristics of self-organizing and organized physical systems in which particles interact via electric fields are consistently considered in terms of the integral Lagrangian minimization. It is shown that the energy dissipation plays a minor role in self-organization processes. Two types of work are distinguished, basic differences and similarities between the systems are revealed, and comparison with living organisms is made.     

Decay rates and survival probabilities in open quantum systems

We provide the first statistical analysis of the decay rates of strongly driven 3D atomic Rydberg states. The distribution of the rates exhibits universal features due to Anderson localization, while universality of the time dependent decay requires particular initial conditions.     

Mass and charge transport in hierarchically organized storage materials. Example: Porous active materials with nanocoated walls of pores

To enhance the kinetics of poorly conducting cathode materials for Li batteries, the authors have proposed a number of strategies based on crushing the active material into nanopowder and embedding the powder into a carbon-based web or coating. Using the well-elaborated example of LiFePO4, we demonstrate that the same goal can be achieved with a different approach where the active material remains in a form of large (1–20 μm) single crystals. Instead of crushing the material, we make it porous—with average pore size around 50 nm and pore surface area of 25 m²/g. The walls of the pores (but also the outer surfaces of crystals) are covered with ca. 1-nm-thick carbon film. Most surprisingly, such a unique nanoarchitecture can be prepared using a simple sol–gel based procedure including a single heat treatment. The crucial part is the selection of appropriate carbon precursor. For example, citric acid decomposes quite vigorously into gases and solid carbon at temperatures up to ca. 450 °C. This range matches exactly the first solidification of LiFePO₄. Thus, the evolving gases can create an interconnected web of pores while the solid parts (carbon) are deposited simultaneously on the walls of pores. We further show that a carbon content of less than 3% is already sufficient for surpassing the percolation threshold with respect to surface conductivity of carbon. Using more carbon can decrease the rate performance so a fine balance is required in this respect. Most importantly, carbonization at a temperature of slightly less than 700 °C is sufficient to achieve a composite conductivity of the order of 10^− 2 S cm^− 2—more than sufficient for good cathode kinetics. In the end, we show new evidence that the phase that is responsible for high conductivity of LiFePO₄–C composites is indeed the carbon phase.     

Decay of transient nutation in two-level spin systems

This paper reports the results of an experimental study of the decay of transient NMR nutations in a two-level spin system with homogeneous line broadening. The NMR nutation signals in glycerin were studied for 10⩽ω ₁ T ₂⩽150, where ω ₁=γH ₁, with γ the gyromagnetic ratio and H ₁ the amplitude of the magnetic component of the radio-frequency field, and T ₂ is the transverse relaxation time. It is found that in a high-power field (ω ₁ T ₂≫1) the nutation decay rate is independent of ω ₁ and is quantitatively described by Bloch’s model. The data is compared with the data on non-Bloch (ω ₁-dependent) EPR-nutation decay in quartz (R. Boscaino, F. M. Gelardi, and J. P. Corb, Phys. Rev. B 48, 7077 (1993)). Zh. éksp. Teor. Fiz. 111, 1207–1213 (April 1997)     

Decay of a thermofield-double state in chaotic quantum systems

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This spreading can be analyzed with the spectral form factor, which is defined in terms of the analytic continuation of the partition function. The latter is equivalent to the survival probability of a thermofield double state under unitary dynamics. Using random matrices from the Gaussian unitary ensemble (GUE) as Hamiltonians for the time evolution, we obtain exact analytical expressions at finite N for the survival probability. Numerical simulations of the survival probability with matrices taken from the Gaussian orthogonal ensemble (GOE) are also provided. The GOE is more suitable for our comparison with numerical results obtained with a disordered spin chain with local interactions. Common features between the random matrix and the realistic disordered model in the chaotic regime are identified. The differences that emerge as the spin model approaches a many-body localized phase are also discussed.     

Decay of correlations in Fermi systems at nonzero temperature

The locality of correlation functions is considered for Fermi systems at nonzero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at nonzero temperature.     

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square-well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent γ=3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the “stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenario.     

Strong-coupling diffusion in relativistic systems

Different from the early universe, heavy-ion collisions at very high energies do not reach statistical equilibrium, although thermal models explain many of their features. To account for nonequilibrium strong-coupling effects, a Fokker-Planck equation with time-dependent diffusion coefficient is proposed. A schematic model for rapidity distributions of participant baryons is set up and solved analytically. The evolution from SIS via AGS and SPS to RHIC energies is discussed. Strong-coupling diffusion produces double-peaked spectra in central collisions at the higher SPS momentum of 158 A.GeV/c and beyond.     

Incommensurate diffusion in confined systems

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate. Furthermore, the physical compatibility between the adsorbate and the adsorbent has a direct effect on the heat of adsorption, the Henry coefficients, the activation energy, and the frequency factors.     

Thermal diffusion in disperse systems

This paper discusses a theory for a new effect, the migration of solid dispersed particles initiated by a nonuniform temperature field. The reason for the motion is the inhomogeneity of the properties of a thin protective layer around a particle. The example of ionic dispersion shows that the sign of the coefficient of thermodiffusion depends on the magnitude of the electrostatic potential at the particle surface and the thickness of the Debye layer and that the coefficientis larger than the values known for molecular systems by a factor of 100 to 10000. In contrast to molecular systems, in disperse systems thermodiffusion should play a much more important role. Zh. éksp. Teor. Fiz. 115, 1721–1726 (May 1999)     

Arnold diffusion in large systems

A new regime of Arnold diffusion in which the diffusion rate has a power-law dependence on the perturbation strength is studied theoretically and in numerical experiments. The theory developed predicts this new regime to be universal in the perturbation intermediate asymptotics, the width of the latter increasing with the dimensionality of the perturbation frequency space, particularly in large systems with many degrees of freedom. The results of numerical experiments agree satisfactorily with the theoretical estimates. Zh. éksp. Teor. Fiz. 112, 1132–1146 (September 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.