Elements of Fractal Generalization of Dual‐Porosity Model for Solute Transport in Unsaturated Fractured Rocks

In this study, new elements were developed to generalize the dual-porosity model for moisture infiltration on and solute transport in unsaturated rocks, taking into account fractal aspects of the percolation process. Random advection was considered as a basic mechanism of solute transport in self-similar fracture systems. In addition to spatial variations in the infiltration velocity field, temporal fluctuations were also taken into account. The rock matrix, a low-permeability component of the heterogeneous geologic medium, acts as a trap for solute particles and moisture. Scaling relations were derived for the moisture infiltration flux, the velocity correlation length, the average velocity of infiltration, and the velocity correlation function. The effect of temporal variations in precipitation intensity on the infiltration processes was analyzed. It showed that the mode of solute transport is determined by the power exponent in the advection velocity correlation function and the dimensionality of the trapping system, both of which may change with time. Therefore, depending on time, various transport regimes may be realized: superdiffusion, subdiffusion, or classical diffusion. The complex structure of breakthrough curves from changes in the transport regimes was also examined. A renormalization of the solute source strength due to characteristic fluctuations of highly disordered media was established

Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200

Beta decay and other processes in strong electromagnetic fields

We consider effects of the fields of strong electromagnetic waves on various characteristics of quantum processes. After a qualitative discussion of the effects of external fields on the energy spectra and angular distributions of the final-state particles as well as on the total probabilities of the processes (such as decay rates and total cross sections), we present a simple method of calculating the total probabilities of processes with production of non-relativistic charged particles. Using nuclear beta-decay as an example, we study the weak and strong field limits, as well as the field-induced beta-decay of nuclei stable in the absence of the external fields, both in the tunneling and multi-photon regimes. We also consider the possibility of accelerating forbidden nuclear beta-decays by lifting the forbiddeness due to the interaction of the parent or daughter nuclei with the field of a strong electromagnetic wave. It is shown that for currently attainable electromagnetic fields all effects on total beta-decay rates are unobservably small.Comment: LaTeX, 30 pages, 2 figures. Invited contribution to the special issue of Yadernaya Fizika dedicated to the centennial anniversary of birthday of A.B. Migdal. V2: references adde

Frequency-dependent (ac) Conduction in Disordered Composites: a Percolative Study

In a recent paper [Phys. Rev. B{\bf57}, 3375 (1998)], we examined in detail the nonlinear (electrical) dc response of a random resistor cum tunneling bond network ($RRTN$, introduced by us elsewhere to explain nonlinear response of metal-insulator type mixtures). In this work which is a sequel to that paper, we consider the ac response of the $RRTN$-based correlated $RC$ ($CRC$) model. Numerical solutions of the Kirchoff's laws for the $CRC$ model give a power-law exponent (= 0.7 near $p = p_c$) of the modulus of the complex ac conductance at moderately low frequencies, in conformity with experiments on various types of disordered systems. But, at very low frequencies, it gives a simple quadratic or linear dependence on the frequency depending upon whether the system is percolating or not. We do also discuss the effective medium approximation ($EMA$) of our $CRC$ and the traditional random $RC$ network model, and discuss their comparative successes and shortcomings.Comment: Revised and reduced version with 17 LaTeX pages plus 8 JPEG figure

Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results

A method of fundamental solutions has been used to investigate transitions in two energy level systems with no level crossing in a real time. Compact formulas for transition probabilities have been found in their exact form as well as in their adiabatic limit. No interference effects resulting from many level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev. {\bf A44} 4280 (1991)) have been detected in either case. It is argued that these results of this work are incorrect. However, some effects of Berry's phases are confirmed.Comment: LaTeX2e, 23 pages, 8 EPS figures. Style correcte

Enrichment of CH3F nuclear spin isomers by resonant microwave radiation

Theoretical model of the coherent control of nuclear spin isomers by microwave radiation has been developed. Model accounts the M-degeneracy of molecular states and molecular center-of-mass motion. The model has been applied to the 13CH3F molecules. Microwave radiation excites the para state (J=11,K=1) which is mixed by the nuclear spin-spin interaction with the ortho state (9,3). Dependencies of the isomer enrichment and conversion rates on the radiation frequency have been calculated. Both spectra consist of two resonances situated at the centers of allowed and forbidden (by nuclear spin) transitions in the molecule. Larger enrichment, up to 7%, can be produced by strong radiation resonant to the forbidden transition. The spin conversion rate can be increased by 2 orders of magnitude at this resonance.Comment: REVTEX, 14 pages + 6 eps figure

Quantum interference in nanofractals and its optical manifestation

We consider quantum interferences of ballistic electrons propagating inside fractal structures with nanometric size of their arms. We use a scaling argument to calculate the density of states of free electrons confined in a simple model fractal. We show how the fractal dimension governs the density of states and optical properties of fractal structures in the RF-IR region. We discuss the effect of disorder on the density of states along with the possibility of experimental observation.Comment: 19 pages, 6 figure

Duality in the Quantum Hall Effect - the Role of Electron Spin

At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of Kramers-Wannier duality for the two dimensional Ising model. The duality group, which is a subgroup of the modular group, is analysed and it is argued that there is a quantitative difference between a situation in which the spin splitting of electron energy levels is comparable to the cyclotron energy and one in which the spin splitting is much less than the cyclotron energy. In the former case the group of symmetries is larger than in the latter case. These duality symmetries are used to constrain the scaling functions of the theory and, under an assumption of complex meromorphicity, a unique functional form is obtained for the crossover of the conductivities between Hall states as a function of the external magnetic field. This analytic form is shown to give good agreement with experimental data. The analysis requires a consideration of the way in which longitudinal resistivities are extracted from the experimentally measured longitudinal resistances and a novel method is proposed for determining the correct normalisation for the former.Comment: 22 pages, 8 figures, typeset in LaTe

Non-zero temperature transport near quantum critical points

We describe the nature of charge transport at non-zero temperatures ($T$) above the two-dimensional ($d$) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order $k_B T/\hbar$. This implies that the transport at frequencies $\omega \ll k_B T/\hbar$ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while $\omega \gg k_B T/\hbar$ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be $e^2 / h$ times a non-trivial universal scaling function of $\hbar \omega / k_B T$, and not independent of $\hbar \omega/k_B T$, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $\hbar \omega/k_B T \to 0$ limit of this function, and is a universal number times $e^2 / h$, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless $\hbar \omega/k_B T \to \infty$ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times $e^2 / h$. We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in $\epsilon=3-d$. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.Comment: Feedback incorporated into numerous clarifying remarks; additional appendix discusses relationship to transport in dissipative quantum mechanics and quantum Hall edge state tunnelling problems, stimulated by discussions with E. Fradki

Analytical approach to bit-string models of language evolution

A formulation of bit-string models of language evolution, based on differential equations for the population speaking each language, is introduced and preliminarily studied. Connections with replicator dynamics and diffusion processes are pointed out. The stability of the dominance state, where most of the population speaks a single language, is analyzed within a mean-field-like approximation, while the homogeneous state, where the population is evenly distributed among languages, can be exactly studied. This analysis discloses the existence of a bistability region, where dominance coexists with homogeneity as possible asymptotic states. Numerical resolution of the differential system validates these findings.Comment: To appear in Int. J. Mod. Phys.