Self-organized criticality and 1/f fluctuation under conditions of nonequilibrium phase transitions

The results are given of an experimental investigation of fluctuation phenomena under conditions of electric arc discharge. Fluctuations are observed whose spectral density is inversely proportional to frequency (1/f noise). Power dependences are revealed of the fluctuation distribution functions. The behavior of spectral density and of distribution functions is associated with the simultaneous occurrence of various nonequilibrium phase transitions. Within the framework of the mean field theory, a mathematical model is suggested of interacting nonequilibrium phase transitions in a distributed system, which predicts the self-organization of the critical state and the generation of fluctuations with diverging spectral characteristics. An adequate agreement is observed between the suggested model and experimental data.     

Electron-acceptor luminescence from a non-Maxwellian distribution of photoexcited electrons in GaAs

Distribution functions are calculated for photoexcited electrons in GaAs, under conditions of continuous, monochromatic excitation. The lattice temperature is taken to be 1.2 K and the excitation intensity such that the density of photoexcited carriers is insufficient for the distribution to be affected by intercarrier scattering. A Boltzmann equation approach is used to take account of the effects of, injection of electrons into the conduction band, at an energy below the threshold for longitudinal optical phonon emission, scattering by acoustic phonons, via the deformation potential and piezoelectric interactions, and recombination. The equation is solved numerically using an iterative technique and the distribution functions are found to differ significantly from a Maxwellian form. Emission spectra due to conduction band to neutral acceptor transitions are derived from the computed distribution functions and are compared with recent experimental results.     

Gravitational phase transitions with an exclusion constraint in position space

We discuss the statistical mechanics of a system of self-gravitating particles with anexclusion constraint in position space in a space of dimension d. Theexclusion constraint puts an upper bound on the density of the system and can stabilize itagainst gravitational collapse. We plot the caloric curves giving the temperature as afunction of the energy and investigate the nature of phase transitions as a function ofthe size of the system and of the dimension of space in both microcanonical and canonicalensembles. We consider stable and metastable states and emphasize the importance of thelatter for systems with long-range interactions. For d ≤ 2, there is nophase transition. For d > 2, phase transitions can take place betweena “gaseous” phase unaffected by the exclusion constraint and a “condensed” phase dominatedby this constraint. The condensed configurations have a core-halo structure made of a“rocky core” surrounded by an “atmosphere”, similar to a giant gaseous planet. For largesystems there exist microcanonical and canonical first order phase transitions. Forintermediate systems, only canonical first order phase transitions are present. For smallsystems there is no phase transition at all. As a result, the phase diagram exhibits twocritical points, one in each ensemble. There also exist a region of negative specificheats and a situation of ensemble inequivalence for sufficiently large systems. We showthat a statistical equilibrium state exists for any values of energy and temperature inany dimension of space. This differs from the case of the self-gravitating Fermi gas forwhich there is no statistical equilibrium state at low energies and low temperatures whend ≥ 4. By a proper interpretation of the parameters, our results haveapplication for the chemotaxis of bacterial populations in biology described by ageneralized Keller-Segel model including an exclusion constraint in position space. Theyalso describe colloids at a fluid interface driven by attractive capillary interactionswhen there is an excluded volume around the particles. Connexions with two-dimensionalturbulence are also mentioned.     

Semi-flexible polymers with attractive interactions

The delocalization and unbinding transitions of two semi-flexible polymers which experience attractive interactions are studied by a variety of theoretical methods. In two-dimensional systems, one has to distinguish four different universality classes for the interaction potentials. In particular, the delocalization transitions from a potential well and the unbinding transitions from such a well in the presence of a hard wall exhibit distinct critical behavior governed by different critical exponents. In three-dimensional systems, we predict first-order transitions with a jump in the energy density but with critical or self-similar fluctuations leading to distribution functions with power law tails. The predicted critical behavior is confirmed numerically by transfer matrix calculations in two dimensions and by Monte Carlo simulations in three dimensions. This behavior should be accessible to experiments on biopolymers such as actin filaments or microtubuli. Received 15 December 1999 and Received in final form 19 May 2000     

Strain phase diagram and domain orientation in SrTiO3 thin films

SrTiO3 thin films were used as a model system to study the effects of strain and epitaxial constraint on structural phase transitions of perovskite films. The basic phenomena revealed will apply to a variety of important structural transitions including the ferroelectric transition. Highly strained SrTiO3 films were grown on different substrates, providing both compressive and tensile strain. The measured strain-temperature phase diagram is qualitatively consistent with theory; however, the increase in the phase transition temperature is much larger than predicted. Because of the epitaxial strain and substrate clamping, the SrTiO3 lattice is tetragonal at all temperatures. The phase transitions involve only changes in internal symmetry. The low temperature phase under tensile strain has a unique structure with orthorhombic Cmcm space group but a tetragonal lattice, an interesting consequence of epitaxial constraint.     

Electromagnetic transitions between rydberg states of a hydrogen atom: Violation of the dipole selection rules in a strong field

One-quantum bound-bound transitions between high-excited states of a hydrogen atom are considered. Electron wave functions involving an electromagnetic field even in a zero-order approximation are constructed semiclassically. With these functions, it is shown that transitions accompanied by violation of the dipole selection rules are possible in strong fields. The probability of such transitions is a nonlinear function of electromagnetic field intensity.     

A mathematical solution for the parameters of three interfering resonances

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used.     

Raynal–Revai coefficients for a general kinematic rotation

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.     

A universal scaling theory for complexity of analog computation

We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability ensembles of linear programming problems. For each one of these we obtain numerically the probability distribution functions of certain quantities which measure the complexity. Remarkably, in the asymptotic limit of very large problems, each of these probability distribution functions reduces to a universal scaling function, depending on a single scaling variable and independent of the details of its parent probability ensemble. These functions are reminiscent of the scaling functions familiar in the theory of phase transitions. The results reported here extend analytical and numerical results obtained recently for the Gaussian ensemble.     

非高斯Lévy噪声驱动下的非对称双稳系统的相转移和平均首次穿越时间

研究了非高斯Lévy噪声激励下非对称双稳系统的相转移和首次穿越问题.首先利用Grünwald-Letnikov有限差分方法数值求解系统所对应的分数阶Fokker-Plank方程,得到了系统的稳态概率密度函数.然后分析了系统的非对称参数以及噪声强度和稳定性指标对稳态概率密度函数的影响,发现了非对称参数和稳定性指标的变化都能够诱导系统发生相转移.进一步研究了系统的平均首次穿越时间,得到了非对称参数、噪声强度和稳定性指标影响系统平均首次穿越时间的不同作用机理. 关键词： 非高斯Lévy噪声 非对称双稳系统 相转移 平均首次穿越时间     

Statistical mechanics of quasi-one-dimensional systems

A definition of a quasi-one-dimensional system as a generalized Cayley or Husimi tree with a nonzero surface to bulk ratio in the thermodynamic limit is given. Sufficient conditions for the existence of the thermodynamic limit of the free energy for such a system are derived and a thorough discussion of the thermodynamic limit properties of the one-particle distribution functions is given. These results are made more precise for the case of systems with Hamiltonians which are invariant under a special type of measure-preserving group of transformations, in particular for the d-dimensional rotation group. For this latter case, the phase transitions which can occur in quasi-one-dimensional systems upon application of small external fields are studied in some detail. A number of completely solved examples is given to illustrate the general theory. These include the classical Heisenberg model on a Cayley tree and generalizations thereof.     

Random walks with nonnearest-neighbor transitions. II. Analytic one-dimensional theory for exponentially distributed steps in systems with boundaries

Exact analytic results for symmetric, nonnearest-neighbor random walks in one-dimensional finite and semiinfinite lattices are presented. Random walks with exponentially distributed step lengths are considered such that variation of a single parameter permits one to cover the whole range of step lengths from nearest-neighbor transitions to steps of aribtrary length. The generating functions for such lattices are derived and used to calculate a number of moment properties (mean first passage times, dispersion in the mean recurrence time). Since explicit expressions for the generating functions for these walks are obtained, additional moment properties can readily be calculated. The results found here for a finite system are compared to results found previously for a system with periodic boundary conditions. Two different semiinfinite systems are also considered.     

Lee–Yang zeros in the Rydberg atoms

Lee–Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase transitions happen in 1d classical Rydberg chains. We investigate how the zeros redistribute as one interpolates between different blockade radii. We also discuss possible experimental measurements of these zeros.     

Existence criteria for Landau-Pekar polarons

We build the distribution function for a system with coexisting self-localized and delocalized fermions. The distribution function is used to study the behavior of the chemical potential of the carriers in such a system, which is found to differ substantially from the behavior of the chemical potential in a system of delocalized fermions. We also find that as the temperature changes, isostructural first-order phase transitions can emerge in the system of self-localized and delocalized fermions. These transitions, for which changes in the state of the macroscopic number of particles are responsible, manifest themselves in the electrical conductivity, in the contribution of carriers to the specific heat, and in the optical properties of such systems. Formulas are derived that approximate the dependence of the temperature of such a phase transition on the binding energy of the self-localized states of carriers and on the maximum group velocity of phonons participating in the formation of such states. Finally, we show that the special features of the behavior of the chemical potential of the carriers in a system with carrier self-localization lead to the possibility of Bose condensation in a system where bipolaron states are metastable. Zh. éksp. Teor. Fiz. 116, 1386–1397 (October 1999)     

Bifurcations in a system of two identical diffusion-coupled relaxational brusselators

We propose a two-parameter bifurcation analysis of the dynamics of a system of two identical asymmetrically coupled Brusselators. The stability boundaries of the inhomogeneous steady states and periodic attractors are calculated as the functions of the constraint force and one of the free parameters. The coexistence of different attractors giving rise to multirhythmicity of the dynamics is studied as well as the bifurcation transitions between them. It is shown that the relaxation ability of an oscillator plays an important role in the simplification of the phase diagram, since it removes the overlapping of the existence region for different solutions. We assume that the results primarily characterize the properties of the diffusion coupling and, therefore, they can be applied in the study of other oscillator systems.P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 5, pp. 373–401, May, 1995.     

Entropy maximum in a nonlinear system with the 1/<Emphasis Type="Italic">f</Emphasis> fluctuation spectrum

Analysis of the control and subordination is carried out for the system of nonlinear stochastic equations describing fluctuations with the 1/f spectrum and with the interaction of nonequilibrium phase transitions. It is shown that the control equation of the system has a distribution function that decreases upon an increase in the argument in the same way as the Gaussian distribution function. Therefore, this function can be used for determining the Gibbs-Shannon informational entropy. The local maximum of this entropy is determined, which corresponds to tuning of the stochastic equations to criticality and indicates the stability of fluctuations with the 1/f spectrum. The values of parameter q appearing in the definition of these entropies are determined from the condition that the coordinates of the Gibbs-Shannon entropy maximum coincide with the coordinates of the Tsallis entropy maximum and the Renyi entropy maximum for distribution functions with a power dependence.     

Optical noise-free image encryption based on quick response code and high dimension chaotic system in gyrator transform domain

A novel optical image encryption scheme is proposed based on quick response code and high dimension chaotic system, where only the intensity distribution of encoded information is recorded as ciphertext. Initially, the quick response code is engendered from the plain image and placed in the input plane of the double random phase encoding architecture. Then, the code is encrypted to the ciphertext with noise-like distribution by using two cascaded gyrator transforms. In the process of encryption, the parameters such as rotation angles and random phase masks are generated as interim variables and functions based on Chen system. A new phase retrieval algorithm is designed to reconstruct the initial quick response code in the process of decryption, in which a priori information such as three position detection patterns is used as the support constraint. The original image can be obtained without any energy loss by scanning the decrypted code with mobile devices. The ciphertext image is the real-valued function which is more convenient for storing and transmitting. Meanwhile, the security of the proposed scheme is enhanced greatly due to high sensitivity of initial values of Chen system. Extensive cryptanalysis and simulation have performed to demonstrate the feasibility and effectiveness of the proposed scheme.     

Numerical simulations of the Euler system with congestion constraint

In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in  and  with the constraint introduced into the system by a singular pressure law, which causes the transition of different asymptotic dynamics between different regions. To overcome these difficulties, we adapt and implement two asymptotic preserving (AP) schemes originally designed for low Mach number limit  and  to our model. These schemes work for the different dynamics and capture the transitions well. Several numerical tests both in one dimensional and two dimensional cases are carried out for our schemes.     

Temperature dependent symmetry to asymmetry transition in wide quantum wells

Quasi-two dimensional electron systems exhibit peculiar transport effects depending on their density profiles and temperature. A usual two dimensional electron system is assumed to have a δ like density distribution along the crystal growth direction. However, once the confining quantum well is sufficiently large, this situation is changed and the density can no longer be assumed as a δ function. In addition, it is known that the density profile is not a single peaked function, instead can present more than one maxima, depending on the well width. In this work, the electron density distributions in the growth direction considering a variety of wide quantum wells are investigated as a function of temperature. We show that the double peak in the density profile varies from symmetric (similar peak height) to asymmetric while changing the temperature for particular growth parameters. The alternation from symmetric to asymmetric density profiles is known to exhibit intriguing phase transitions and is decisive in defining the properties of the ground state wavefunction in the presence of an external magnetic field, i.e from insulating phases to even denominator fractional quantum Hall states. Here, by solving the temperature and material dependent Schrödinger and Poisson equations self-consistently, we found that such a phase transition may be elaborated by taking into account direct Coulomb interactions together with temperature.     

Alternative formulation for invariant optical fields: Mathieu beams

Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.