Fractional approach,quantum statistics,and non-crystalline solids at very low temperatures

We consider nonlocal effects, obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, to analyze physical properties of non-crystalline solids at very low temperature. By using thermal Green functions, we deduce some experimentally observable quantities such as the particle momentum distribution function, the particle energy distribution function, and the specific heat. The agreement between the results obtained for the specific heat and the experimental data suggests that the approach presented here may be useful as a phenomenological model to investigate thermal properties of non-crystalline solids at low temperature.     

Quantum heat engines, the second law and Maxwell's daemon

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells, or even special cases of continuous spectra.     

Dielectric and anharmonic behaviour of mixed alkali halides

Summary In the present paper an analysis of the dielectric behaviour and anharmonic contribution to the dielectric constants has been made of KCl−KBr mixed ionic crystals. The temperature and volume derivatives of static (ε₀), electronic (ε_∞) dielectric constants and energy gap parameter (E _g) have been calculated using the Szigeti and Havinga and Bosman dielectric theories. The anharmonic contributions have been estimated in terms of temperature derivatives of dielectric constants at constant volumes. The modified form of Clausius-Mossotti theory of dielectric polarization has been used for the mixed crystal under study. The calculated quantities have been compared with the available experimental data. A good agreement has been obtained. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

The sign of interband interaction and stability of the superconducting ground state in the multiband model

Summary It is stressed that the stability of the superconducting ground state in the two-band model is guaranteed for both signs of the leading interband interactionW. Thereby the requirement for the energy minimum fixed the phase differences of two order parameters as |ϕ₁-ϕ₂|=0,2π, … ifW<0 and |ϕ₁-ϕ₂|=π 3π, … ifW>0, and this difference is reflected in the ground-state wave function.     

Socio-economical dynamics as a solvable spin system on co-evolving networks

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantitieswhich arrange towards a minimum energy state in the canonical framework:the spins, s_i, and the adjacency matrix elements, c_ij.The model is exactly solvable because microcanonical partition functions reduce to productsof binomial factors as a direct consequence of the c_ij minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discussthe phase diagrams.     

Relativistic effects in the time evolution of an one-dimensional model atom in a laser pulse

We define 1D Volkov states as solutions of the one-dimensional Dirac equation in a time dependent electric field, similar to the Volkov solutions in the three dimensional case. They are eigenspinors of the momentum operator and reduce in the absence of the field to free solutions of positive or negative energy. Then we add a time independent attractive Gausssian potential and, by integrating the Dirac equation for a laser pulse of Gaussian shape, we determine the state which coincides initially with the ground state of the system in the absence of the electric field. Our main objective is the study of the population dynamics on the Volkov states during the pulse action. For different values of the laser pulse intensity and two values of the potential depth, we find that the Volkov states which evolve from free solutions of negative energy are practically not populated, in contrast to the population on free negative energy states.     

Interaction of molecules with a semiconductor wall

Summary In this paper we consider the interaction of vibrationally and electron-excited molecules with a wall made of a semiconductor with the widths of the forbidden zone close to the excitation energy of the molecules. It is shown that the main process induced by the collision of a molecule with such a wall is the production of an electron-hole pair. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Inclusion of retardation effects in the nonrelativistic treatment of the lamb shift

Summary The retardation effects are included in the nonrelativistic calculation of the Lamb shift, by using a method which exploits theO(4) symmetry of the nonrelativistic hydrogen atom. This method has been previously applied by Lieber to the treatment of the Lamb shift. However, in contrast to his calculations, no kind of dipole approximation, leading to the introduction of an inconsistent cut-off frequency, is used in our treatment. Apart from obtaining cut-off-independent results, the inclusion of retardation effects makes also possible the calculation of the spin-radiation-field Lamb-shift contribution (which vanishes in the dipole approximation). Furthermore, our unambiguous renormalization, consisting of removing the unobservable free-electron self-energy contribution from our expressions, leads to finite analytical and numerical results for the energy level (Lamb) shifts. The comparison of these results with those obtained in a nonrelativistic treatment by other authors shows that our results are in better agreement with the experiment.     

Analysis of the CO vibrational distribution obtained from formaldehyde laser photodecomposition

Summary A simple analysis of the overall CO vibrational distribution obtained from formaldehyde laser photodecomposition has been carried out. Extrapolation to zero vibrational energy transfer to CO gives an energy value of (27770±80) cm⁻¹ for the intermediate assumed in the formaldehyde predissociation. The result obtained turns out to be very reasonable and consistent with several mechanisms suggested in previous studies To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

q-deformed Fermions

This is a study of q-Fermions resulting from q-deformed algebra of harmonic oscillators arising from two distinct algebras. Employing the first algebra, the Fock states are constructed for the generalized Fermions obeying Pauli exclusion principle. The distribution function and other thermodynamic properties such as the internal energy and entropy are derived. Another generalization of fermions from a different q-deformed algebra is investigated which deals with q-fermions not obeying the exclusion principle. Fock states are constructed for this system. The basic numbers appropriate for this system are determined as a direct consequence of the algebra. We also establish the Jackson Derivative, which is required for the q-calculus needed to describe these generalized Fermions.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

Storage of electromagnetic field energy in matter

The partitioning, uniqueness and form of field energy stored in matter, and its properties as a state function, is established. Consequently, the first and second laws apply to the nonfield and field parts of the internal energy as separate entities. This provides a bridge between thermodynamics and the classical theory of electromagnetism. Presentation of the temperature as the sum of nonfield and field contributions is used to establish field dependent barriers to temperature decrease toward the absolute zero, and the existence of field induced temperature jumps. These temperature jumps appear at the instant the field is switched on, or turned off. The partitioning of field and nonfield energies is illustrated for a specific case of an ideal gas, and the heat absorbed by the field is derived in terms of difference in adiabatic magnetization. Finally, the current, restrictive, form of electromagnetic field energy density is redefined with respect to the effect of field energy stored outside the system boundaries. Received 6 June 2000 / Received in final form 26 March 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: zimmels@tx.technion.ac.il     

Influence of the electric characteristics of II–VI semiconductor material on the electroluminescence of lanthanide complex

The organic-inorganic combined structural device (ITO/PVK:Eu/ZnS/Al) is fabricated based on layered optimization scheme. II–VI semiconductor material ZnS is acted as an electron function (transporting and acceleration) layer. The hot electrons which have been accelerated in the ZnS layer directly impact excitation europium ions through resonant energy transfer and then recombine with injected holes to form excitons in PVK or EuTTA₂(N-HPA)Phen. Europium (Eu) ions may also be excited by intramolecular energy transfer from ligands. There are two kinds of excitation mechanisms: impacted excitation and injected recombination for the combined structural device. The electroluminescence (EL) intensity of the combined structural device is strongly improved and reaches up to 381 cd/m² at 20 V compared with the pure organic structural device. It may be an effective method to improve the EL intensity of the lanthanide complex by using electric characteristics of inorganic semiconductor materials.     

Adsorption of a Gaussian random copolymer chain at an interface

We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption, leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed (or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases, the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface. The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface. Received 21 January 1999     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged It? stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.     

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

Transport and recombination in organic light-emitting diodes studied by electrically detected magnetic resonance

We have used electrically detected magnetic resonance (EDMR) to study a series of multilayer organic devices based on aluminum (III) 8-hydroxyquinoline (Alq₃). These devices were designed to identify the microscopic origin of different spin-dependent processes, i.e. hopping and exciton formation. The EDMR signal in organic light-emitting diodes (OLEDs) based on Alq₃ is only observed when the device is electroluminescent and is assigned to spin-dependent exciton formation. It can be decomposed in at least two Gaussians: one with peak-to-peak line ( ΔH_PP) of 1.6 mT and another with ΔH_PP of 2.0 to 3.4 mT, depending on bias and temperature. The g-factors of the two components are barely distinguishable and close to 2.003. The broad line is attributed to the resonance in Alq₃ anions, while the other line is attributed to cationic states. These attributions are supported by line shape and its electrical-field dependence of unipolar Alq₃-based diodes, where hopping process related to dication and dianion formation is observed. In these unipolar devices, it is shown that the signal coming from spin-dependent hopping occurs close to organic semiconductor/metal interfaces. The sign of the magnetic-resonance-induced conductivity change is dominated by charge injection rather than charge mobility. Our results indicate that the probability of singlet exciton formation in our OLEDs is smaller than 25%.     

Non-uniformities in polymer/liquid crystal mixtures

We theoretically model the nucleation of nematic droplets during phase ordering in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By appealing to classical nucleation theory (CNT), we calculate the energy barrier to nucleation and the size of a critical nucleus. We study the influence of a metastable intermediate phase on the nucleation of the nematic. Below a triple point in the phase diagram, there are two distinct mechanisms for the formation of a nematic nucleus: 1) direct nucleation from the isotropic phase and 2) nucleation via a precursor metastable isotropic phase. We calculate the crossover concentration as a function of temperature, delineating the regions of the phase diagram in which each mechanism prevails. In the latter case, the presence of a hidden metastable isotropic-isotropic binodal may either promote or delay the nucleation of a nematic phase. Received 9 August 2002 RID="a" ID="a"e-mail: matuyama@chem.mie-u.ac.jp     

Nonextensive interpretation of radiative recombination in electron cooling

An interest for the low-energy range of the nonextensive distribution function arises from the study of radiative recombination in electron cooling devices in particle accelerators, whose experimentally measured reaction rates are much above the theoretical prediction. The use of generalized distributions, that differ from the Maxwellian in the low energy part (due to subdiffusion between electron and ion bunches), may account for the observed rate enhancement. In this work, we consider the isotropic distribution function and we propose a possible experiment for verifying the existence of a cut-off in the generalized momentum distribution, by measuring the spectrum of the X-rays emitted from radiative recombination reactions.