Contribution of the electron-phonon interaction to the broadening of cyclotron resonance line of a two-dimensional electron gas in multiple quantum well structures

Summary The theory of cyclotron resonance (CR) lineshape of a two-dimensional electron gas (2 DEG) due to the electron-phonon interaction in multiple-quantum-well structures (MQWS) is investigated. The contribution of the deformation potential acoustic and piezoelectric phonon scattering to the broadening of the cyclotron resonance spectra (CRSB) of such a system is calculated fro GaAs/AlAs. The piezoelectric phonon scattering contribution to the linewidth is smaller as compared to the deformation potential acoustic phonon scattering but is significantly comparable. The magnetic-field dependence of CRSB due to the deformation potential acoustic and piezoelectric phonons isB ^1/2 andB ^1/4, respectively, and the frequency shift Δ _N,p =0 for both interactions in the elastic-scattering approximation. Observed numerical values of the CRSB indicate that at low temperatures acoustic and piezoelectric phonons are dominant scatterers and interact strongly with 2 DEG in MQWS where the impurity scattering is suppressed due to the modulation doping. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

A unified grand canonical description of the nonextensive thermostatistics of the quantum gases: Fractal and fractional approach

In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered. Received 17 September 1999     

玻恩对量子力学的实际贡献初探

玻恩和海森伯在矩阵力学创建过程中的各自贡献,在许多相关物理学史著述中已有"定论",即基本上都认为海森伯是矩阵力学的创立者,而玻恩只是伯乐,仅在数学方面对矩阵力学的建立有一定具体贡献.然而据我们所得到的大量文献却无可辩驳地说明,事实并非如此.经过多年探索,玻恩的哥廷根学派做好了建立量子力学的从数学到思想的所有必要的前期准备工作,海森伯取得的突破只是这些准备下的必然的延拓.本文除必要的分析外,尽量更多依靠引用足够的权威文献来得出可靠结论,相信这样更有说服力,更易于改变人们的成见.     

理想气体压强公式的一种推导方法

本文从球形容器中理想气体入手，用一种简单易懂且不失一般性的方法，推导出理想气体压强公式。     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

On a modified quantum statistical mechanics based on the Hartley information

The theoretical method described by Campos [D. Campos, A thermodynamic-like approach for the study of probabilistic systems, Physica A 390 (2011) 214. http://dx.doi.org/10.1016/j.physa.2010.09.023] is used for the study of quantum systems giving rise to a modified quantum statistical mechanics. The core of this approach includes a nonlinear relationship between Hartley information (pseudo-energy) and energy eigenvalues, and the use of thermodynamic-like functions parameterized by the continuous entropic parameter q$q$ (q∈[0,∞)$q\in [0,\infty )$).     

On the consistent histories approach to quantum mechanics

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnès, and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnès' characterization of true statements—statements which can be deduced unconditionally in his interpretation—is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction, and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yetunknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.     

Identification of the transition responsible for the visible emission in ZnO using quantum size effects

The emission properties of suspensions of nanocrystalline ZnO particles with different particle sizes were studied. Two emission bands were observed, one being an exciton emission and the other the visible emission of ZnO. The energy of both emissions depends on the particle dimensions due to size quantization. A linear relationship between the energetic maxima of the two emission bands is found. Because of the difference in effective masses of electrons and holes in ZnO, the slope of the linear relationship clearly indicates that the visible emission is due to the transition of an electron from the conduction band to a deep trap. The nature of the deep trap is also considered.     

On the standard quantum Brownian equation and an associated class of non-autonomous master equations

It is shown that the standard quantum Brownian equation (QBE) can violate positivity not only past the thermal correlation time, but at arbitrarily long times at high system frequencies. In an effort to improve the standard QBE, exact operator solutions are provided for a class of non-autonomous master equations. These exact solutions are used to derive sufficient positivity conditions for the coefficients of the master equations.     

On the geometrization of quantum mechanics

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.     

Remarks on the independence of the free energy from crystalline boundary conditions in the two-dimensional one-component plasma

We study the two-dimensional one-component plasma. We show that given a bound on the one-particle correlation functions in the thermodynamic limit the canonical free energy is independent or free of the Dobrushin-type boundary conditions obtained by putting outside the vessel a regular configuration of fixed charges.Supported by the Deutsche Forschungsgemeinschaft (D.F.G.), Forschungsprojekt Stochastische Felder.     

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into. Received 13 June 2002 / Received in final form 14 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: jochen@theol.physik.uni-stuttgart.de     

Typicality of Pure States Randomly Sampled According to the Gaussian Adjusted Projected Measure

Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator ρ of low purity, tr ρ ² ≪1, and yielding the ensemble averaged expectation value tr (ρ A) for any observable A. Assuming that the given statistical ensemble ρ is generated by randomly sampling pure states |ψ〉 according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value 〈ψ|A|ψ〉 is shown to be extremely close to the ensemble average tr (ρ A) for the overwhelming majority of pure states |ψ〉 and any experimentally realistic observable A. In particular, such a ‘typicality’ property holds  whenever the Hilbert space ℋ of the system contains a high dimensional subspace ℋ₊⊂ℋ with the property that all |ψ〉∈ℋ₊ are realized with equal probability and all other |ψ〉∈ℋ are excluded.     

A convergent nonequilibrium statistical mechanical theory for dense gases. II. Transport coefficients to first order in the density

Using the two-body distribution function found earlier by the authors with the aid of new boundary conditions, the kinetic equation and the transport coefficients are obtained to zeroth and first order in the density. To zeroth order we recover the Boltzmann kinetic equation. To first order the resulting expressions differ from the ones obtained by Choh and Uhlenbeck, due to effects of the medium.3 Reference 2 will be referred to as I. Here we use the same notation as in I.     

Higher Landau levels contribution to the energy of interacting electrons in a quantum dot

Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At “filling factor” near , this contribution proves to be larger than energy differences between states with different spin polarizations. After checking convergence of the method in small systems, we show results for a 12-electron quantum dot, a system which is hardly tractable by means of exact diagonalization techniques.     

First order quantum correction to the free energy of simple liquids

Using the perturbation theory of Weekset al the first order quantum correction to the free energy of a simple fluid characterised by a double Yukawa potential function has been expressed in a simple closed analytical form which allows numerical calculation simply on a desk calculator.     

关于“滴状冷凝中液滴内外压强差及临界半径”的评注

从力学和热力学角度简要证明了滴状冷凝时壁面球冠形液滴内外压强差不同于冷凝器内部球 形液滴的内外压强差，并指出有关文献对壁面自由能增量的理解存在概念上的混乱。 关键词： 滴状冷凝 压差 自由能     

On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models

Several classical problems in symbolic dynamics concern the characterization of the simplex of measures of maximal entropy. For subshifts of finite type in higher dimensions, methods of statistical mechanics are ideal for dealing with these problems. R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical mechanics and symbolic dynamics—a correspondence which was later formalized by O. Häggström. In this paper, we revisit and discuss this correspondence with the aim of presenting a simplified version of it and present some applications of rigorous results concerning the Potts model and the six-vertex model to symbolic dynamics, illustrating in this way the possibilities of this correspondence.