Quantum corrections to the conductivity and periodic orbits: Integrable systems

We extend the recently developed semiclassical theory for the conductivity to periodic semiconductor structures whose classical dynamics is integrable. We find that the conductivity of integrable systems exhibits quantum oscillations as function of magnetic field and Fermi energy which are closely related to both the Shubnikov-de Haas oscillations and the oscillations observed in the conductivity of antidot lattices. A general expression for the quantum oscillations is derived which is analogous to the Berry-Tabor formula for the spectral density of integrable systems.     

Semiclassical and quantum transport in the two-dimensional electron gas in a hard-wall antidot lattice

Commensurate peaks of magnetoresistance and Shubnikov-de Haas and Aharonov-Bohm oscillations in the two-dimensional electron gas (2DEG) in a lattice of antidots with hard potential walls have been experimentally studied. The behavior of both classical magnetoresistance peaks and quantum oscillations has been shown to fundamentally depend on the lattice period and the antidot size, as well as on the smoothness of the potential at the 2DEG-antidot interface. This result indicates the necessity of revising the interpretation of all numerous experiments with antidot lattices, since this effect has been explicitly or implicitly neglected in them.     

Classical Limit of Quantum Dissipative Systems

We discuss the Lindblad equation for the density matrix where the dissipation is linear in the position operator. We consider a potential which is a bounded perturbation of the harmonic oscillator. We show that the perturbation of the potential leads to an analytic perturbation of the Wigner distribution. Then the Wigner distribution of the quantum dissipative system tends (uniformly in time) to the classical phase space distribution of the classical dissipative system (if the initial distribution converges when 0).     

Classical Projections of Quantum Mechanics and the Limit ħ → 0

The convergence of the dynamics of classical projection to the dynamics of the classical limit is investigated for 0. A mistake from a previous paper is pointed out, and the correct version of the result is given. A new, similar result is presented if the function generating the Hamiltonian of both the classical projection and the classical limit is a polynomial.     

Transquantum Dynamics

Segal proposed transquantum commutation relations with two transquantum constants , besides Planck's quantum constant and with a variable i. The Heisenberg quantum algebra is a contraction—in a more general sense than that of Inönü and Wigner—of the Segal transquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit ,0. One physical consequence is a discrete spectrum for canonical variables and space-time coordinates. Another is an interconversion of time and energy accompanying space-time meltdown (disorder), with a fundamental conversion factor of some kilograms of energy per second.     

Temperature effects on the magnetoplasmon spectrum of a weakly modulated graphene monolayer

In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as a two-dimensional electron gas (2DEG). The intra-Landau band magnetoplasmon spectrum within the self-consistent field approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Haas (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, have a greater amplitude and are more robust against temperature in graphene compared to a conventional 2DEG. Furthermore, there is a π phase shift between the magnetoplasmon oscillations in the two systems which can be attributed to Dirac electrons in graphene acquiring a Berry's phase as they traverse a closed path in a magnetic field.     

The effect of optically-induced random anisotropic disorder on a two-dimensional electron system

We have studied the effect of optically-induced random, anisotropic disorder on the magnetoresistance of a Al_0.3Ga_0.7As/ GaAs two-dimensional electron system by exposing the heterojunction to an asymmetric laser speckle pattern. Changes in the amplitude of the Shubnikov-de Haas oscillations can be explained in terms of easy and hard conductivity paths parallel and perpendicular to the long axis of the oval speckle grains. We also observe corresponding changes in the electron scattering rates.     

Electronic conductance of a multi-channel point contact in a magnetic field

We present the numerical results of the electronic conductanceG of a quantum wire with a multichannel point contact structure in a perpendicular external magnetic fieldH at zero temperature, based on the rigorous quantum mechanics of a two-dimensional noninteracting electron gas. Computational results show the approximate quantization of the electronic conductance. WheH is weak,Ginteger multiples of 2e ²/h; and whenH is trong, Ginteger multiples of 2ne ²/h, wheren is the number of channels in the point contact structure of the quantum wire. Quantum leaps take place whenH±2m ^* E _F /[e(2j+1)], wherej is either zero or a positive integer small enough for the external magnetic fieldH to be strong, andm ^* is the effective mass of an electron in the device. To our knowledge, no report on this quantization of electronic conductance has been published. Oscillations are manifest in theGH curves for comparatively narrow channels because of the quantum size effect.     

Sinai Billiards, Ruelle Zeta-functions and Ruelle Resonances: Microwave Experiments

We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as scars in eigenfunctions. The semiclassical and classical Ruelle zeta-functions lead to quantum and classical resonances, both of which are observed in microwave experiments on n-disk hyperbolic billiards.     

Low-energy elementary surface excitations of symmetric films of liquid4He atT=0 K

It is known that low-energy elementary excitations of symmetric films of liquid⁴He atT=0 K are characterized by a momentum q parallel to the surface and may be described by bound states. We have evaluated wave functions and energies of these states for both best short-ranged and optimal long-ranged correlations. Quantities of physical interest may be expressed in terms of these eigenstates and, in particular, for very small momenta (q<0.2 Å^–1) they are mainly determined by the contribution due to the lowest-lying one. We propose analytic expressions for the lowest-lying excitations and fluctuations in the long-wavelength limit. It is proved that in this limiting case, the excitation energy _LW(q) and the averaged static structure functionS _LW(q) should go linearly to zero asq0, whereas the averaged direct correlationX _LW ^Dg (q) should diverge at the origin as 1/q. It is shown that numerical solutions exhibit the expected long-wavelength behavior provided that optimal correlations are used. All these results are displayed in a series of figures and are discussed in detail.     

On the pointwise behavior of semi-classical measures

In this paper we concern ourselves with the small asymptotics of the inner products of the eigenfunctions of a Schrödinger-type operator with a coherent state. More precisely, let _j and E _j denote the eigenfunctions and eigenvalues of a Schrödinger-type operator H with discrete spectrum. Let _(x,) be a coherent state centered at the point (x, ) in phase space. We estimate as 0 the averages of the squares of the inner products ( _a ^(x,) , _j ) over an energy interval of size around a fixed energy, E. This follows from asymptotic expansions of the form for certain test function and Schwartz amplitudes a of the coherent state. We compute the leading coefficient in the expansion, which depends on whether the classical trajectory through (x, ) is periodic or not. In the periodic case the iterates of the trajectory contribute to the leading coefficient. We also discuss the case of the Laplacian on a compact Riemannian manifold.Research supported in part by NSF grant DMS-9303778     

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.     

Nonlinear dynamics of the infinite classical Heisenberg model: Existence proof and classical limit of the corresponding quantum time evolution

For any initial spin configuration we prove the existence, unicity and regularity properties of the solution of Hamilton's equations for the infinite classical Heisenberg model with stable interactions, along with the essential selfadjointness of the associated Liouville operator. We also prove new properties of SU (2)-coherent states which, together with the concept of Trotter approximations for one-parameter (semi-) groups, are used to show that this dynamics is nothing but the classical limit of the time evolution generated by the infinite quantum (suitably normalized) Heisenberg Hamiltonian. The classical limit emerges when the spin magnitude S goes to infinity while Plank's constant goes to zero, their product S remaining fixed. The main results are stated in the form of intertwining relations between the classical and the quantum unitary group.Work supported in part by the Swiss National Science Foundation under Grant 820-436-76 and in part by the U.S. Department of Energy under contract EG-77-C-03-1538.     

ИЗУЧЕНИЕ ИНТЕГРАЛЬН ОЙ И ЛОКАЛЬНОЙ ЧУВСТВИТЕЛЬНОСТИ ФО ТОКАТОДОВ И ИХ ВЛИЯНИ Е НА ГОРИЗОНТАЛЬНЫЙ УЧ АСТОК ХАРАКТЕРИСТИК И СЦИНТИЛЛЯЦИОННОГО Д ЕТЕКТОРА

, RCA 5819, 19 41PK411 ( ). - , .     

Some results on electronic two- and one photon raman scattering in CdS

Two photon Raman scattering (TPRS) via virtually excited biexcitons is observed in CdS over a rather large spectral region in a scattering configuration which favours stimulated emission. We observe either a pure longitudinal exciton or-for the first time—a bound exciton (I ₂) as final state particles. Furthermore, the anomaly in the relation between _exc and _R at _exc= E_blex is observed for the first time in a II–VI compound, indicating an energy of the ₁ biexciton level of 5.098 eV in agreement with two photon absorption measurements. With an applied magnetic fieldB, the corresponding shift of the exciton eigenenergies can be observed. For the longitudinal exciton, the diamagnetic shift is 0.35 meV atB=10T forBc in agreement with theoretical predictions. In this configuration also a stimulated one photon spin flip Raman scattering is observed, yielding the well known electronicg-value of 1.78.     

Smoothed Wigner functions: a tool to resolve semiclassical structures

The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order 2. On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size and then, it only displays structures of size . We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size , with 1. Within this representation, the Husimi and Wigner functions are recovered when =1 and respectively. We treat the application of this intermediate representation to explore the semiclassical limit of quantum mechanics. In particular we show how this representation uncover semiclassical hyperbolic structures of chaotic eigenstates.     

The effective potential as an energy density: The one phase region

An explicit formula is given relating the effective potential in a finite volumeP()₂ quantum field theory to the expected energy density under the constraint of a fixed average filed. In the one phase region, i.e., where the classical potential equals its convex hull and has nonvanishing second derivative, it is shown via a central limit theorem that in the infinite volume limit the effective potential is equal to the constrained energy density, provided is sufficiently small.     

Thermal correction to resistivity in dilute Si-MOSFET two-dimensional systems

Neglecting electron-electron interactions and quantum interference effects, we calculate the classical resistivity of a two-dimensional electron (hole) gas, taking into account the degeneracy and the thermal correction due to the combined Peltier and Seebeck effects. The resistivity is found to be a universal function of the temperature, expressed in units of (h/e²)(k_Fl)^?1. Analysis of the compressibility and thermopower points to the thermodynamic nature of the metal-insulator transition in two-dimensional systems. We reproduce the beating pattern of Shubnikov-de Haas oscillations in both the crossed field configuration and Si-MOSFET valley splitting cases. The consequences of the integer quantum Hall effect in a dilute Si-MOSFET two-dimensional electron gas are discussed. The giant parallel magnetoresistivity is argued to result from the magnetic-field-driven disorder.     

Spatial extension of quantum gravitational particles inR 4×K N

It is observed that the magnitude relationma ² l _P/c holds if the non-Euclidean incremental spatial volume associated with a fundamental particle of massm and radiusa is characteristically quantum gravitational in a Kaluza-Klein or superstringR ⁴×K ^N . HereR ⁴ is the four-dimensional Riemannian space-time of general relativity andK ^N is a small-scale, compact,N-dimensional space of characteristic quantum gravitational volumel _P ^N , withl _P (G/c ³)^1/2= 1.61×10^–33 cm denoting the Planck length. For the electron and electron neutrino (assumed to possess nonzero mass bounded empirically by <30 eV) the derived magnitude relationa(l _P/mc)^1/2 yields the estimatesa _e 2.5×10^–22 cm and 3.3×10^–20 cm, spatial extensions which may be detectable by way of fine-scale effects in SSC experiments.     

锯齿形石墨烯反点网络加工与输运性质研究

具有特定边界的石墨烯纳米结构在纳电子学、自旋电子学等研究领域表现出良好的应用前景.然而石墨烯加工成纳米结构时,无序的边界不可避免地会降低其载流子迁移率.氢等离子体各向异性刻蚀技术是加工具备完美边界石墨烯微纳结构的一项关键技术,刻蚀后的石墨烯呈现出规则的近原子级平整的锯齿形边界.本文研究了氮化硼上锯齿形边界石墨烯反点网络的磁输运性质,低磁场下可以观测到载流子围绕着一个空位缺陷运动时的公度振荡磁阻峰.随着磁场的增大,朗道能级简并度逐渐增大,载流子的磁输运行为从Shubnikov-de Haas振荡逐渐向量子霍尔效应转变.在零磁场附近可以观测到反点网络周期性空位缺陷的边界散射所导致的弱局域效应.研究结果表明,在氮化硼衬底上利用氢等离子体刻蚀技术加工锯齿形边界石墨烯反点网络,其样品质量会明显提高,这种简单易行的方法为后续高质量石墨烯反点网络的输运研究提供了新思路.