Spectrum of localized states in graphene quantum dots and wires

We developed semiclassical method and show that any smooth potential in graphene describing elongated a quantum dot or wire may behave as a barrier or as a trapping well or as a double barrier potential, Fabry–Perot structure, for 1D Schrödinger equation. The energy spectrum of quantum wires has been found and compared with numerical simulations. We found that there are two types of localized states, stable and metastable, having finite life time. These life times are calculated, as is the form of the localized wave functions which are exponentially decaying away from the wire in the perpendicular direction.     

Localization estimates for a random discrete wave equation at high frequency

It is shown that at high frequencies matrix elements of the Green's function of a random discrete wave equation decay exponentially at long distances. This is the input to the proof of dense point spectrum with localized eigenfunctions in this frequency range. The proof uses techniques of Fröhlich and Spencer. A sequence of renormalization transformations shows that large regions where wave propagation is easily maintained become increasingly sparse as resonance is approached.     

Localized Excitations of (2+1)-Dimensional Korteweg-de Vries System Derived from a Periodic Wave Solution

With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2 1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.     

Quantum analog of Lienard-Wichert potentials

In the framework of quantum electrodynamics the vector potential is computed of the electromagnetic field created by a localized wave packet corresponding to a uniformly moving charged particle. It is shown that the field distribution near the particle trajectory depends on mass renormalization due to the interaction with the transverse quantum field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–70, September, 1990.     

一维无公度系统的电子波函数特征

本文研究了存在无序及不存在无序两种情况下,一维无公度系统的电子波函数特征。发现存在无序的无公度系统的电子波函数都是指数局域的,而不存在无序的无公度系统则不然。 关键词：     

Numerical evaluation of the one-loop effective action in static backgrounds with spherical symmetry

The problem of evaluating the one-loop quantum corrections to the energy of classical solution is ubiquitous in elementary particle physics. In many cases already the classical solution is known only numerically so that methods based on exact wave functions for the quantum excitations cannot be applied. We propose here a numerical method based on the use of Euclidean Green's functions which allows to extract the finite parts after Lorentz covariant regularization and renormalization.     

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.     

Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model

We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0相似文献   

Generalized on-shell renormalization of heavy quarks

A generalized on-shell (GOS) renormalization scheme of QCD is developed to evaluate the renormalization of heavy quark wave functions and currents. All large logarithms arising from the physical range of quark masses and momentum transferq ² can be absorbed into wave function and vertex renormalization. Our results are more general than those of the heavy quark effective theory and agree with the latter only at zero recoil. The proposed GOS scheme is very suitable for the /m _Q expansion. As an application we discuss the renormalization of the flavour changing currentsb-c, t-b andt-c.Supported by Bundesministerium für Forschung und Technologie (BMFT)     

Two classes of fractal structures for the （2＋1）-dimensional dispersive long wave equation

Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Critical dynamics of a localized moment system coupled to conduction electrons

We discuss the critical dynamics of a system of localized spins interacting with conduction electrons via an isotropic exchange coupling between the respective spin densities. It is shown that the elimination of the conduction electrons by an adiabatic approximation is not allowed for small wave vectors. The quantum mechanical Fokker-Planck equation derived in a previous paper is used to investigate the renormalization of the kinetic coefficients due to nonlinear mode coupling contributions.     

Factorizing coupled quantum systems and damped nonlinear Schrödinger equations

We show that the wave function of a coupled quantum system may factorize for certain coupling operators, resulting in wave functions and effective nonlinear Hamiltonians for the subsystems. Systems of coupled harmonic oscillators with discrete or continuous spectra are considered, where all degrees of freedom move in time-dependent coherent Glauber states.We present the general formalism and study two examples in detail. The problem of radiation damping results under drastic assumptions in exponentially damped harmonic motion, obeying a nonlinear Schrödinger equation. In the second example, a different type of coupling is studied which yields inverse power law damping.     

Deterministic non-periodic structures

Summary Aperiodic structures which are perfectly ordered, but lack translational symmetry, can be considered as intermediate between crystalline and amorphous systems. Their wave-functions and spectra exhibit unusual properties. A one-dimensional model, known as the Thue-Morse lattice, is here investigated; it is particularly interesting because it is deterministic non-periodic, but not quasi-periodic. The propagation of both electrons and photons is considered and the corresponding spectra are characterized with a multifractal analysis. The multifractal scaling function τ(q) tends in both cases to a non-analytic limit that implies the presence of both extended and exponentially localized states, as confirmed by the behaviour of the wave functions. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Time evolution of quantum fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.     

Carrier dynamics in type-II GaAsSb/GaAs quantum wells

Time-resolved photoluminescence (PL) characteristics of type-II GaAsSb/GaAs quantum wells are presented. The PL kinetics are determined by the dynamic band bending effect and the distribution of localized centers below the quantum well band gap. The dynamic band bending results from the spatially separated electron and hole distribution functions evolving in time. It strongly depends on the optical pump power density and causes temporal renormalization of the quantum well ground-state energy occurring a few nanoseconds after the optical pulse excitation. Moreover, it alters the optical transition oscillator strength. The measured PL lifetime is 4.5 ns. We point out the critical role of the charge transfer processes between the quantum well and localized centers, which accelerate the quantum well photoluminescence decay at low temperature. However, at elevated temperatures the thermally activated back transfer process slows down the quantum well photoluminescence kinetics. A three-level rate equation model is proposed to explain these observations.     

Using the Renormalization Group to Classify Boolean Functions

This paper argues that the renormalization group technique used to characterize phase transitions in condensed matter systems can be used to classify Boolean functions. A renormalization group transformation is presented that maps an arbitrary Boolean function of N Boolean variables to one of N−1 variables. Applying this transformation to a generic Boolean function (one whose output for each input is chosen randomly and independently to be one or zero with equal probability) yields another generic Boolean function. Moreover, applying the transformation to some other functions known to be non-generic, such as Boolean functions that can be written as polynomials of degree ξ with ξ ≪ N and functions that depend on composite variables such as the arithmetic sum of the inputs, yields non-generic results. One can thus define different phases of Boolean functions as classes of functions with different types of behavior upon repeated application of the renormalization transformation. Possible relationships between different phases of Boolean functions and computational complexity classes studied in computer science are discussed.     

Multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory

We consider models of statistical mechanics and quantum field theory (in the Euclidean formulation) which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action. We obtain multiscale formulas for the generating and correlation functions aftern renormalization group transformations which bring out the relation with thenth effective action. We derive and compare the formulas for different RGs. The formulas for correlation functions involve (1) two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and (2) field derivatives of the nth effective action. For the case of the block field -function RG the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed; the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions. The simplicity can be traced to an orthogonality-of-scales property which follows from an implicit wavelet structure. Other commonly used RGs do not have the orthogonality of scales property.     

Tamm states and quantum dots in carbon and heteroatomic nanotubes

The electronic structure of C-BN nanotubes is discussed in the π approximation. Two types of such structures with (n,0)-tubulet topology are investigated: 1) semiinfinite C-BN and C nanotubes and 2) C-BN nanotubes, consisting of two semiinfinite BN nanotubes coupled by a ring-shaped carbon fragment C_mn. It is shown that, in the first case, energy levels (Tamm levels) whose wave functions are localized on the terminal fragment can exist under certain conditions. In the second case, bound states localized on atoms of the carbon fragment exist. It is established that if a quite extended, cylindrical, carbon cluster is present at the end of a semiinfinite BN nanotube, then such a system can be viewed as a very simple model of a quantum dot. C-BN nanotubes where the carbon fragment couples two semiinfinite BN nanotubes can also be interpreted similarly. A simple analytic method is proposed for finding the Tamm energy levels in heteroatomic nanotubes. Fiz. Tverd. Tela (St. Petersburg) 41, 1515–1519 (August 1999)     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.