Infinite Barrier Research Articles

压力及屏蔽对无限深量子阱中施主结合能的影响

压力及屏蔽对无限深量子阱中施主结合能的影响

外场下压力及屏蔽对无限深量子阱中施主结合能的影响

外场下压力及屏蔽对无限深量子阱中施主结合能的影响

Absorbing phenomena and escaping time for Muller's ratchet in adaptive landscape

BackgroundThe accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist, a process often described as Muller's ratchet with the absorbing phenomenon. The key to understand this absorbing phenomenon is to characterize the decaying time of the fittest class of the population. Adaptive landscape introduced by Wright, a re-emerging powerful concept in systems biology, is used as a tool to describe biological processes. To our knowledge, the dynamical behaviors for Muller's ratchet over the full parameter regimes are not studied from the point of the adaptive landscape. And the characterization of the absorbing phenomenon is not yet quantitatively obtained without extraneous assumptions as well.MethodsWe describe how Muller's ratchet can be mapped to the classical Wright-Fisher process in both discrete and continuous manners. Furthermore, we construct the adaptive landscape for the system analytically from the general diffusion equation. The constructed adaptive landscape is independent of the existence and normalization of the stationary distribution. We derive the formula of the single click time in finite and infinite potential barrier for all parameters regimes by mean first passage time.ResultsWe describe the dynamical behavior of the population exposed to Muller's ratchet in all parameters regimes by adaptive landscape. The adaptive landscape has rich structures such as finite and infinite potential, real and imaginary fixed points. We give the formula about the single click time with finite and infinite potential. And we find the single click time increases with selection rates and population size increasing, decreases with mutation rates increasing. These results provide a new understanding of infinite potential. We analytically demonstrate the adaptive and unadaptive states for the whole parameters regimes. Interesting issues about the parameters regions with the imaginary fixed points is demonstrated. Most importantly, we find that the absorbing phenomenon is characterized by the adaptive landscape and the single click time without any extraneous assumptions. These results suggest a graphical and quantitative framework to study the absorbing phenomenon.

Exciton states and excitonic absorption spectra in a cylindrical quantum wire under transverse electric field

The effects of transverse electric field on the electronic structures, exciton states and excitonic absorption spectra in a cylindrical quantum wire are theoretically investigated in detail. The quantum wire is assumed to GaAs material surrounded by the infinite potential barrier. The results show that the external electric field removes the degeneracy of the electron or hole states. The energy levels of electron and hole, exciton binding energy, excitonic absorption coefficient and absorption energy decrease with increasing the strength of the electric field or the wire radius. The effects of the electric field become more significant for wide wires. The phenomena can be explained by the reduced spatial overlap of ground electron and hole states.

Exact investigation of the electronic structure and the linear and nonlinear optical properties of conical quantum dots

Intersubband linear and third-order nonlinear optical properties of conical quantum dots with infinite barrier potential are studied. The electronic structure of conical quantum dots through effective mass approximation is determined analytically. Linear, nonlinear, and total absorption coefficients, as well as the refractive indices of GaAs conical dots, are calculated. The effects of the size of the dots and of the incident electromagnetic field are investigated. Results show that the total absorption coefficient and the refractive index of the dots largely depend on the size of the dots and on the intensity and polarization of the incident electromagnetic field.

Oscillator strengths of the intersubband electronic transitions in the hydrogenic nano-antidots

We calculate the oscillator strengths of the quantum antidots with hydrogenic donor impurity at the center, for transitions from the ground state to the first as well as the second excited state, in two and three dimensions, with both finite and infinite potential energy barriers. For this purpose, the binding energy spectrum and the corresponding wavefunctions, are first determined in terms of the Whittaker and the hypergeometric functions. The results are tested against the well understood limiting cases such as the free hydrogen atom in the bulk material, and also compared with the previously reported work. It is found, in particular, that the oscillator strength characterizing the transitions from the ground state to the second excited state, though negligible for small antidot radii, becomes significantly large and indeed comparable with that of the transitions to the first excited state for large enough antidot radii.

On Two Superintegrable Nonlinear Oscillators in N Dimensions

We consider the classical superintegrable Hamiltonian system given by $$\mathcal{H}_{\lambda}=\mathcal{T}+\mathcal{U}=\frac{\mathbf{p}^2}{2(1+{\lambda}\mathbf{q}^2)} + \frac{ \omega^2\mathbf{q}^2}{2(1+{\lambda}\mathbf{q}^2)},$$ where $\mathcal{U}$ is known to be the “intrinsic” oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term $\mathcal{T}$ and parametrized by λ. We show that $\mathcal{H}_{\lambda}$ is Stäckel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for $\mathcal{H}_{\lambda}$ . Furthermore, we analyze in terms of λ the three different underlying manifolds whose geodesic motion is provided by $\mathcal{T}$ . As a consequence, we find that $\mathcal{H}_{\lambda }$ comprises three different nonlinear physical models that, by constructing their radial effective potentials, are shown to be two different nonlinear oscillators and an infinite barrier potential. The quantization of these two oscillators and its connection with spherical confinement models is briefly discussed.

LBMP: A Logarithm-Barrier-Based Multipath Protocol for Internet Traffic Management

Traffic management is the adaptation of source rates and routing to efficiently utilize network resources. Recently, the complicated interactions between different Internet traffic management modules have been elegantly modeled by distributed primal-dual utility maximization, which sheds new light for developing effective management protocols. For single-path routing with given routes, the dual is a strictly concave network optimization problem. Unfortunately, the general form of multipath utility optimization is not strictly concave, making its solution quite unstable. Decomposition-based techniques like TRaffic-management Using Multipath Protocol (TRUMP) alleviates the instability, but their convergence is not guaranteed, nor is their optimality. They are also inflexible in differentiating the control at different links. In this paper, we address the above issues through a novel logarithm-barrier-based approach. Our approach jointly considers user utility and routing/congestion control. It translates the multipath utility maximization into a sequence of unconstrained optimization problems, with infinite logarithm barriers being deployed at the constraint boundary. We demonstrate that setting up barriers is much simpler than choosing traditional cost functions and, more importantly, it makes optimal solution achievable. We further demonstrate a distributed implementation, together with the design of a practical Logarithm Barrier-based-Multipath Protocol (LBMP). We evaluate the performance of LBMP through both numerical analysis and packet-level simulations. The results show that LBMP achieves high throughput and fast convergence over diverse representative network topologies. Such performance is comparable to TRUMP, and is often better. Moreover, LBMP is flexible in differentiating the control at different links, and its optimality and convergence are theoretically guaranteed.

New expression for the expectation value integral for a confined helium atom

A new expression for the expectation value integral of Hermitian operators for spherically symmetric states is derived in elliptical coordinates for the Helium atom confined in a cavity with infinite potential barrier walls. The expression is comprised of two components spanning different domains of space. For an atom in infinite space, with a wave function which satisfies Dirichlet boundary conditions, one of these terms is shown to vanish, but for a confined atom that same term cannot be neglected. In a variational calculation of the energy, for a helium atom confined by finite spheres of various radii, it is observed that the principal contribution is due to the first component, with the relative magnitude of the second component becoming smaller as the size of the cavity is increased. The expression derived is shown to be computationally faster than the conventionally employed expression for confined systems derived by ten Seldam-de Groot.

Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r

The MCMC analysis of the CMB + LSS data in the context of the Ginsburg–Landau approach to inflation indicated that the fourth degree double-well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r ≃ 0.05, within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index n s and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg–Landau class too. The theoretical values in the ( n s , r) plane for all double well inflaton potentials in the Ginsburg–Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region B . The upper border of the banana-shaped region B is given by the fourth order double-well potential and provides an upper bound for the ratio r. The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index n s = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations.

Topological lattice actions

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility \chi_t = \l< Q^2 >/V is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.

"Graphene-Like" Exfoliation of Atomically-Thin Films of Bi2Te3 and Related Materials: Applications in Thermoelectrics and Topological Insulators

In this paper we overview our results on "graphene-inspired" exfoliation of crystalline bismuth telluride films with a thickness of just a few atoms. The atomically thin films were suspended across trenches in Si/SiO2 substrates, and subjected to detail material characterization. The presence of the van der Waals gaps allowed us to disassemble Bi2Te3 crystal into its quintuple building blocks - five mono-atomic sheets - consisting of Te(1)-Bi-Te(2)-Bi-Te(1). By altering the thickness and sequence of atomic planes we were able to create "designer" quasi-2D crystalline films, change their composition, the type of charge carriers as well as other properties. The exfoliated quintuples and ultra-thin films have low thermal conductivity, relatively high electrical conductivity and enhanced thermoelectric properties. The obtained results pave the way for producing stacks of crystalline bismuth telluride quantum wells with nearly infinite potential barriers, strong spatial confinement of charge carriers and acoustic phonons, beneficial for thermoelectric devices.

Using a one-dimensional lattice applied to the thermodynamic study of DNA

In this work it is analyzed a one-dimensional lattice which is composed by mass-spring systems with one additional Rosen-Morse potential on site. This kind of lattice is used to study thermodynamic properties of DNA, especially its thermal denaturation. On the context of this work, the Rosen-Morse potential simulates hydrogen bonds between double strands of the molecule. From the graphic of the average stretching of base pairs versus temperature it is possible to observe the thermal denaturation of the system. This result shows that it is possible to obtain phase transition with an asymmetric potential without an infinite barrier.

POSITION DEPENDENT EFFECTIVE MASSES FOR DONOR BINDING ENERGIES IN QUANTUM CONFINED SYSTEMS IN AN ELECTRIC FIELD

In our earlier works, the effective mass theory (EMT) was critically examined for a hydrogenic donor in a quantum well (QW) and in a quantum dot (QD) after introducing position dependent effective masses (PDEMs). Our results showed that the use of constant effective mass was justified for all well dimensions a*, the effective Bohr radius which is 100 Å in GaAs. Here the validity of EMT in the presence of an electric field is examined. The electric field dependent donor ionization energies in both the systems with finite and infinite barriers for different well dimensions have been calculated. It is shown that the electric field affects donor binding energies appreciably, the variation being larger in the case of finite barrier systems when PDEM is used. The donor polarizability has also been estimated in both the systems and the results are compared with other works in the literature. The use of EMT is justified if constant effective mass is used in general, even though large variation in the ionization energies occur in the finite barrier cases when position dependent mass is included correctly.

An exciton trapped by an arbitrary shaped nanoring in a magnetic field

We propose a simple method for calculating the energy spectrum of a magnetoexciton confined in a narrow infinite barrier planar quantum ring with a centreline of an arbitrary shape and a variable width. We show that in the adiabatic approximation the analysis of the low-lying levels of the exciton in such structure can be reduced to study of the angular two-particle motion. We present numerical results for energies of some low-lying levels in circular and elliptical quantum rings with weak variations in their widths as functions of the magnetic field strength. We show that variations in widths produce the quenching of the Aharonov-Bohm oscillations of the energy levels of the magnetoexciton.

The Faraday effect in a semiconductor rectangular quantum wire

We theoretically study the interband Faraday rotation (FR) in a rectangular quantum wire (QWR) with infinite barriers in a transverse magnetic field. The FR is calculated as a function of an incident light energy for different values of magnetic field and wire size. It is shown that on the FR curve, the resonance peaks appear and they split at large magnetic fields. The selection rules are derived. Numerical results are presented for GaAs/AlGaAs rectangular QWR.

Revisiting the problem of a single electron cylindrical quantum dot in constant magnetic field

We present detailed results of the calculation for single electron states in a cylindrical quantum dot in the presence of a constant magnetic field in the axial direction. The quantum dot structure considered is with a finite barrier potential in the radial direction and infinite barrier potential in the z-direction. We show how the states and energy levels depend on the strength of the magnetic field for different quantum numbers. It is observed that energy levels with different quantum numbers group together at high magnetic fields.

Interface roughness effect on density of states and mobility of narrow Si/Si1−xGex quantum wells: path-integral approach

The in-plane transport of a two-dimensional hole gas in narrow Si/Si1−xGex quantum wells (QWs) with the interface roughness effect was investigated using path-integral theory. The random variation of the well width causes the fluctuation potential in the in-plane direction. This fluctuation was integrated into the path integral via the eigenvalue model of the infinite barrier height QW. The hole mobility and the density of states can be derived in an analytic form. The calculated hole mobility was compared with the experimental data and a different theoretical approach based on the wavefunction model. We found that Δ = 0.2 nm and Λ = 4.5 nm give a good description of the experimental data. Our theory predicted the existence of the localized states, which reduces the hole mobility in addition to the prediction from the wavefunction method.

Quantum fluctuations of a Bose-Josephson junction in a quasi-one-dimensional ring trap

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi-one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long-range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting one-dimensional fluid. We also evaluate the particle-density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger-liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction in the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

Photoionization cross-section and binding energy of donor impurities in GaAs, Ge and Si quantum wires with infinite barriers

Within the effective-mass approximation, we have investigated the binding energies of donor impurities as a function of the wire dimensions and the photoionization cross-section for a hydrogenic donor impurity placed on the center of the quantum well-wire as a function of the normalized photon energy in the GaAs, Ge and Si quantum wires with infinite barriers. The calculations are performed by the variational method based on a two-parametric trial wave function. The results show that the impurity binding energy and the photoionization cross-section depend strongly on both wire dimensions and material parameters.