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1.
We discuss three Hamiltonians, each with a central-field part H0 and a PT-symmetric perturbation igz. When H0 is the isotropic Harmonic oscillator the spectrum is real for all g because H is isospectral to H0+g2/2. When H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all g. If the potential in H0 is linear in the radial variable r then the spectrum of H exhibits real eigenvalues for 0<g<gc and a PT phase transition at gc. 相似文献
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The ideality factor n and the barrier height Φap of the sputtered Ni/p-InP Schottky diodes have been calculated from their experimental Current–voltage (I–V) characteristics in the temperature range of 60–400 K with steps of 10 K. The n and Φap values for the device have been obtained as 1.27 and 0.87 eV at 300 K and 1.13 and 0.91 eV at 400 K, respectively. The n values larger than unity at high temperatures indicate the presence of a thin native oxide layer at the semiconductor/metal interface. The barrier height (BH) has been assumed to be bias dependent due to the presence of an interfacial layer and interface states located at the interfacial layer-semiconductor interface. Interfacial layer-thermionic emission current mechanism has been fitted to experimental I–V data by considering the bias-dependence of the BH at each temperature. The best fitting values of the series resistance Rs and interface state density Ns together with the bias-dependence of the BH have been used at each temperature, and the Rs and Ns versus temperature plots have been drawn. It has been seen that the experimental and theoretical forward bias I–V data are in excellent agreement with each other in the temperature range of 60–400 K. It has been seen that the Rs and Ns values increase with a decrease in temperature, confirming the results in the literature. 相似文献
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For every diffeomorphism φ:M→N between 3-dimensional Riemannian manifolds M and N, there are locally two 2-dimensional distributions D± such that φ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of D±. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from φ∗. We investigate the integrability condition of D+ and D−. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves. 相似文献
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We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H and transverse magnetic field Ω. Using the effective-field theory (EFT) with correlation in cluster with N=1 spin we calculate the thermodynamic properties as a function of temperature with values H and Ω fixed. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction, and it is found that for H/Jy∈[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1 (isotropic square lattice). 相似文献
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Creation of coherent superpositions in quantum systems with Na states in the lower set and Nb states in the upper set is presented. The solution is drived by using the Morris–Shore transformation, which step by step reduces the fully coupled system to a three-state Λ-like system and a set of decoupled states. It is shown that, for properly timed pulse, robust population transfer from an initial ground state (or superposition of M ground states) to an arbitrary coherent superposition of the ground states can be achieved by coincident pulses and/or STIRAP techniques. 相似文献
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We study reduction of generalized complex structures. More precisely, we investigate the following question. Let J be a generalized complex structure on a manifold M, which admits an action of a Lie group G preserving J. Assume that M0 is a G-invariant smooth submanifold and the G-action on M0 is proper and free so that MG?M0/G is a smooth manifold. Under what condition does J descend to a generalized complex structure on MG? We describe a sufficient condition for the reduction to hold, which includes the Marsden–Weinstein reduction of symplectic manifolds and the reduction of the complex structures in Kähler manifolds as special cases. As an application, we study reduction of generalized Kähler manifolds. 相似文献
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Fluxmetric and magnetometric demagnetizing factors, Nf and Nm, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ and the ratio γ of length to diameter. The results have an accuracy better than 0.1% with respect to min(Nf,m,1-Nf,m) and are tabulated in the range of 0.01?γ?500 and -1?χ<∞. Nm along the radial direction is evaluated with a lower accuracy from Nm along the axis and tabulated in the range of 0.01?γ?1 and -1?χ<∞. Some previous results are discussed and several applications are explained based on the new results. 相似文献
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The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear. 相似文献
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In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional N=2 supersymmetry and we find multiple N=2, d=1 supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with Nf flavors and these are N-extended supersymmetric structures with non-trivial topological charges, with “N” depending on the fermion flavors. 相似文献
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We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n dimensional vector space which we call Hn. The Zp gauge particles act on the vertex particles and thus Hn can be thought of as a C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n and p, though we believe this feature holds for all n>p. We will see that non-Abelian anyons of the quantum double of C(S3) are obtained as part of the vertex excitations of the model with n=6 and p=3. Ising anyons are obtained in the model with n=4 and p=2. The n=3 and p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Zp. This makes them possible candidates for realizing quantum computation. 相似文献
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We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 相似文献
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A multi-parametric version of the nonadditive entropy Sq is introduced. This new entropic form, denoted by Sa,b,r, possesses many interesting statistical properties, and it reduces to the entropy Sq for b=0, a=r:=1−q (hence Boltzmann–Gibbs entropy SBG for b=0, a=r→0). The construction of the entropy Sa,b,r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of Sa,b,r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy Sa,b,r can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles N of the system, or even stabilizes, by increasing N, to a limiting value. 相似文献
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We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of distributions pl and qm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l, the power-law exponent is (2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically. 相似文献
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As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–τ0 (R is the reciprocal coefficient of variance, and τ0 is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as τ0 is small, and R has a significant minimum with increasing τ as τ0 is large. (4) large values of ζ reduce noise induced spikes regularity. 相似文献
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Geometrical characterizations are given for the tensor R⋅S, where S is the Ricci tensor of a (semi-)Riemannian manifold (M,g) and R denotes the curvature operator acting on S as a derivation, and of the Ricci Tachibana tensor ∧g⋅S, where the natural metrical operator ∧g also acts as a derivation on S. As a combination, the Ricci curvatures associated with directions on M, of which the isotropy determines that M is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on M, and of which the isotropy determines that M is Ricci pseudo-symmetric in the sense of Deszcz. 相似文献
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I examine the role of entropy in the transition from incoherence to phase synchronisation in the Kuramoto model of N coupled phase oscillators on a general undirected network. In a Hamiltonian ‘action-angle’ formulation, auxiliary variables Ji combine with the phases θi to determine a conserved system with a 2N dimensional phase space. In the vicinity of the fixed point for phase synchronisation, θi≈θj, which is known to be stable, the auxiliary variables Ji exhibit instability . This manifests Liouville’s Theorem in the phase synchronised regime in that contraction in the θi parts of phase space are compensated for by expansion in the auxiliary dimensions. I formulate an entropy rate based on the projection of the Ji onto eigenvectors of the graph Laplacian that satisfies Pesin’s Theorem. This leads to the insight that the evolution to phase synchronisation of the Kuramoto model is equivalent to the approach to a state of monotonically increasing entropy. Indeed, for unequal intrinsic frequencies on the nodes, the networks that achieve the closest to exact phase synchronisation are those which enjoy the highest entropy production. I compare numerical results for a range of networks. 相似文献
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Dust ion-acoustic (DIA) rogue waves are reported for a three-component ultracold quantum dusty plasma comprised of inertialess electrons, inertial ions, and negatively charged immobile dust particles. The nonlinear Schrödinger (NLS) equation appears for the low frequency limit. Modulation instability (MI) of the DIA waves is analyzed. Influence of the modulation wave number, ion-to-electron Fermi temperature ratio ρ and dust-to-ion background density ratio Nd on the MI growth rate is discussed. The first- and second-order DIA rogue-wave solutions of the NLS equation are examined numerically. It is found that the enhancement of Nd and carrier wave number can increase the envelope rogue-wave amplitudes. However, the increase of ρ reduces the envelope rogue-wave amplitudes. 相似文献