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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 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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A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences CAB, CAC, CBC, the tangle τABC and the fifth parameter J5 of Acín et al. (2000) Ref. [19], while the other new one is the entanglement charge Qe. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given. 相似文献
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A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3. We propose to use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity fX to display quantum features, i.e., we find a threshold CX for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity fX,0 that can be greater than fX. In addition, we find the threshold concurrence of the channel CX,0 in order for the average fidelity fX,0 to display quantum features and surprisingly, the threshold concurrence CX,0 can be less than CX. Even more, we find some special cases for which the threshold values become zero. 相似文献
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The third-harmonic generation (THG) in asymmetric coupled quantum wells (ACQWs) for different values of the well parameter Δ and width of barrier (WB) are theoretically studied. The analytical expression of the third-harmonic generation is derived by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for typical GaAs/AlxGa1−xAs asymmetric coupled quantum wells. Results obtained show that the third-harmonic generation in the asymmetric coupled quantum wells can be importantly modified by the parameter Δ and WB. Moreover, third-harmonic generation also depends on the relaxation rate of the asymmetric coupled quantum wells. 相似文献
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We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J1>0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0 space, with a Lifshitz point at p=1/4, for d>2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0 phase diagram, there is a critical border, gc=gc(p) for d≥2, with a singularity at the Lifshitz point if d<(m+4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4. 相似文献
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The paper addresses details of the single-particle electron spectrum ?l(p) in narrow Coulomb channels (l is the transverse spectrum part discrete index and p is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?l(p) are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?F≥?ωc, the spectrum ?l(p) first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?F is the Fermi energy of the 2D electron system ?ωc is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?F≤?ωc. Calculated results are compared with available experimental data. 相似文献
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Using a fully self-consistent envelope function approach, we focus on wide conduction band NMS (non-magnetic semiconductor)/DMS (dilute magnetic semiconductor)/NMS quantum wells, under weak external parallel magnetic field, where many spin-subbands are usually present. We concentrate on small values of the magnetic field because we want to investigate the influence of the feedback mechanism due to the difference of the concentrations of spin-up and spin-down carriers which could induce spontaneous spin-polarization i.e. in the absence of a magnetic field. We study the spin-subband structure, the spin-subband populations and the spin-polarization as functions of the sheet carrier concentration, Ns, for different values of the magnitude of the exchange interaction, |J|, between the itinerant carriers and the magnetic impurities. Our calculations for 0.01 T show that at 20 K the values of |J| necessary to make this feedback mechanism sufficiently strong are too high compared to the |J| values of common Mn-doped systems in the conduction band. However, the feedback mechanism will be sufficiently strong at low enough temperatures below 20 K for realistic values of |J|. Moreover, we explain how increasing the sheet carrier concentration the heterostructure is transformed from an almost square quantum well to a system of two coupled heterojunctions with an intermediate soft barrier. 相似文献
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In this work, we present a general scheme to improve quantum state transfer (QST) by taking advantage of quantum partially collapsing measurements. The scheme consists of a weak measurement performed at the initial time on the qubit encoding the state of concern and a subsequent quantum reversal measurement at a desired time on the destined qubit. We determine the strength qr of the post quantum reversal measurement as a function of the strength p of the prior weak measurement and the evolution time t so that near-perfect QST can be achieved by choosing p close enough to 1, with a finite success probability, regardless of the evolution time and the distance over which the QST takes place. The merit of our scheme is twofold: it not only improves QST, but also suppresses the energy dissipation, if any. 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 consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L×N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix TL. Using a combinatorial method, we establish the decomposition Z(L,N)=∑l,Dkb(l,Dk)Kl,Dk, where the characters Kl,Dk=i∑N(λi) are simple traces. In this decomposition, the amplitudes b(l,Dk) of the eigenvalues λi of TL are labelled by the number l=0,1,…,L of clusters which are non-contractible with respect to the transfer (N ) direction, and a representation Dk of the cyclic group Cl. We obtain rigorously a general expression for b(l,Dk) in terms of the characters of Cl, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur. 相似文献
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Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z) in He-like atomic ions for the range of (fractional) nuclear charges Z lying between the known critical value Zc=0.911 at which I(Z) tends to zero and Z=2. They showed that it is possible to fit I(Z) to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of Zc for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z) for these series. 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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Chuan-bing Rong Hong-wei Zhang Ren-jie Chen Shu-li He Bao-gen Shen 《Journal of magnetism and magnetic materials》2006
The effects of dipolar interactions on the magnetization behaviors and magnetic properties of the nanocomposite magnets have been studied by micromagnetic simulations. Numerical results show that the dipolar interaction plays an important role during the demagnetization process, especially in the magnets with large soft-phase content vs. For the isotropic nanocomposites, the remanence enhancement can be controlled through adjustments of the grain size D and vs. However, the appearance of magnetic vortex state leads to a very low remanence in the magnets with large D and vs. The dependence of coercivity on D and vs can be attributed to the exchange-induced magnetization reversal near the grain boundaries and the low nucleation field of soft phase, respectively. For the anisotropic nanocomposites, the reduced remanence mr is equal to 1.0 for the magnets with small D or with low vs. However, mr decreases with increasing vs for the magnet with large D due to the influence of dipolar interactions. The difference between the calculated coercivity Hc with and without considering dipolar interaction shows that the dipolar interaction plays a more important role during the magnetization reversal in the soft phase than that in the hard phase. The maximum calculated energy product of the isotropic nanocomposites is only about 40 MGOe due to the conflicting relation between remanence and coercivity, while that of the anisotropic nanocomposites is 112 MGOe. This reminds us that the alignment of hard grain is important to obtain high performance. 相似文献
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G. Yañez-Navarro Guo-Hua Sun T. Dytrych K.D. Launey Shi-Hai Dong J.P. Draayer 《Annals of Physics》2014
The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position Sx and momentum Sp information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the Sx entropy as well as for the Fourier transformed wave functions, while the Sp quantity is calculated numerically. We notice the behavior of the Sx entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of Sp on the width is contrary to the one for Sx. Some interesting features of the information entropy densities ρs(x) and ρs(p) are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases. 相似文献
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We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we construct proper Unruh modes admitting general α-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α. Moreover, an one-to-one correspondence between convergent points Hc of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved. 相似文献
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In this paper we study the Lagrangian reduction of generalized nonholonomic systems (GNHS) with symmetry. We restrict ourselves to those GNHS, defined on a configuration space Q, with kinematic constraints given by a general submanifold CK⊂TQ, and variational constraints given by a distribution CV on Q. We develop a reduction procedure that is similar to that for nonholonomic systems satisfying d’Alembert’s principle, i.e. with CK a distribution and CV=CK. Special care is taken in identifying the geometrical structures and mappings involved. We illustrate the general theory with an example. 相似文献
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We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T, the magnitude of the external driving field E, and the lattice size. The DLG model undergoes an order–disorder second-order phase transition at the critical temperature Tc(E), such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value Dsat that depends only on T. Dsat increases for T<Tc(E=∞), decreases for T>Tc(E=∞) and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T. Also, we investigated damage spreading for a range of finite fields as a function of T, finding a behavior similar to that of the case with E=∞. 相似文献