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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
2.
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
3.
We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin S. The exact classical magnetic phase diagram at zero temperature is determined using the LK cluster method. The cluster method results show that the classical ground-state phase diagram of the model is very rich, including first-order and second-order phase transitions. In the absence of dimerization, a second-order phase transition occurs between antiferromagnetic (ferromagnetic) and spiral phases at the critical frustration αc=±0.25, a well-known result. In the vicinity of the critical points αc, the exact classical critical exponent of the spiral order parameter is found to be 1/2. In the case of a dimerized chain (δ≠0), the spiral order shows stability and exists in some part of the ground-state phase diagram. We have found two first-order phase boundaries separating antiferromagnetic (uud and duu) phases from the spiral phase. 相似文献
4.
Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V are almost the right triangles with α≈90°. We highlight a very suggestive parametrization of V and show that its CP-violating phase ? is nearly equal to α (i.e., ?−α≈1.1°). Both ? and α are stable against the renormalizaton-group evolution from the electroweak scale MZ to a superhigh energy scale MX or vice versa, and thus it is impossible to obtain α=90° at MZ from ?=90° at MX. We conjecture that there might also exist a maximal CP-violating phase φ≈90° in the MNS lepton mixing matrix U. The approximate quark–lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |Vub| and |Ve3|. 相似文献
5.
The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, Ps, ranked in order of performance were well described by the simplified canonical law Ps∝(r+?)−α, where r is the rank, and ? and α are the parameters of the distribution. The parameter α did not significantly change from 1987 to 2007 (α=0.92±0.03), indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ? significantly increased from ?=1.32 for 1987 RWC, ?=2.30 for 1999 to 2003 RWC and ?=5.60 for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38) and ?(?=0.70) in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α nor ? significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion. 相似文献
6.
Denise A. do Nascimento Minos A. Neto J. Ricardo de Sousa Josefa T. Pacobahyba 《Journal of magnetism and magnetic materials》2012
In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H ) and transverse (Ω) fields by using the effective-field theory. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction in the presence of the H and Ω fields. We obtain the phase diagrams in the H–T and Ω–T planes changing values of the Ω and H parameters, respectively for fixed value at λ=Jx/Jy=1. At null temperature, the ground state phase diagram in the Ω–H plane for several values of λ parameter is analyzed. In the particular case of λ=1 we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field Hc/Jy=2.0 for Ω=0 by using EFT. 相似文献
7.
The aim of this paper is to develop local theory of future timelike, nonspacelike and null reachable sets from a given point q0 in the sub-Lorentzian geometry. In particular, we prove that if U is a normal neighbourhood of q0 then the three reachable sets, computed relative to U, have identical interiors and boundaries with respect to U. Further, among other things, we show that for Lorentzian metrics on contact distributions on R2n+1, n≥1, the boundary of reachable sets from q0 is, in a neighbourhood of q0, made up of null future directed curves starting from q0. Every such curve has only a finite number of non-smooth points; smooth pieces of every such curve are Hamiltonian geodesics. For general sub-Lorentzian structures, contrary to the Lorentzian case, timelike curves may appear on the boundary. It turns out that such curves are always Goh curves. We also generalize a classical result on null Lorentzian geodesics: every null future directed Hamiltonian sub-Lorentzian geodesic initiating at q0 is contained, at least to a certain moment of time, in the boundary of the reachable set from q0. 相似文献
8.
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
9.
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
10.
We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff λ→0 may be obtained from the eigenvalues of the Hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit λ→0 on a finite momentum grid. Another issue we investigate is the location on the diagonal of the Hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A=2,3,4 systems are investigated and related to the occurrence of a Tjon-line which emerges as the minimum of an avoided crossing between Eα=4Et−3Ed and Eα=2Et. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S-waves. 相似文献
11.
We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state σi(t)∈{0,1} of a cell i does not only depend on the states in its local neighborhood at time t-1, but also on the memory of its own past states σi(t-2),σi(t-3),…,σi(t-τ),… . We assume that the weight of this memory decays proportionally to τ-α, with α?0 (the limit α→∞ corresponds to the usual CA). Since the memory function is summable for α>1 and nonsummable for 0?α?1, we expect pronounced changes of the dynamical behavior near α=1. This is precisely what our simulations exhibit, particularly for the time evolution of the Hamming distance H of initially close trajectories. We typically expect the asymptotic behavior H(t)∝t1/(1-q), where q is the entropic index associated with nonextensive statistical mechanics. In all cases, the function q(α) exhibits a sensible change at α?1. We focus on the class II rules 61, 99 and 111. For rule 61, q=0 for 0?α?αc?1.3, and q<0 for α>αc, whereas the opposite behavior is found for rule 111. For rule 99, the effect of the long-range memory on the spread of damage is quite dramatic. These facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory. Finite size scaling studies varying system size N indicate that the range of the power-law regime for H(t) typically diverges ∝Nz with 0?z?1. 相似文献
12.
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
13.
Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consist of two spin degenerate doublets hybridized to a singlet by the promotion of an electron to two conduction bands, as a function of the energy separation δ between both doublets. For δ=0 or very large, the model is equivalent to a one-level SU(N) Anderson model, with N=4 and 2 respectively. We study the evolution of the spectral density for both doublets (ρ1σ(ω) and ρ2σ(ω)) and their width in the Kondo limit as δ is varied, using the non-crossing approximation (NCA). As δ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy ρ2σ(ω) shifts above the Ferrmi energy. The Kondo temperature TK (determined by the half-width at half maximum of the Kondo peak in density of the doublet of lower energy ρ1σ(ω)) decreases dramatically. The variation of TK with δ is reproduced by a simple variational calculation. 相似文献
14.
15.
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
16.
We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡μoil/μwater) and the inter-well (injector-producer) distance r on the oil production rate C(t) and the breakthrough time tbr are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m and r, tbr∝rαmβ, with α=1.8 and β=−0.25 for the random porosity type, and α=1.0 and β=−0.2 for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝tγ, with γ=−1.81, where P(t) is the time derivative of C(t). The curves related to different values of m and r may be collapsed suggesting a universal behavior for the oil production rate. 相似文献
17.
A.P. Moina 《Physica B: Condensed Matter》2012,407(23):4550-4556
Within the framework of two-sublattice Mitsui model with taking into account the shear strain ε4 and the diagonal strains ε2 and ε3, a dynamic dielectric response of Rochelle salt X-cuts is considered. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance, and microwave dispersion are described. Analytical expressions for the resonant frequencies of these cuts, associated with the shear vibration mode of ε4 and with the extensional in-plane modes of ε2, ε3, are derived. It is shown that the lowest resonant frequency is always associated with the ε4 shear mode. 相似文献
18.
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
19.
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