Remarks on 2–q-bit states

We distinguish six classes of families of locally equivalent states in a straightforward scheme for classifying all 2–q-bit states; four of the classes consist of two subclasses each. The simple criteria that we stated recently for checking a given state’s positivity and separability are justified, and we discuss some important properties of Lewenstein–Sanpera decompositions. An upper bound is conjectured for the sum of the degree of separability of a 2–q-bit state and its concurrence. Received: 17 July 2000 / Published online: 6 December 2000     

A Pfaffian formula for the monomer–dimer model on surface graphs

We consider the monomer–dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function, which generalises the one obtained by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) for graphs embedded in the disc. Our proof is based on an extension of a bijective method mentioned in Giuliani et al. (2016), together with the Pfaffian formula for the dimer partition function of Cimasoni–Reshetikhin (Commun Math Phys 275(1):187–208, 2007).     

BPS solutions to a generalized Maxwell–Higgs model

We look for topological BPS solutions of an Abelian Maxwell–Higgs theory endowed by non-standard kinetic terms to both gauge and scalar fields. Here, the non-usual dynamics are controlled by two positive functions, G(|ϕ|) and w(|ϕ|), which are related to the self-dual scalar potential V(|ϕ|) of the model by a fundamental constraint. The numerical results we found present interesting new features, and contribute to the development of the recent issue concerning the study of generalized models and their applications.     

Radiative lifetimes for the A2Σ+ (v′ = 0–7) and D2Σ+ (v′ = 0–5) Rydberg states of NO

Intensities for the γ(A²Σ⁺?→?X²Π), ε(D²Σ⁺?→?X²Π) and (D²Σ⁺?→?A²Σ⁺) bands for NO have been calculated using the Molecular Quantum Defect Orbital (MQDO) methodology. Radiative lifetimes for the A²Σ⁺ and D²Σ⁺ vibrational Rydberg states have also been determined. The present results are in excellent accord with measurements available in the literature. Additionally, predictions for a number of unknown intensities and radiative lifetimes are made, given their potential usefulness.     

Speech emotion recognition based on statistical pitch model

A modified Parzen-window method, which keep high resolution in low frequencies and keep smoothness in high frequencies, is proposed to obtain statistical model. Then, a gender classification method utilizing the statistical model is proposed, which have a 98% accuracy of gender classification while long sentence is dealt with. By separation the male voice and female voice, the mean and standard deviation of speech training samples with different emotion are used to create the corresponding emotion models. Then the Bhattacharyya distance between the test sample and statistical models of pitch, are utilized for emotion recognition in speech. The normalization of pitch for the male voice and female voice are also considered, in order to illustrate them into a uniform space. Finally, the speech emotion recognition experiment based on K Nearest Neighbor shows that, the correct rate of 81% is achieved, where it is only 73.85% if the traditional parameters are utilized.     

A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics

The Euler–Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler–Maclaurin summation formula and the Poisson summation formula as special cases. By making use of the modified formula, a possible numerical summation method is obtained and the remainder can be controlled. The modified formula is also generalized from one dimension to two dimensions. Approximate expressions of partition functions of a classical particle in square well in 1D and 2D and that of a quantum rotator are obtained with error estimation.     

A note on the B*B,B*B*,D*,D** molecular states

In the framework of the one-boson-exchange model, we have performed an extensive study of the possible B*B,B*B*,D*,D** molecular states with various quantum numbers after considering the S-wave and D-wave mixing. We also discuss the possible experimental research of these interesting states.     

A note on the M2–M5 brane system and fuzzy spheres

This note covers various aspects of recent attempts to describe membranes ending on fivebranes using fuzzy geometry. In particular, we examine the Basu–Harvey equation and its relation to the Nahm equation as well as the consequences of using a non-associative algebra for the fuzzy three-sphere. This produces the tantalising result that the fuzzy funnel solution corresponding to Q   coincident membranes ending on a five-brane has Q3/2$Q^{3/2}$ degrees of freedom.     

A unifying 2D action for integrable $$sigma $$σ-models from 4D Chern–Simons theory

Letters in Mathematical Physics - In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and...     

Coherent states for the Kepler–Coulomb problem on a sphere

An algebraic approach to Kepler problem in a curved space is introduced. By using this approach, the creation and annihilation operators associated to this system and their algebra are calculated. These operators satisfy a deformed Weyl–Heisenberg algebra which can be assumed as a deformed su(2)$\mathfrak{s}\mathfrak{u}\left(2\right)$ algebra. By using this fact, the nonlinear coherent states of this system are constructed. The scalar product and Bargmann representation of this family of nonlinear coherent states are constructed. The present contribution shows that these nonlinear coherent states possess some non-classical features which strongly depend on the Kepler coupling constant and space curvature. Depending on the non-classical measures, the smaller the curvature parameter, the more the non-classical features. Moreover, the stronger Kepler constant provides more non-classical features.     

Terahertz laser-induced 1D–0D crossover in the density of states for electrons in a cylindrical semiconductor quantum wire

The effects of a linearly polarized, terahertz laser field on the density of states (DOS) for carriers confined in a cylindrical semiconductor quantum wire are investigated here within a nonperturbative scheme, based upon a Green’s function approach. In our model, the functional dependence of the DOS on energy is significantly modified in two ways: (i) an uniform blueshift with respect to the laser-free DOS; and (ii) a strong suppression, with the appearance of Franz–Keldysh-like oscillations. Interestingly, with the increase (decrease) of the laser intensity (frequency) the DOS profile evolves from the usual shape for one-dimensional (1D) systems to a discrete set of sharp peaks that resembles the DOS for quasi-zero-dimensional (quasi-0D) electrons confined in quantum dots.     

A generalized Peierls–Nabarro model for kinked dislocations

We present a generalized Peierls–Nabarro model for curved dislocations incorporating directly the Peierls energies for both straight dislocations and dislocation kinks. In our model, the anisotropic elastic energy is calculated efficiently using the discrete Fourier transform on the discrete lattice sites of the slip plane, and the discreteness in both the elastic energy and the misfit energy is included. We have used our model to calculate the kink migration and nucleation energies of the 30° dislocations in silicon. The results agree well with those obtained using atomistic potentials and first principles calculations, and the experimental results.     

A phase field model for vesicle–substrate adhesion

In this paper, a phase field model is developed for vesicle adhesion involving complex substrate and vesicle geometries. The model takes into account an adhesion potential that depends on the distance of vesicle to the substrate. A variational problem is solved in a 3D computational domain by minimizing the contribution of bending elastic energy and the adhesion energy under the constraints of total surface area and volume, described via a phase function. An adaptive finite element method is used to efficiently compute the numerical solutions of the model. The computational results are validated through comparison of several axisymmetric shapes with the sharp-interface ODE solution. Moreover, we compute shapes for non-axisymmetric situations to support the observation that concave substrates favor adhesion.     

A new pressure-dominant approximation model for acoustic–structure interaction

A high accuracy approximation modeling approach for the acoustic–structure interaction problem with a shell structure is presented in this paper. The new approximation model aims to accurately reveal the relationship between pressure and velocity in the acoustic field. The main idea of this model is to separate the velocity terms into a combination of velocity and pressure by using a weighting parameter. The modal analysis was performed to find an appropriate weighting parameter for the new model for the spherical case. The stability range of the model is limited during this process. An approximation model was coupled with the equation of motion of a spherical shell to check the performance of the model. Responses of a spherical shell excited by a plane step wave and cosine-type incident pressure from the new model were compared to the exact solution and solutions from former approximation models such as Doubly Asymptotic Approximations (DAAs). The new proposed model can approximate high accuracy responses in both early and late time.     

Landauer–Datta–Lundstrom model for terahertz transistor amplifier based on graphene

A transistor has been considered in the form of three electrodes connected by graphene ribbons or by metal quantum wires (nanowires) that operate on the principle of the current control by the changing voltage at the central electrode (gate). The analysis has been carried out according to the Landauer–Datta–Lundstrom model in equilibrium approximation for electrodes while fixing their potentials. We have obtained linear models and nonlinear terms in the determining current, and calculated the nonlinear current–voltage performances of graphene nanoribbons.     

Sinkhorn–Knopp theorem for PPT states

Letters in Mathematical Physics - Given a PPT state $$A=sum _{i=1}^nA_iotimes B_i in M_kotimes M_k$$ and a rank k tensor v within the image of A, we provide an algorithm that checks whether the...