共查询到20条相似文献,搜索用时 31 毫秒
1.
D. V. Georgievskii 《Russian Journal of Mathematical Physics》2016,23(4):475-483
Compatibility equations are derived for the components of generalized strains of rank m associated with generalized displacements of rank m ? 1 by analogs of Cauchy kinematic relations in n-dimensional space (multi-dimensional continuous medium) (m ≥ 1, n ≥ 2). These relations can be written in the form of equating to zero all components of the incompatibility tensor of rank m(n ? 2) or its dual generalized Riemann–Christoffel tensor of rank 2m. The number of independent components of these tensors is found; this number coincides with that of compatibility equations in terms of generalized strains or stresses. The inequivalence of the full system of compatibility equations to any of its weakened subsystems is discussed, together with diverse formulations of boundary value problems in generalized stresses in which the number of equations in a domain can exceed the number of unknowns. 相似文献
2.
O. V. Kukin 《Bulletin of the Russian Academy of Sciences: Physics》2007,71(2):212-216
Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a exp(T). 相似文献
3.
Associated to any (pseudo)-Riemannian manifold M of dimension n is an n + 1-dimensional noncommutative differential structure (Ω1, d) on the manifold, with the extra dimension encoding the classical Laplacian as a noncommutative ‘vector field’. We use the classical connection, Ricci tensor and Hodge Laplacian to construct (Ω2, d) and a natural noncommutative torsion free connection \({(\nabla,\sigma)}\) on Ω1. We show that its generalised braiding \({\sigma:\Omega^1\otimes\Omega^1\to \Omega^1\otimes\Omega^1}\) obeys the quantum Yang-Baxter or braid relations only when the original M is flat, i.e. their failure is governed by the Riemann curvature, and that σ 2 = id only when M is Einstein. We show that if M has a conformal Killing vector field τ then the cross product algebra \({C(M)\rtimes_\tau\mathbb{R}}\) viewed as a noncommutative analogue of \({M\times\mathbb{R}}\) has a natural n + 2-dimensional calculus extending Ω1 and a natural spacetime Laplacian now directly defined by the extra dimension. The case \({M=\mathbb{R}^3}\) recovers the Majid-Ruegg bicrossproduct flat spacetime model and the wave-operator used in its variable speed of light prediction, but now as an example of a general construction. As an application we construct the wave operator on a noncommutative Schwarzschild black hole and take a first look at its features. It appears that the infinite classical redshift/time dilation factor at the event horizon is made finite. 相似文献
4.
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n ? 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schrödinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension. 相似文献
5.
P. Yu. Tarasenko 《Russian Journal of Mathematical Physics》2007,14(4):505-508
Let ?n be n-dimensional Euclidean space and let M ? ?n be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?n. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½ΔM, where ΔM stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?n (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold. 相似文献
6.
In this paper, a generalized scheme is proposed for designing multistable continuous dynamical systems. The scheme is based on the concept of partial synchronization of states and the concept of constants of motion. The most important observation is that by coupling two m-dimensional dynamical systems, multistable nature can be obtained if i number of variables of the two systems are completely synchronized and j number of variables keep a constant difference between them i.e., their differences are constants of motion, where i + j = m and 1 ≤ i, j ≤ m?1. The proposed scheme is illustrated by taking coupled Lorenz systems and coupled chaotic Lorenz-like systems. According to the scheme, two coupled systems reduce to single modified system with some initial condition-dependent parameters. Time evolution plots, phase diagrams, variation of maximum Lyapunov exponent and bifurcation diagrams of the systems are presented to show the multistable nature of the coupled systems. 相似文献
7.
General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω i (N) at the symmetry points of the Brillouin zone and the elastic constants C ik . A number of relations between the values of ω i (N) and C ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co. 相似文献
8.
S. Yu. Davydov 《Physics of the Solid State》2004,46(7):1200-1205
The pressure dependences of the second-order elastic constants C ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model. The third-order elastic constants C ijk for 3C-SiC are determined from the dependences of the second-order elastic constants C ij on the pressure p. 相似文献
9.
The vibrational frequencies of the BiFeO3 crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure. 相似文献
10.
Edmundo Lazo Alejandro Garrido Félix Neira 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(11):249
This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The VC,n voltage across each capacitor is selected as a non-linear function of the electric charge qn, i.e., VC,n = qn(1/Cn -εn|qn|2)where Cn is the linear part of the capacitance and εn the amplitude of the non-linear term. We follow a binary distribution of values of εn, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention. 相似文献
11.
Boundary Conditions for Topological Quantum Field Theories,Anomalies and Projective Modular Functors
We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level m, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for n-characters on ∞-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for n + 1-dimensional TQFTs produce n-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory. 相似文献
12.
Alexander Davydov 《International Journal of Theoretical Physics》2011,50(5):1451-1467
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schrödinger’s equation. These results, with support from numerical simulations, strongly suggest that two uncoupled classical harmonic oscillators, which initially have a 90° relative phase shift and then are simultaneously disturbed by the same parametric perturbation of a finite duration, manifest behavior which can be mapped to that of a single quantum particle, with classical ‘range relations’ analogous to the uncertainty relations of quantum physics. 相似文献
13.
We establish a relation between Coulomb and oscillator systems on n-dimensional spheres and hyperboloids for n≥2. We show that, as in Euclidean space, the quasiradial equation for the (n+1)-dimensional Coulomb problem coincides with the 2n-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schrödinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem. 相似文献
14.
The thermodynamics of a phase transition is investigated within an isotropic m-vector model on a graph with sparse random connections. This model adequately describes superconductivity and superfluidity (m=2), Heisenberg magnets (m=3), and some structural transitions in different systems with macroscopic disorder (gels, composites, and porous media). It is demonstrated that the phase transition is characterized by classical effective-field anomalies. The thermodynamics of the phase transition is also analyzed in terms the proposed model at low temperatures. The dependences of the thermodynamic parameters on the external field, the mean coordination number, and the dimension of the order parameters are determined. 相似文献
15.
Alexander Ivanovich Aptekarev Dmitry Nikolaevich Tulyakov Irene Valero Toranzo Jesús Sanchez Dehesa 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(3):85
The Rényi entropies Rp [ ρ], p> 0,≠ 1 of the highly-excited quantum states of the D-dimensional isotropicharmonic oscillator are analytically determined by use of the strong asymptotics of theorthogonal polynomials which control the wavefunctions of these states, the Laguerrepolynomials. This Rydberg energetic region is where the transition from classical toquantum correspondence takes place. We first realize that these entropies are closelyconnected to the entropic moments of the quantum-mechanical probability ρn(r)density of the Rydberg wavefunctions Ψn,l, { μ}(r); so, to the?p-norms of the associated Laguerrepolynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques ofapproximation theory based on the strong Laguerre asymptotics. Finally, we determine thedominant term of the Rényi entropies of the Rydberg states explicitly in terms of thehyperquantum numbers (n,l), the parameter order p and the universedimensionality D for all possible cases D ≥ 1. We find that (a) theRényi entropy power decreases monotonically as the order p is increasing and (b) thedisequilibrium (closely related to the second order Rényi entropy), which quantifies theseparation of the electron distribution from equiprobability, has a quasi-Gaussianbehavior in terms of D. 相似文献
16.
A. D. Pierce 《Acoustical Physics》2005,51(1):5-10
Variational principles are derived for the analysis of dynamical phenomena associated with spherical inclusions embedded in homogeneous isotropic elastic solids. The starting point is Hamilton’s principle, with the material properties assumed to vary only with the radial distance r from the origin. Attention is restricted to disturbances that are symmetric about the polar (z) axis, such that the nonzero displacement components in spherical coordinates, u r and uθ, are independent of the polar coordinate φ. The symmetry allows for a decoupling of the polar components, the nth of which is described by U r, n (r, t)P n (cosθ) and Uθ, n(r, t)dP n /dθ. A variational principle is subsequently derived for the field quantities U r, n and Uθ, n. Concepts analogous to those of the theory of matched asymptotic expansions are used to embellish the principle in order to allow for the damping associated with the outward radiation of elastic waves. Examples illustrating the use of the variational principle for formulating plausible lumped-parameter models are given for the cases of n = 0 and n = 1. 相似文献
17.
E. M. Aver’yanov 《Physics of the Solid State》2016,58(8):1634-1641
The dimension D of a polycrystalline film and the optical anisotropy m = εz/εx of uniaxial crystallites with the principal components εx = εy and εz of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant εD* and the effective refractive index nD* = (εD*)1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals BDl ≤ εD* ≤ BDu. The intervals Δ2(m) = B2l–B2u and Δ3(m) = B3l–B3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε2*(m) is separated by a gap from the interval Δ3(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (noP) and theoretical (nD*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components εx,z(λ) on the light wavelength λ, the refractive indices noP2(λ) = εoP(λ) are consistent with the theoretical values of ε2*(λ) and lie outside the interval Δ3(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of εoP(λ) lie in the region of the overlap of the intervals Δ2(m) and Δ3(m). The boundaries mc of the range 1 < m < mc are determined, for which the interval Δ2(m) is separated by a gap from the dependences ε3*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε3*(m). 相似文献
18.
E. Bartoš S. R. Gevorkyan E. A. Kuraev N. N. Nikolaev 《Journal of Experimental and Theoretical Physics》2005,100(4):645-655
As an archetype reaction for pQCD multigluon hard processes in collisions of ultrarelativistic nuclei, we analyze generic features of lepton pair production via multiphoton processes in peripheral heavy ion scattering. We report explicit results for collisions of two photons from one nucleus with two photons from the other nucleus, 2γ + 2γ → l+l?. The results suggest that the familiar eikonalization of Coulomb distortions breaks down for oppositely moving Coulomb centers. The breaking of eikonalization in QED suggests that multigluon pQCD processes cannot be described in terms of collective nuclear gluon distributions. We discuss a logarithmic enhancement of the contribution from the 2γ + 2γ → l+l? process to production of lepton pairs with large transverse momentum; similar enhancement is absent for the nγ + mγ → l+l? processes with m, n > 2. We comment on the general structure of multiphoton collisions and properties of higher-order terms that cannot be eikonalized. 相似文献
19.
Two-dimensional structures obtained by the Hastings-Levitov conformal mapping were studied for a relatively small number of mappings n. The fractal dimension D of these structures is computed by the recent Davidovitch-Procaccia technique [6] as a function of n. For small n < n0 (where n0 is the number of particles at the first layer), D exponentially decreases, which should have supported the conclusion made in [6] about the possibility of determining the fractal dimension with an arbitrary accuracy using a relatively small number of mappings n≈ n0. On the other hand, it turned out that D irregularly deviates from a certain quantity D0 depending on the initial size of the bump \(\sqrt {\lambda _0 } \), which contradicts the main assertion of 相似文献
20.
Xian Shi 《International Journal of Theoretical Physics》2018,57(10):3056-3065
Monogamy of entanglement is a fundamental property of multipartite entangled states. In this article, due to the convexity of Trρq with respect to q when q ≥ 1, we give a monogamy-like relation in terms of Tsallis-q entanglement entropy of assistance (TqEEA) for pure states over an n- partite any dimensional system and monogamy-like relations in terms of Tsallis-q entanglement entropy (TqEE) for mixed states for any dimensional system, we also give a lower bound for the TqEE of a four-partite pure state. At last, we show that the generalized W-class states satisfy the polygamy relation in terms of TqEE when q = 2. 相似文献