Lorentzian Form Research Articles

Thermal transport in the intermetallic compound CeNi4Cr

Electrical resistivity, thermopower (TEP), thermal conductivity and the thermoelectric figure of merit are studied for the CeNi4Cr compound, which has been previously suggested to be a fluctuating valence system with a tendency to the increase of the effective mass at low temperatures. The analysis of the thermoelectric properties confirms such a possibility and provides characteristic parameters like the Debye temperature, Fermi energy and the position of the f band. Both the thermopower and the magnetic part of the electrical resistivity could be analyzed within a similar model assuming a narrow f-band of the Lorentzian form near the Fermi energy. The thermal conductivity shows that the phonon contribution exceeds the electronic one below 220 K.

Quasi-biharmonic Lagrangian surfaces in Lorentzian complex space forms

In this paper, we introduce the notion of a quasi-biharmonic submanifold in a pseudo-Riemannian manifold and classify quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms.

Non-Markovian and Non-Perturbative Entanglement Dynamics of Biomolecular Excitons

We investigate the entanglement dynamics of two coupled chromophore pairs embedded in a protein-solvent environment. The non-Markovian and non-perturbative hierarchical expansion technique is used in the solution of the quantum dynamics. The spectral distribution function of the bath is set with the Drude—Lorentz form. It is shown that the evolutions of the entanglement described by the measures of negativity and concurrence are in agreement with each other. They decay to zero in a short time and the sudden death and sudden birth can be observed in the process of the evolutions of the entanglement.

Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.

Semi-invariant submanifolds of Lorentzian Sasakian manifolds

Abstract In this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian Sasakian space form.

Imprisonment dynamics of resonance radiation in gases

Imprisonment of resonant radiation in gases on the basis of the numerical solution of the rate balance equation for the excited atoms and the transfer resonant radiation equation is investigated. Calculations of the escape factor for the slab, cylinder and sphere at Doppler and Lorentz forms of absorption and scattering profiles are executed. Calculation results of the escape factor for the cylinder and slab are compared with Holsten's asymptotical solutions. The numerical data for time dependence of a spectrum, the intensity of resonant radiation and the spatial distribution of the excited atomic concentration in a regime of afterglow are also considered.

Energy-dependent target widths in a coupled-channel scattering study

The question of how the scattering cross section changes when the spectra of the colliding nuclei have low-excitation particle-emitting resonances is explored using a multichannel algebraic scattering method. As a test case, the particle-unstable nucleus $^{8}\mathrm{Be}$ has been considered as a target. Nucleon-nucleus scattering cross sections, as well as the spectra of the compound nuclei formed, have been determined from calculations that consider, as well as those that disregard, particle-emission widths of the target nuclear states. The resonant character of the unstable excited states introduces a problem because the low-energy tails of these resonances can intrude into the subthreshold, bound-state region. This unphysical behavior needs to be corrected by modifying, in an energy-dependent way, the shape of the target resonances from the usual Lorentzian form. The resonance function must smoothly reach zero at the elastic threshold. We explore herein a way of achieving this condition.

CLASSIFICATION OF PSEUDO-UMBILICAL SLANT SURFACES IN LORENTZIAN COMPLEX SPACE FORMS

In this paper we prove that slant surfaces in a non-flat Lorentzian complex space form must be Lagrangian. By applying this result, we completely classify pseudo-umbilical slant surfaces in Lorentzian complex space forms. Our classification results state that there exist two families of pseudo-umbilical slant surfaces in Lorentzian complex plane $\mathbb{C}^2_1$, three families in complex projective plane $CP^2_1$, and three families in complex hyperbolic plane $CH^2_1$.

Pseudo-Hermitian realization of the Minkowski world through DLF theory

Segal's chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in terms of which the pseudo-Hermitian realization of the Minkowski space–time is introduced and studied. The world L is based on the oscillator Lie algebra. The main idea of the DLF approach to modeling particles and interactions is that there are three Hamiltonians (the ‘Russian Troika’) to drive the evolution of a physical system.

Fluctuations, jamming, and yielding for a driven probe particle in disordered disk assemblies

Using numerical simulations we examine the velocity fluctuations and velocity-force curve characteristics of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of ϕJ=0.843. As ϕ increases toward ϕJ, the average velocity of the probe particle decreases and the velocity fluctuations show an increasingly intermittent or avalanchelike behavior. When ϕ is within a few percent of the jamming density, the velocity distributions are exponential, while when ϕ is less than 1% away from jamming, the velocity distributions have a power-law character with exponents in agreement with recent experiments. The velocity power spectra exhibit a crossover from a Lorentzian form to a 1/f shape near jamming. We extract a correlation length exponent ν which is in good agreement with recent shear simulations. For ϕ>ϕJ, there is a critical threshold force F(c) that must be applied for the probe particle to move through the sample which increases with increasing ϕ. The velocity-force curves are linear below jamming, while at jamming they have a power-law form. The onset of the probe motion above ϕJ occurs via a local yielding of the particles around the probe particle which we term a local shear banding effect.

Typical weak and superweak values

Weak values, resulting from the action of an operator on a preselected state when measured after postselection by a different state, can lie outside the spectrum of eigenvalues of the operator: they can be ‘superweak’. This phenomenon can be quantified by averaging over an ensemble of the two states, and calculating the probability distribution of the weak values. If there are many eigenvalues, distributed within a finite range, this distribution takes a simple universal generalized lorentzian form, and the ‘superweak probablility’, of weak values outside the spectrum, can be as large as 1–1/ = 0.293.... By contrast, the familiar expectation values always lie within the spectral range, and their distribution, although approximately gaussian for many eigenvalues, is not universal.

Complete classification of parallel Lorentz surfaces in four-dimensional neutral pseudosphere

A Lorentz surface of an indefinite space form is called parallel if its second fundamental form is parallel with respect to the Van der Waerden–Bortolotti connection. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Parallel Lorentz surfaces in four-dimensional (4D) Lorentzian space forms are classified by Chen and Van der Veken [“Complete classification of parallel surfaces in 4-dimensional Lorentz space forms,” Tohoku Math. J. 61, 1 (2009)]. Recently, explicit classification of parallel Lorentz surfaces in the pseudo-Euclidean 4-space E24 and in the pseudohyperbolic 4-space H24(−1) are obtained recently by Chen et al. [“Complete classification of parallel Lorentzian surfaces in Lorentzian complex space forms,” Int. J. Math. 21, 665 (2010); “Complete classification of parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space,” Cent. Eur. J. Math. 8, 706 (2010)], respectively. In this article, we completely classify the remaining case; namely, parallel Lorentz surfaces in 4D neutral pseudosphere S24(1). Our result states that there are 24 families of such surfaces in S24(1). Conversely, every parallel Lorentz surface in S24(1) is obtained from one of the 24 families. The main result indicates that there are major differences between Lorentz surfaces in the de Sitter 4-space dS4 and in the neutral pseudo 4-sphere S24.

A classification of Einstein lightlike hypersurfaces of a Lorentzian space form

We study Einstein lightlike hypersurfaces of a semi-Riemannian manifold of constant curvature c , whose shape operator is conformal to the shape operator of its screen distribution. Our main result is a classification theorem for Einstein lightlike hypersurfaces of Lorentzian space forms.

On the Fundamental Limitations of Artificial Magnetic Materials

Fundamental limitations are presented on the performance of artificial magnetic materials based on the geometrical and physical characteristics of the inclusions comprising the medium. The permeability and magnetic susceptibility of the medium are formulated in terms of newly defined geometrical and physical parameters. Based on the Lorentzian form of the effective permeability function of the medium, it is shown that the flatness of the permeability function is limited by the desired operational bandwidth. Also, by applying a specific circuit-based model for inclusions, geometric invariant fundamental constraints are derived. It is shown that inclusions with larger surface area result in higher value of permeability. Next, the magnetic loss tangent in the medium is expressed as a function of the newly defined geometrical and physical parameters. It is found that there is a tradeoff between increasing the permeability and decreasing the loss on the one hand and reducing dispersion, on the other hand.

On spacelike hypersurfaces with two distinct principal curvatures in Lorentzian space forms

We investigate the spacelike hypersurfaces in Lorentzian space forms N 1 n + 1 ( c ) ( n ⩾ 4 ) with two distinct non-simple principal curvatures without the assumption that the (high order) mean curvature is constant. We prove that any spacelike hypersurface in Lorentzian space forms with two distinct non-simple principal curvatures is locally conformal to the Riemannian product of two constant curved manifolds. We also obtain some characterizations for hyperbolic cylinders in Lorentzian space forms in terms of the trace free part of the second fundamental form.

Spacelike S-Willmore spheres in Lorentzian space forms

We show that spacelike S-Willmore surfaces are the only spacelike Willmore surfaces with a duality in Lorentzian space forms. We obtain a classification of S-Willmore spheres in Lorentzian conformal space forms. Such a sphere must be congruent to either a complete spacelike stationary (H = 0) surface in R n 1 ; a super-Willmore sphere in S 2m+2 ; or a polar transform of a (j―1)― isotropic complete spacelike stationary (H = 0) surface in R 2j+2 1 . We also show that all Willmore spheres in Q 4 1 are conformal to a complete spacelike stationary surface in R 4 1 .

COMPLETE CLASSIFICATION OF PARALLEL LORENTZIAN SURFACES IN LORENTZIAN COMPLEX SPACE FORMS

A surface of a pseudo-Riemannian manifold is called parallel if its second fundamental form is parallel with respect to the Van der Waerden–Bortolotti connection. Such surfaces are fundamental since the extrinsic invariants of the surfaces do no change from point to point. In this article, we completely classify parallel Lorentzian surfaces in Lorentzian complex space forms of complex dimension two.

Macroscopic Maxwell’s equations and negative index materials

We study the linear phenomenological Maxwell’s equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, nonabsorptive, medium with equal electric and magnetic permeabilities ε(ω) and μ(ω), the latter can assume the value of −1 (+1 is their vacuum value) for a discrete set of frequencies ±ω̂n, i.e., for these frequencies the medium behaves as a negative index material (NIM). We show that such systems have a well-defined time evolution. In particular, the fields remain square integrable (and the electromagnetic energy finite) if this is the case at some initial time. Next we turn to Green’s function G(x,y,z) (a tensor), associated with the electric Helmholtz operator for a set of parallel layers filled with a material. We express it in terms of the well-known scalar s and p ones. For a half space filled with the material and with a single dispersive Lorentz form for ε(ω)=μ(ω), we obtain an explicit form for G. We find the usual behavior for NIMs for ω=±ω̂, there is no refection outside the evanescent regime and the transmission (refraction) shows the usual NIM behavior. We find that G has poles in ±ω̂, which lead to a modulation of the radiative decay probability of an excited atom. The formalism is free from ambiguities in the sign of the refractive index.

SCREEN CONFORMAL EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

Classification of Lagrangian surfaces of curvature ɛ in non-flat Lorentzian complex space form % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8WrFz0dbbf9q8 % WrFfeuY-Hhbbf9v8qqaqFr0dd9qqFj0dXdbba91qpepGe9FjuP0-is % 0dXdbba9pGe9xq-Jbba9suk9fr-xfr-xfrpeWZqaaeaabiGaciaaca % qabeaadaabauaaaOqaaiqbd2eanzaaiaWaa0baaSqaaiabigdaXaqa % aiabikdaYaaakiabcIcaOiabisda0eXafv3ySLgzGmvETj2BSbacgi % Gae8xTduMaeiykaKcaaa!4CAA! $$ \tilde M_1^2 (4\varepsilon ) $$ )

It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form \( \tilde M_1^2 (4\varepsilon ) \) of constant holomorphic sectional curvature 4ɛ is of constant curvature ɛ. A natural question is “Besides totally geodesic ones how many Lagrangian surfaces of constant curvature ɛ in \( \tilde M_1^2 (4\varepsilon ) \) are there?” In an earlier paper an answer to this question was obtained for the case ɛ = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ɛ ≠ 0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ɛ in \( \tilde M_1^2 (4\varepsilon ) \) with ɛ ≠ 0. Conversely, every Lagrangian surface of curvature ɛ ≠ 0 in \( \tilde M_1^2 (4\varepsilon ) \) is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.