Isometric Uncertainty Relations

Journal of Statistical Physics - We generalize the link between fluctuation theorems and thermodynamic uncertainty relations by deriving a bound on the variance of fluxes that satisfy an isometric...     

Isometric embeddings in cosmology and astrophysics

Recent interest in higher-dimensional cosmological models has prompted some significant work on the mathematical technicalities of how one goes about embedding spacetimes into some higher-dimensional space. We survey results in the literature (existence theorems and simple explicit embeddings); briefly outline our work on global embeddings as well as explicit results for more complex geometries; and provide some examples. These results are contextualized physically, so as to provide a foundation for a detailed commentary on several key issues in the field such as: the meaning of ‘Ricci equivalent’ embeddings; the uniqueness of local (or global) embeddings; symmetry inheritance properties; and astrophysical constraints.     

Differential Invariants of Immersions of Manifolds with Metric Fields

The problem of finding all r^th order differential invariants of immersions of manifolds with metric fields, with values in a left (G¹_m×G¹_n)-manifold is formulated. For obtaining the basis of higher order differential invariants the orbit reduction method is used. As a new result it appears that r^th order differential invariants depending on an immersion f:M N of smooth manifolds M and N and metric fields on them can be factorized through metrics, curvature tensors and their covariant differentials up to the order (r–2), and covariant differentials of the tangent mapping Tf up to the order r. The concept of a covariant differential of Tf is also introduced in this paper. The obtained results are geometrically interpreted as well.This research is supported by grants GAR 201/03/0512 and MSM 143100006.     

Isometric motion in relativistic magnetohydrodynamics

The general relativistic barometric formulas of a perfect charged relativistic ther modynamical fluid with constant magnetic permeability and infinite conductivity are deduced if the space-time, in which this fluid is moving, has two Killing vector fields: the first collinear to the 4-velocity with the second one proportional to the magnetic field.     

Isometric motion in relativistic magnetohydrodynamics

It is shown that if the flow of a plasma coupled to a frozen-in magnetic field is isometric, the velocity field, the vorticity tensor and the four-vector magnetic field are invariant under the group of motions. A generalization of Ferraro's theorem of isorotation and of the Bernoulli's theorem for force-free fluids is found.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

Compensated adiabatic inversion pulses: broadband INEPT and HSQC

When adiabatic fast passage is used to flip nuclear spins, sites with different chemical shifts are inverted at different times, causing refocusing errors. By mapping the phase evolution diagrams, we show that these effects can be accurately compensated with matched pairs of adiabatic pulses, either opposed or in the same sense, depending on the application. Applied to well-known heteronuclear polarization transfer experiments such as INEPT and HSQC, the requisite evolution of J-vectors is achieved irrespective of chemical shift or the duration of the adiabatic sweeps. By replacing conventional 180 degrees pulses, these new adiabatic sequences offer an order of magnitude improvement in effective bandwidth for the X-spins. Alternatively the experiments can be carried out with significantly reduced radiofrequency power. One- and two-dimensional spectra of (13)C in 13-cis-retinal at 600MHz have been used to demonstrate these advantages.     

Split and Compensated Hyperfine Fields in Magnetic Metal Clusters

As prominent characteristics of magnetic metal cluster found in vanadium sulfides, we point out marked separation and compensation of the hyperfine field at the nuclear site; these are in somewhat discordance with the common sense for 3d transition-metal magnets, where the on-site isotropic field, scaling the ordered moment magnitude, is dominant.     

Isometric motions of a perfect charged fluid

Space-times with perfect charged fluids as sources, that admit groups G_r of isometric motions, are investigated. It is assumed that the velocity vector of the fluid is collinear to the timelike Killing vector ⁱ of group G_r. It is shown that the macroscopic motion of a perfect charged fluid can occur only in the direction of such a Killing vector ⁱ that defines an operator in an invariant subgroup or, in particular, an operator of the center of the group. Parametric representations of the generalized equations of state for the pressure p, the energy density of the fluid, , and the electric charge density are established. All these quantities are functions of the norm of the Killing vector ⁱ and the projection of the 4-potential of the electromagnetic field onto this vector ⁱ. In the approximation of the weak field in the coordinate system where ⁱ= ₄ ⁱ , these functional dependences imply that p, , and are functions of Newtonian and electrostatic potentials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–29, October, 1987.     

Isometric embedding for homogeneous compact 3-manifolds

The anisotropic homogeneous ³ is isometrically globally embedded into a nine-dimensional Euclidean or pseudo-Euclidean space. In a special case the Euclidean space is six-dimensional. The space-sections of the anti-Mach metric appear as a submanifold of theE ⁹. We obtain also the isometric embedding ofSO(3) with its natural Killing metric.     

Quantum-Sensitive Ionizing Radiation Detectors Compensated by Gallium Arsenide

The state-of-the art of and outlook for semiconductor GaAs ionizing radiation detectors are discussed. A comparative analysis of the most essential features of detectors based on semi-insulating GaAs is performed.     

Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass

The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface \({\Sigma=\partial \Omega}\) and should be independent of whichever space-like region \({\Sigma}\) bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been taken by Brown-York [4,5] and Liu-Yau [16,17] (see also related works [3,6,9,12,14,15,28,32]) to define such notions using the isometric embedding theorem into the Euclidean three space. However, there exist surfaces in the Minkowski space whose quasilocal mass is strictly positive [19]. It appears that the momentum information needs to be accounted for to reconcile the difference. In order to fully capture this information, we use isometric embeddings into the Minkowski space as references. In this article, we first prove an existence and uniqueness theorem for such isometric embeddings. We then solve the boundary value problem for Jang’s [13] equation as a procedure to recognize such a surface in the Minkowski space. In doing so, we discover a new expression of quasi-local mass for a large class of “admissible” surfaces (see Theorem A and Remark 1.1). The new mass is positive when the ambient space-time satisfies the dominant energy condition and vanishes on surfaces in the Minkowski space. It also has the nice asymptotic behavior at spatial infinity and null infinity. Some of these results were announced in [29].     

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias （EB） of the ferromagnetic （FM）/antiferromagnetic （AFM） bilayers in a compensated case is studied by use of the many-body Green＇s function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interracial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interracial coupling strength oi2 the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and He decrease with temperature increasing. The anisotropy of the FM layer only slightly influence He, but does not influence HE.     

Compensated Polarization Scrambler for Raman Depolarization and Intensity Measurements on Microsamples

It has long been recognized ^1,2,3,4,5 in measuring relative intensities and depolarization ratios of Raman lines that prism and grating spectrometers have different transmittances for light polarized parallel (T_∥) and perpendicular (T_⊥) to the slit. Several methods have been used to give equal instrument response to parallel and perpendicular polarization. Stitt and Yost³ used a Nicol prism parallel to the high-transmittance direction of the spectrometer, combined with a rotatable mica half-wave plate to transmit either vector to the Nicol prism. This method has the advantage of having a higher spectrometer transmittance, but the mica plate gives exact half-wave retardation at only a single wavelength. A mica quarter-wave plate ^4,5 averages the transmittances of the spectrometer for the two polarization directions, but is also wavelength dependent. Virtually achromatic circular polarizers have been designed and constructed ^6,7, but these devices are too bulky and expensive for the clear apertures needed for fast spectrometers.     

Isometric groups,selection rules and irreducible tensors of semi-rigid molecules

A systematic treatment of multipole selection rules of non-rigid molecules is presented, based on the isomorphism of the isometric group to the symmetry group of the rotation-internal motion hamiltonian. A classification of isometric groups and relations among the representations of the isometric group on various substrates are discussed. A set of general transformation formulae for irreducible tensor operators of semi-rigid molecular models is derived. These formulae are used for the derivation of dipole and quadrupole selection rules of a considerable number of semi-rigid models. The relations among the representations of the isometric group give rise to some theorems which allow a compact presentation of selection rules of non-rigid molecules.     

On the Nature of Radiation Resistance in Compensated Silicon

Russian Physics Journal -     

利用相位共轭技术补偿光纤中色散效应的条件

利用相位共轭器的频率反转特性的,补偿光纤中的色散效应,在理论上和实验上得到了证明.由色散脉冲的傅里叶交换确定了光纤中二次色散效应可以被忽略的条件,得到了共轭器的反射率和带宽与非线性介质的长度L,参数|K|L之间的关系曲线,找到了影响补偿效果的主要因素.