Martin-Dynkin boundaries of random fields

Analogous of exit spaces of Dynkin [4] for Markov processes are constructed for random fields introduced by Dobrushin [2].     

Cosmological magnetic fields

Magnetic fields are observed not only in stars, but in galaxies, clusters, and even high redshift Lyman-α systems. In principle, these fields could play an important role in structure formation and also affect the anisotropies in the cosmic microwave background radiation (CMB). The study of cosmological magnetic fields aims not only to quantify these effects on large-scale structure and the CMB, but also to answer one of the outstanding puzzles of modern cosmology: when and how do magnetic fields originate? They are either primoridial, i.e. created before the onset of structure formation, or they are generated during the process of structure formation itself.     

On spectral asymptotics for domains with fractal boundaries

We discuss the spectral properties of the Laplacian for domains Ω with fractal boundaries. The main goal of the article is to find the second term of spectral asymptotics of the counting functionN(λ) or its integral transformations: Θ-function, ξ-function. For domains with smooth boundaries the order of the second term ofN(λ) (under “billiard condition”) is one half of the dimension of the boundary. In the case of fractal boundaries the well-known Weyl-Berry hypothesis identifies it with one half of the Hausdorff dimension of ∂Ω, and the modified Weyl-Berry conjecture with one half of the Minkowski dimension of ∂Ω. We find the spectral asymptotics for three natural broad classes of fractal boundaries (cabbage type, bubble type and web type) and show that the Minkowski dimension gives the proper answer for cabbage type of boundaries (due to “one dimensional structure” of the cabbage type fractals), but the answers are principally different in the two other cases.     

宇宙磁场

磁场在宇宙中无处不在,贯穿各种天体。磁场对天体形成、辐射和演化起重要作用,也是宇宙线研究的基础。以前人们对宇宙磁场的理解主要是来自对地球和太阳磁场的测量和物理解释。近20年来,对宇宙更大尺度天体的磁场测量取得很大进展：发现了银河系具备沿着银河旋臂的几万光年尺度磁场,强度为2—4 μG;发现了银河系晕里具有环向磁场,在银道面上下方向相反;发现了银河系中心有极向磁场的观测证据;发现了邻近旋涡星系可能具有万光年尺度磁场的证据;发现了星系团几千万光年范围内磁场存在的证据。宇宙学模拟也显示在宇宙超大纤维结构中应该有磁场存在。这些磁场可能都是宇宙早期产生并在天体形成和演化过程中得以发扬光大。     

Fluctuating magnetic fields

Some problems pertaining to the behaviour of a classical spin under the influence of a random Gaussian magnetic field are discussed. It is shown that, in agreement with simple expectations, the magnetic moment is effectively decreased to lowest order. Various physical applications and connections with group theory are pointed out.     

Strong linear amplification of quantum fields

Going ahead with investigations started by ideas of H. Paul it is examined how different quantum properties in the initial field state show up in the strongly amplified output field. As examples of extreme quantum fields the number state and the recently introduced phase optimized state are used. For the linear laser amplifier the inevitable noise is fully taken into account. These results are compared with those for a coherent input field. The characteristic differences in the macroscopic output fields allow unique conclusions onto the initial field. For the calculations the positive definite Glauber's P-representation after strong amplification is applied.     

Axion-like particles,cosmic magnetic fields and gamma-ray astrophysics

Axion-like particles (ALPs) are predicted by many extensions of the Standard Model and give rise to characteristic dimming and polarization effects in a light beam travelling in a magnetic field. In this Letter, we demonstrate that photon-ALP mixing in cosmic magnetic fields produces an observable distortion in the energy spectra of distant gamma-ray sources (like AGN) for ranges of the ALP parameters allowed by all available constraints. The resulting effect is expected to show up in the energy band 100 MeV–100 GeV, and so it can be searched with the upcoming GLAST mission.     

Strong gravitational fields and geometry in the large

The problem of strong gravitational fields (1) can be neither formulated invariantly nor solved in a local manner; it belongs to geometry in the large and requires the discussion of a complete atlas of maps. At 1 a complicated topology of space-time is possible. Requirements for a solution with a complete atlas of maps and a physical example, a rigorous discussion of which has led to new results, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 15–19, January, 1984.     

Nonlocal pseudopotentials and magnetic fields

We show how to describe the coupling of electrons to nonuniform magnetic fields in the framework of the widely used norm-conserving pseudopotential approximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules within density functional theory (DFT) in the local density approximation. Our results are compared with high-quality all-electron DFT results obtained using Gaussian basis sets and another recently proposed pseudopotential formalism.     

Persistent spectral holes in external fields

Experimental results and model calculations of the effects of an external electric field on persistent spectral holes are reviewed. Hole-burning spectroscopy of impurity centers in crystals and amorphous solids yields information on various properties of the centers and their interaction with the electric field. The applications of persistent spectral hole burning presented in this paper include: optical-data storage in the electric-field dimension, modulation and pulse shaping of light beams, determination of the Debye-Waller factor of host-guest systems with strongly inhomogeneously broadened transitions, detection of ultra-sound and high-frequency acoustic phonons. The effects of a magnetic field and external pressure on persistent spectral holes are discussed.     

Polarimetric and spectral changes in random electromagnetic fields

Beginning with a recently formulated unified theory of coherence and polarization for random electromagnetic fields, we show how partially polarized light can be generated through correlation of unpolarized components. The effect is demonstrated by use of a Mach-Zehnder interferometer, showing the possibility of producing light with adjustable spectral density and an adjustable degree of polarization.     

Biexciton in magnetic fields

The binding energy and structure of biexcitons in strong magnetic field is investigated using the stochastic variational method. The magnetic field confines the electrons and positrons in a small volume leading to Wigner-crystal like states of particles.     

Tunneling in magnetic fields

Tunneling effects in external magnetic fields are discussed in the model problem of a charged particle on a vertical rotating circle in a uniform gravitational field. The magnetic fields used are the ones for the monopole and a certain solution that arises in the context of the classical Weinberg-Salam model. Using instanton methods and the Gaussian approximation, various consequences regarding the tunnelling amplitudes and the level splittings in the presence of magnetic fields are obtained.