Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Generalization of $1/N$ expansion in theories with matrix fields

### D.V. Malyshev

Moscow University Physics Bulletin 2002. 57. N 6. P. 28

The Feynman diagrams in theories with matrix fields $\Phi\in\mathop{\bf Mat}\nolimits(N,N)$ are ribbon graphs. There is a one-to-one correspondence between the ribbon graphs and surfaces with boundary having cell structures. The exponents of $N$ in the Feynman integrals depend only on the topology of the corresponding surfaces. It is shown that this is also true of generalized ribbon graphs. Such graphs correspond to surfaces with decomposition into spheres with holes.

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## A remark on the instability of eigenvalues of the Helmholtz equation

### M.D. Malykh

Moscow University Physics Bulletin 2002. 57. N 6. P. 33

The filled waveguide spectral problem eigenvalues embedded in the continuous spectrum are considered. An example of waveguide filling perturbation under which the embedded eigenvalues of the filled waveguide spectral problem disappear is given.

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## Reduced description method in quantum statistical thermodynamics

### P.N. Nikolaev

Moscow University Physics Bulletin 2002. 57. N 6. P. 36

Expressions £or thermodynamic functions in terms of simple statistical operators are obtained. The problem of thermodynamic compatibility of the thermal and caloric equations of state for quantum systems is solved.

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Atomic and nuclear physics

## Dynamics of molecules in a strong laser field under low dissociation conditions

### M.S. Molodenskii, O.V. Tikhonova

Moscow University Physics Bulletin 2002. 57. N 6. P. 41

In the rigid rotator model, the rotational dynamics of a two-dimensional molecular hydrogen ion was studied. The effect of dynamic orientation of a nuclear wave packet along and across the laser field polarization direction at the laser parameters for which the dissociation probability is low was revealed.

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Solid state physics

## Magnetic ordering near crossover in singlet paramagnetic materials HoBa$_2$Cu$_3$O$_{7-\delta}$ ($\delta=0,\,1.0$)

### Z.A. Kazei

Moscow University Physics Bulletin 2002. 57. N 6. P. 47

In an isothermal mode for HoBa$_2$Cu$_3$O$_6$ in a tetragonal phase including anisotropic bilinear interaction, the Zeeman effect, magnetization and differential magnetic susceptibility are calculated. Magnetic ordering in a basal plane in an external magnetic field $\bH\paral[001]$ near the energy levels crossover that is accompanied with the magnetic moment deflection from the field direction is shown to exist. The phase diagram dependence on the anisotropic bilinear interaction parameters, temperature and other factors is studied.

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Geophysics

## Analysis of seismotectonic strain in the Japan region

### E.V. Voronina, A.V. Lyusina

Moscow University Physics Bulletin 2002. 57. N 6. P. 53

Using the Japan region as an example, the relationship between seismicity and parameters of the seismotectonic strain rate tensor is studied. It is shown that the ranges of minimum values of the seismotectonic strain rate tensor determine localization of zones of relative seismic quiescence preceding strong earthquakes. To identify the seismic quiescence zones, the seismotectonic strain rate tensors and their invariants are calculated using the data on seismic focus mechanisms in Japan.

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## Application of the measurement reduction method to mean monthly temperature prediction

### Yu.P. Pyt'ev and I.V. Mazaeva

Moscow University Physics Bulletin 2002. 57. N 6. P. 59

Prediction of mean monthly temperature by the probabilistic method of reduction of measurement of the dynamic pattern of space-time temperature variations over the former USSR territory is studied. Based on the dynamics of the temperature distribution fronts isolines, the vector field of prevalent heat flows is determined and a model of the temperature field dynamics for each region is constructed.

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