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E. L. Rumyantsev

Publications and source records attributed to E. L. Rumyantsev.

7 recordsLinked to original sources
arXiv2023

The guide to the guiding center aka pseudo-momentum operator construction

The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations, describing the wave functions of highly degenerate Landau levels in the classical non-relativistic case, are formulated. The proposed gauge-invariant approach was used also for the construction of the equations describing the quasi-relativistic carriers behavior in the homogeneous/inhomogeneous magnetic field in the single layer graphene.

cond-mat.mes-hall↗
arXiv2017

The quantum mechanical probability density and probability current density operators in the Pauli theory

We present systematic construction of probability and probability current densities operators for one-band single particle Pauli equations starting from the operators in Dirac electron model within Second Quantized Approach. These operators are of importance as in probability interpretation of experimental data, so in establishing of boundary conditions. It is shown that derived operators differ significally from their convential Schrodinger-type counterparts. The generalization of continuity equation for probability density under external perturbations and physical meaning of additional source terms is discussed. The presented approach can be useful in analysis of carriers dynamics described within generic multicomponent $\vec{k} \cdot \vec{p}$ Hamiltonians in Envelope Function Approximation (EFA).

cond-mat.mes-hall↗
arXiv2016

Pauli equations and non-commutative position operators in 2D Dirac-like semiconductors in view of second quantization

The Pauli equations describing electron (hole) dynamics in 2D Dirac-like intrinsic semiconductors in external (impurity) scalar potential and for inhomogeneous lattice distortions are obtained within second quantization approach. We show that the modifying external perturbation terms in formulated no-pair equations are in general non-local and demonstrates singular behavior in gapless situation where they do not depend on semiconductor parameters. It is shown that lattice distortion perturbation can cause confinement of both electrons and holes in the same spatial region. The proposed approach is verified by comparison with well-established results in low energy limit. The consideration of position operator in second quantization approach allows elucidating the physical meaning of spin-orbit-like and Darwin-like terms.

cond-mat.mes-hall↗
arXiv2016

Default contagion risks in Russian interbank market

Systemic risks of default contagion in the Russian interbank market are investigated. The analysis is based on considering the bow-tie structure of the weighted oriented graph describing the structure of the interbank loans. A probabilistic model of interbank contagion explicitly taking into account the empirical bow-tie structure reflecting functionality of the corresponding nodes (borrowers, lenders, borrowers and lenders simultaneously), degree distributions and disassortativity of the interbank network under consideration based on empirical data is developed. The characteristics of contagion-related systemic risk calculated with this model are shown to be in agreement with those of explicit stress tests.

q-fin.RM↗
arXiv2014

Systemic Interbank Network Risks in Russia

Modelling of contagion in interbank networks is discussed. A model taking into account bow-tie structure and dissasortativity of interbank networks is developed. The model is shown to provide a good quantitative description of the Russian interbank market. Detailed arguments favoring the non-percolative nature of contagion-related risks in the Russian interbank market are given.

physics.soc-ph↗
arXiv2014

Spin-orbit interaction in 2D Dirac-like and Kane semiconductors

The single particle equations describing motion of carriers in external potential in 2D Dirac-like and Kane intrinsic semiconductors are obtained within second quantization method. The terms renormalizing external potential in these equations, referred to as spin-orbit (SO) terms, are compared with their classical counterpart. The well-known expression for SO obtained in relativistic Dirac theory arises in considered approach in the second order in $γk / E_g$ ($γ$ - characteristic velocity, $E_g$ - energy gap) parameter if electron-hole pair production terms are neglected. It is shown that in Kane problem the modifying terms are of standard SO functional Dirac-like form only for electrons in the case of ``positive'' energy gap and for light holes in semiconductors with ``negative'' energy gap. The general expression for renormalizing terms has in all cases non-local character. The arising of correction terms to single particle potentials which do not depend on band parameters is demonstrated for 2D gapless Dirac problem (graphene) and for Kane model. The origin of such ``topological'' terms is attributed to the presence of degenerate bands in considered problems.

cond-mat.mes-hall↗