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New functional integration method for the 1D random potential problem. The statistics of localized wave functions
Physica D: Nonlinear Phenomena. 1995. Vol. 86. No. 1-2. P. 134-148.
start from the derivation of the Abrikosov-Ryzhkin model for the 1D random potential problem. In its framework I find closed functional representations for various physical quantities. The representation uses number-valued fields only. These functional integrals are calculated exactly without the use of any perturbative expansions. Expressions for the multipoint densities correlators are obtained. These correlators allow to compute the distribution function of inverse sizes of localized wave functions valid both for an infinite sample and for a sample with a finite length.
Kolokolov I., JETP Letters 1994 Vol. 59 P. 879-882
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Added: March 28, 2017
Kolokolov I., EPL 1994 Vol. 28 No. 3 P. 193-196
For a given wave function one can define a quantity μE having the meaning of its inverse spatial size. The Laplace transform of the distribution function P(μE) is calculated analytically for a 1D disordered sample with a finite length L. ...
Added: March 28, 2017
Kolokolov I., Journal of Experimental and Theoretical Physics 1993 Vol. 76 No. 6 P. 1099-1109
Starting from the Abrikosov-Ryzhkin formulation of the
1D random potential problem I find closed functional representations
for various physical quantities. These functional integrals are
calculated exactly without the use of any perturbative expansions.
The expressions for the multipoint densities correlators are
obtained. Then I evaluate the mean square dispersion of the size
of localized wave functions. As a physical application of ...
Added: March 29, 2017
Kolokolov I., International Journal of Modern Physics B 1996 Vol. 10 No. 18-19 P. 2189-2215
A number of problems in statistical physics can be reformulated in terms of a two-state system evolving in a random field. The corresponding evolution operator can be written in the form of time-ordered operator exponential. Functional formalism allows us to rewrite the latter as a product of usual matrix exponentials using a nonlinear change of ...
Added: March 28, 2017
Kolokolov I., Gamba A., Cattaneo A. S., Journal of Statistical Physics 1994 Vol. 76 No. 3 P. 1065-1074
The set of moments and the distribution function of the one-electron current in a one-dimensional disordered ring with arbitrary magnetic flux are calculated. ...
Added: March 28, 2017
Kolokolov I., Annals of Physics 1994 Vol. 231 No. 2 P. 234-255
Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any perturbative expansions. The expressions for the multipoint densities correlators are obtained. Then I evaluate the mean square dispersion of the size of localized wave ...
Added: March 28, 2017
Tikhonov K., Mirlin A. D., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 P. 184203-1-184203-16
We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity ...
Added: March 9, 2017
Kolokolov I., Gamba A., Martellini M. et al., Physics Letters A 1994 Vol. 190 No. 2 P. 206-212
We investigate the conductance of a 1D disordered conducting loop with two contacts, immersed in a magnetic flux. We show the appearance in this model of the Al'tshuler-Aronov-Spivak behaviour. We also investigate the case of a chain of loops distributed with finite density: in this case we show that the interference effects due to the ...
Added: March 28, 2017
Tikhonov K., Mirlin A. D., Skvortsov M. A., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 P. 220203-1-220203-6
A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal disorder is performed.
The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.
In a certain sense, the RRG ensemble can be seen as an infinite-dimensional (d→∞) cousin of the Anderson ...
Added: March 9, 2017
Slunyaev A., Кокорина А. В., Water Waves, Springer 2019 P. 1-20
The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate ...
Added: October 13, 2019
Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222
We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...
Added: February 28, 2013
Prazdnichnykh A., Glazov M., Ren L. et al., Physical Review B: Condensed Matter and Materials Physics 2021 Vol. 103 No. 8 P. 085302-1-085302-12
The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenide monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study ...
Added: March 5, 2021
Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1-054505-10
We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...
Added: February 9, 2015
Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8
We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...
Added: October 26, 2017
Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416-432
We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...
Added: November 19, 2014
Pelinovsky E., Kurkin A. A., Kozelkov A. et al., European Journal of Mechanics - B/Fluids 2018 Vol. 72 P. 616-623
The paper presents results of numerical simulations of freely rising solid spheres in a viscous fluid. The
diameter of spheres was 5 mm, 7 mm, 10 mm, and 20 mm, and the corresponding Reynolds numbers
varies in the interval 1400 < Re < 10100. It has been found that the free rise path varies, as the
Galileo number ...
Added: October 21, 2018
М. : ИКИ РАН, 2011
Added: March 26, 2013
Akhmedov E., Musaev E. T., Physical Review D - Particles, Fields, Gravitation and Cosmology 2010 Vol. 81 P. 085010
We show that Polchinski equations in the D-dimensional matrix scalar field theory can be reduced at large N to the Hamiltonian equations in a (D+1)-dimensional theory. In the subsector of the Trϕl (for all l) operators we find the exact form of the corresponding Hamiltonian. The relation to the holographic renormalization group is discussed. ...
Added: February 27, 2013
Musaev E., Berman D. S., Thompson D. C., Journal of High Energy Physics 2012 Vol. 1210
The reduction of the duality invariant approach to M-theory by a U-duality group valued
Scherk-Schwarz twist is considered. We show that all gaugings of SUGRA can be obtained
by dimensional reduction of the extended space. ...
Added: October 20, 2014
Semenov-Tian-Shansky K. M., Поляков М. В., Смирнов А. О. et al., Теоретическая и математическая физика 2019 Т. 200 № 2 С. 290-309
Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear
recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity,
analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group
technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions
of nonlinear recurrence relations relevant for field ...
Added: September 29, 2020
Budkov Y., Kolesnikov A. L., Polymer Science - Series C 2018 Vol. 60 No. Supplement 1 P. 148-159
Theoretical models of the conformational behavior of flexible polymer chains in mixed solvents enunciated in the world literature during the last decade are critically reviewed. Models describing different mechanisms of coil-to-globule transitions in a good solvent induced by cosolvent addition are highlighted. Special attention is given to the analysis of theoretical approaches to describing the ...
Added: November 30, 2018
Bodrova A., Osinsky A., Brilliantov N., Scientific Reports 2020 Vol. 10 Article 693
We study analytically and numerically the distribution of granular temperatures in granular mixtures for
different dissipation mechanisms of inelastic inter-particle collisions. Both driven and force-free systems
are analyzed. We demonstrate that the simplified model of a constant restitution coefficient fails to
predict even qualitatively a granular temperature distribution in a homogeneous cooling state. At the
same time we reveal ...
Added: February 25, 2020
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Zhuzhoma E. V., Medvedev V., Исаенкова Н. В., Нелинейная динамика 2017 Т. 13 № 3 С. 399-412
В статье, используя методы теории динамических систем Морса–Смейла, авторы рассматривают топологическую структуру для точечно-зарядной модели магнитного поля областей фотосферы. Для произвольного количества зарядов (безотносительно к их местоположению) и не предполагая потенциальности поля <span data-mathml="B⃗ (следовательно, не используя конкретных формул), авторы приводят оценки, связывающие количества зарядов определенного типа с количеством нуль-точек. Для граничных оценок описывается топологическая структура магнитного ...
Added: October 12, 2017