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## Functional-integration method for 1-d localization, multipoint correlators and persistent current in mesoscopic ring at arbitrary magneic fields

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 functions. As a physical application of the method, I find the expectation value of the persistent current in mesoscopic ring with arbitrary magnetic flux Φ. (For small φ this problem has been solved by O. Dorokhov.) The case when the random potential has finite correlation length is considered too.

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., JETP Letters 1994 Vol. 59 P. 879-882

...

Added: March 28, 2017

Kolokolov I., Annals of Physics 1990 Vol. 202 No. 1 P. 165-185

The representation of the generating functional for quantum Heisenberg ferromagnets as an integral over two uncostrained c-number valued fields, charged and neutral, obeying the initial conditions (instead of commonly used periodic boundary conditions) is obtained. With the help of this representation the long-time dynamics of the longitudinal spin component at low temperatures is studied. The infrared-singular ...

Added: March 29, 2017

Kolokolov I., Lebedev V., Balkovsky E. et al., JETP Letters 1995 Vol. 61 No. 12 P. 1049-1054

Advection of a passive scalar $\theta$ in $d=2$ by a large-scale velocity
field rapidly changing in time is considered. The Gaussian feature of the
passive scalar statistics in the convective interval was discovered in
\cite{95CFKLa}. Here we examine deviations from the Gaussianity: we obtain
analytically the simultaneous fourth-order correlation function of $\theta$.
Explicit expressions for fourth-order objects,
like $\langle(\theta_1-\theta_2)^4\rangle$ are ...

Added: March 27, 2017

Kolokolov I., Physics Letters A 1986 Vol. 114 No. 2 P. 99-104

The partition function of the quantum Heisenberg ferromagnet is represented in a closed functional form. The resulting expression is a path integral for two interacting scalar Bose fields with non-polynomial action. ...

Added: March 31, 2017

Kolokolov I., 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 ...

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., 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., 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

Budkov Y., Kolesnikov A., Journal of Statistical Mechanics: Theory and Experiment 2016 Vol. 2014 P. 1-12

We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and potential energy in the parabolic well. In both cases we obtain the exact relations for the characteristic function ...

Added: October 27, 2016

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

Semenov A. G., Zaikin A. D., 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

Праздничных А. И., 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

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

Bodrova A., Osinsky A., Brilliantov N. V., Scientific Reports 2020 Vol. 10 No. 693 P. 1-15

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

Akhmedov E., Musaev E., 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

Min N., 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

Budkov Y., Kolesnikov A., 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

Zhukov A., Shapiro D., Pogosov W. et al., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 93 P. 063845

Superconducting circuits provide a new platform for study of nonstationary cavity QED phenomena. An example of such a phenomenon is the dynamical Lamb effect, which is the parametric excitation of an atom due to nonadiabatic modulation of its Lamb shift. This effect was initially introduced for a natural atom in a varying cavity, while we ...

Added: October 18, 2016

Semenov-Tian-Shansky K., Поляков М., Смирнов А. 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