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## Functional Integration for Quantum Magnets: New Method and New Results

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 part of effective action is calculated for the longitudinal fluctuations in 3D-quantum antiferromagnets as well.

Kolokolov I., Podivilov E., Journal of Experimental and Theoretical Physics 1989 Vol. 68 No. 1 P. 119-125

Added: March 30, 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., 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., Chertkov M., Journal of Experimental and Theoretical Physics 1994 Vol. 79 No. 5 P. 824-832

Using the functional integration method we compute exactly the time-dependent correlation
functions of local spins in a finite quantum Heisenberg magnet with a position-independent
exchange between spins. Explicit expressions for such correlation functions for an arbitrary
number (N) of spins in the cluster and for all temperatures are presented. The spin correlation
function for a cluster placed in an ...

Added: March 28, 2017

Kolokolov I., Journal of Experimental and Theoretical Physics 1986 Vol. 64 No. 6 P. 1373-1375

Added: March 31, 2017

Kolokolov I., Chertkov M., Physical Review B: Condensed Matter and Materials Physics 1994 Vol. 49 No. 5 P. 3592-3595

Infinite-temperature long-time dynamics of Heisenberg model H^=-1/2tsumi,jJijS^i⋅S^j is investigated. It is shown that the quantum-spin pair correlator is equal to the correlator of a classically evaluated vector field averaged over the initial conditions with respect to the Gaussian measure. In the continuous-limit case, the scaling estimations allow one to find the one-point correlator that turns out to ...

Added: March 28, 2017

Kolokolov I., Chertkov M., Physical Review B: Condensed Matter and Materials Physics 1995 Vol. 51 No. 6 P. 3974-3977

The transverse autocorrelation function at an arbitrary temperature is calculated rigorously for a system with an arbitrary number of quantum spins, each of which is coupled to all the other spins with equal exchange. It is shown that the cluster approximation, formed by a model for a real magnet, explains short- and intermediate-time (up to ...

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

Kolokolov I., L'vov V., Cherepanov V. B., Journal of Experimental and Theoretical Physics 1984 Vol. 59 No. 5 P. 1131-1139

Added: March 31, 2017

Budkov Y., Kolesnikov A. L., 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

Kolokolov I., L'vov V., Cherepanov V. B., Physics Reports 1993 Vol. 229 No. 3 P. 81-144

A review of magnon properties of yttrium-iron garnet (YIG), a classical object for experimental studies in magnetism, is presented. Both experimental and theoretical results concerned with thermodynamics and kinetics of YIG are described. The main purposes of the review are to introduce a new method of approximate calculation of the magnon spectra in magnets with ...

Added: March 29, 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., Vorobyov P. V., JETP Letters 1998 Vol. 67 P. 910-912

The energy losses due to Cherenkov emission of magnons during the interaction of a slow heavy monopole with magnetically ordered media are discussed. ...

Added: March 5, 2017

Glazov M., Oxford : Oxford University Press, 2018

In recent years, the physics community has experienced a revival of interest in spin effects in solid state systems. On one hand, the solid state systems, particularly, semiconductors and semiconductor nanosystems, allow us to perform benchtop studies of quantum and relativistic phenomena. On the other hand, this interest is supported by the prospects of realizing ...

Added: January 13, 2021

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

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

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

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., 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

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