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Том 201, № 2 (2019)
- Год: 2019
- Статей: 11
- URL: https://journals.rcsi.science/0040-5779/issue/view/10517
Article
In Memory of Sergei Yuryevich Slavyanov
1543-1544
Bethe Vectors for Orthogonal Integrable Models
Аннотация
We consider quantum integrable models associated with the \(\mathfrak{so}_3\) algebra and describe Bethe vectors of these models in terms of the current generators of the \(\mathcal{D}Y(\mathfrak{so}_3)\) algebra. To implement this program, we use an isomorphism between the R-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type B-, C-, and D-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the \(\mathfrak{so}_3\) algebra.
1545-1564
Relativistic Interacting Integrable Elliptic Tops
Аннотация
We propose a relativistic generalization of integrable systems describing M interacting elliptic gl(N) Euler-Arnold tops. The obtained models are elliptic integrable systems that reproduce the spin elliptic GL(M) Ruijsenaars-Schneider model with N = 1 and relativistic integrable GL(N) elliptic tops with M = 1. We construct the Lax pairs with a spectral parameter on the elliptic curve.
1565-1580
Quasiexact Theory of Three-Dimensional Optical Self-Focusing
Аннотация
We find a quasiexact three-dimensional analytic solution of the nonlinear Schrödinger equation describing the field of a stationary optical beam in an unbounded homogeneous nonlinear isotropic medium supporting a state of linear polarization.
1581-1584
Revealing Nonperturbative Effects in the SYK Model
Аннотация
In the large-N limit, we study saddle points of two SYK chains coupled by an interaction that is nonlocal in Euclidean time. We study the free model with the order of the fermionic interaction q = 2 analytically and also investigate the model with interaction in the case q = 4 numerically. We show that in both cases, there is a nontrivial phase structure with an infinite number of phases. Each phase corresponds to a saddle point in the noninteracting two-replica SYK. The nontrivial saddle points have a nonzero value of the replica-nondiagonal correlator in the sense of quasiaveraging if the coupling between replicas is turned off. The nonlocal interaction between replicas thus provides a protocol for turning the nonperturbatively subleading effects in SYK into nonequilibrium configurations that dominate at large N. For comparison, we also study two SYK chains with local interaction for q = 2 and q = 4. We show that the q=2 model has a similar phase structure, while the phase structure differs in the q = 4 model, dual to the traversable wormhole.
1585-1605
Partition Functions of \(\mathcal{N}=(2,2)\) Supersymmetric Sigma Models and Special Geometry on the Moduli Spaces of Calabi-Yau Manifolds
Аннотация
We study a new example of a mirror relation between the exact partition functions of \(\mathcal{N}=(2,2)\) super-symmetric gauged linear sigma models on the sphere S2 and the special Kähler geometry on the moduli spaces of Calabi-Yau manifolds. Using exact calculations, we show this relation indeed holds for Calabi-Yau manifolds of the Berglund-Hubsch type with two moduli.
1606-1613
Group Analysis of the One-Dimensional Boltzmann Equation: IV. Complete Group Classification in the General Case
Аннотация
We consider the one-dimensional Boltzmann equation \(f_t+cf_x+(\mathcal{F}f)_c=0\) with a function \(\mathcal{F}\) depending on (t,x,c,f) and obtain the complete group classification of such equations in the class of point changes of whole set of variables (t,x,c,f). for this, we impose additional conditions on the transformations for the invariance of (a) the relations dx = c dt and \(dc=\mathcal{F}dt\), (b) the lines dt = dx = 0, and (c) the form f dx dc, which fix the physical meaning of the used variables and the relations between them.
1614-1643
Coset Space Construction for the Conformal Group: Spontaneously Broken Phase and Inverse Higgs Phenomenon
Аннотация
We establish a mathematically rigorous way to construct effective theories resulting from the spontaneous breaking of conformal invariance. We show that the Namby-Goldstone field corresponding to spontaneously broken generators of special conformal transformations is always a nondynamical degree of freedom. We prove that the developed approach and the standard approach including application of the inverse Higgs mechanism are equivalent.
1644-1654
Magnetic Susceptibility of a Diluted Ising Magnet
Аннотация
for the Ising model with nonmagnetic dilution, we consider a method for constructing the “pseudochaotic” impurity distribution based on the condition that the position correlation of movable impurity atoms in neighboring sites vanishes. For the one-dimensional Ising model with nonmagnetic dilution, we find the exact solution and show that the pseudochaotic approximation method gives the exact value of the magnetic susceptibility for this model in a zero external field. We assume that the pseudochaotic impurity distribution is completely uncorrelated in the region of zero magnetization for any lattice. This assumption is based on calculating the correlation functions for the Ising model with nonmagnetic dilution on the Bethe lattice. We find the magnetic susceptibility for that model.
1655-1663
Quantum Entanglement in the Nonrelativistic Collision Between Two Identical Fermions with Spin 1/2
Аннотация
In the framework of nonstationary scattering theory, we study the formation of an entangled state of two identical nonrelativistic spin-1/2 particles as a result of their elastic scattering. The measure of particle entanglement in the final channel is described using pair concurrence. For the indicated quantitative criterion, we obtain general expressions in terms of the direct and exchange scattering amplitudes in the cases of pure and mixed spin states of the pair in the initial channel. We consider the violation of Bell’s inequality in the final channel. We show that as a result of a collision between unpolarized particles, a Werner spin state of the pair forms, which is entangled if the singlet component of the angular differential scattering cross section in the center-of-mass reference frame exceeds the triplet component. We use the process of free electron-electron scattering as an example to illustrate the developed formalism.
1664-1679
Erratum
1680-1680