arXiv subjects
Publications and source records attributed to A. A. Vladimirov.
The question about asymptotical behaviour of solutions for the system $\dot x=A_νx+f$ for big values of the parameter $ν\in\frak A$ is considered. An approach to the reduction of a large class of problems to easily solvable problem with diagonal coefficient matrix is described. This approach is based on the approximation of summable matrix function $A_ν$ by specially constructed smooth matrix functions.
For one boundary problem of fourth order with a spectral parameter in the boundary condition we prove the simplicity of the spectrum and the oscillation properties of the system of the eigenfunctions derivatives.
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id'-type mediated by the antiferromagnetic exchange is found. The superconducting Tc as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.
It is obtained that every constructive (in A.A.Markov's sense) function is summable, if it is defined almost everywhere in the interval $[0,1]$ and integrable in Riemann's sense.
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t-J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t_J model on the square lattice.
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, N'eel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. The Néel temperature is calculated for arbitrary interlayer couplings. Our results are in a good agreement with numerical computations for finite clusters and with available experimental data on the β-Cu2V2O2 compound.
In terms of triples of Banach spaces, we define a large class of boundary problems for ordinary differential equations (of arbitrary order) with singular coefficients.
Due to multiple possible polarizations hard exclusive production of tensor mesons by virtual photons or in heavy meson decays offers interesting possibilities to study the helicity structure of the underlying short-distance process. Motivated by the first measurement of the transition form factor $γ^*γ\to f_2(1270)$ at large momentum transfers by the BELLE collaboration we present an improved QCD analysis of this reaction in the framework of collinear factorization including contributions of twist-three quark-antiquark-gluon operators and an estimate of soft end-point corrections using light-cone sum rules. The results appear to be in a very good agreement with the data, in particular the predicted scaling behavior is reproduced in all cases.
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation (RPA) for four different ordered phases, observed in the parameter space of the model: antiferomagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.
Let $M_γ$ be precise a priori majorant of first eigenvalues of Sturm--Liouville problems $-y"+qy=λy,\quad y(0)=y(1)=0$, where $q\leqslant 0$ and $\int_0^1 |q|^γ\,dx=1$, $γ\in (0,1/2)$. It is shown that the inequality $M_γ<π^2$ is true.
It is shown that positivity in $(0,1)\times (0,1)$ of Green function of positively defined fourth-order ordinary differential operator (with separated boundary conditions) is a criterium of sign-regularity of this operator.
We provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present an application of a new tool, TMDlib, to parton density fits and parameterizations.
A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, N'eel temperature T_N, specific heat, and uniform static spin susceptibility $χ$ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of T_N on the compass-model interaction is studied. We find that T_N is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of $χ$.
It is proved that for class $A_γ=\{q\in L_1[0,1]: q\geq 0, \int_0^1 q^γ\,dx=1\}$, where $γ\in (0,1)$, there exists a potential $q_*\in A_γ$ such that minimal eigenvalue $λ_1(q_*)$ of boundary problem $$ -y"+q_*y=λy, y'(0)=y'(1)=0 $$ is equal to $m_γ=\inf_{q\in A_γ}λ_1(q)$. The equality $m_γ=1$ for $γ\leq 1-2π^{-2}$ and the inequality $m_γ<1$ for $γ>1-2π^{-2}$ are also obtained.
It is constructively proved that for class $A_{r,γ}=\{q\in L_{1,loc}(0,1): q\leq 0, \int_0^1 rq^γ\,dx\leqslant 1\}$, where $r\in C[0,1]$ is uniformly positive weight and $γ>1$, there exists a unique potential $\hat q\in A_{r,γ}$ such that minimal eigenvalue $λ_0(\hat q)$ of boundary problem $$-y"+\hat qy=λy, y(0)=y(1)=0 $$ is equal to $M_{r,γ}=\sup_{q\in A_{r,γ}}λ_0(q)$. For case $γ=1$ we obtain that there exists a unique potential $\hat q\inΓ_{r,γ}$ with analogous property. Here $Γ_{r,γ}$ is a closure of $A_{r,γ}$ in the space $W_{2,loc}^{-1}(0,1)$ of generalized functions.
The spin-wave excitation spectrum, the magnetization, and the Néel temperature for the quasi-two-dimensional spin-1/2 antiferromagnetic Heisenberg model with compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Neel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.
Sturm-Liouville spectral problem for equation $-(y'/r)'+qy=λpy$ with generalized functions $r\ge 0$, $q$ and $p$ is considered. It is shown that the problem may be reduced to analogous problem with $r\equiv 1$. The case of $q=0$ and self-similar $r$ and $p$ is considered as an example.
We present the description of the exponentiated diagrams in terms of generating function within the universal diagrammatic technique. In particular, we show the exponentiation of the gauge theory amplitudes involving products of an arbitrary number of Wilson lines of arbitrary shapes, which generalizes the concept of web diagrams. The presented method gives a new viewpoint on the web diagrams and proves the non-Abelian exponentiation theorem.