S. I. Matveenko - Landau Inst., Moscow

S. I. Matveenko
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S. I. Matveenko
Landau Inst., Moscow

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Physics - Strongly Correlated Electrons (13)
Physics - Mesoscopic Systems and Quantum Hall Effect (3)
Physics - Superconductivity (3)
Mathematics - Spectral Theory (2)
Physics - Statistical Mechanics (2)
Mathematics - Mathematical Physics (2)
Mathematical Physics (2)
Quantum Physics (1)
Nonlinear Sciences - Exactly Solvable and Integrable Systems (1)
Mathematics - Analysis of PDEs (1)
Nonlinear Sciences - Pattern Formation and Solitons (1)
Physics - Atomic Physics (1)

Publications Authored By S. I. Matveenko

We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the s-wave and p-wave pairing in the order parameter. Read More

Spatial cruciform quantum waveguides (the Dirichlet problem for Laplace operator) are constructed such that the total multiplicity of the discrete spectrum exceeds any preassigned number. Read More

We show that recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological $p$-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer $p$-wave superfluid of polar molecules in a bilayer geometry. Read More

In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schr\"odinger equation and Kadomtsev-Petviashvili and Hirota equations that exhibit the behavior of almost-periodic "freak waves". We also study the dependency of the solution parameters on the spectral curves. Read More

Solutions of the Bogoliubov-de Gennes equations for the two-dimensional self-consistent Hubbard t-U-V model of superconductors with $d_{x^2-y^2}$ symmetry of the order parameter in the presence of a magnetic field are found. It is shown that spatial inhomogeneity of superconducting order parameter results in the emergence of stripe-like domains that are stabilized by applied magnetic field leading to emergence of space-modulated composite spin-charge-superconducting order parameter. Read More

This paper starts a series devoted to the vector-valued Sturm-Liouville problem $-\psi''+V(x)\psi=\lambda\psi$, $\psi\in L^2([0,1];\mathbb{C}^N)$, with separated boundary conditions. The overall goal of the series is to give a complete characterization of classes of spectral data corresponding to potentials $V=V^*\in L^p([0,1];\mathbb{C}^{N\times N})$ for a fixed $1\le p <+\infty$ and separated boundary conditions having the most general form. In the first paper we briefly describe our approach to this inverse problem and prove some preliminary results including the relevant uniqueness theorem. Read More

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hopps only to the right. In the commensurate case when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. Read More

We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. Read More

A system of N interacting bosons or fermions in a two-dimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for matrix elements of any interaction, in the basis of angular momentum eigenstates. For the fermion "ground state" (N=1 Laughlin state), this makes it possible to exactly calculate its energy all the way up to the mesoscopic regime N ~ 1000. Read More

We found solutions of the Bogoliubov-de Gennes equations for the two-dimensional self-consistent model of superconductors with $d_{x^2-y^2}$ symmetry of the order parameter, taking into account spin and charge distributions. Analytical solutions for spin-charge density wave phases in the absence of the superconductivity ("stripe" and "checkerboard" structures) are presented. Analytical solutions for coexisting superconductivity and stripes are found. Read More

We have found an exact analytical solution of the Bogoliubov-de Gennes equations for the Tkachenko modes of the vortex lattice in the lowest Landau level (LLL) in the thermodynamic limit at any momenta and calculated their damping rates. At finite temperatures both Beliaev and Landau damping leads to momentum independent damping rates in the low-energy limit, which shows that at sufficiently low energies Tkachenko modes become strongly damped. We then found that the mean square fluctuations of the density grow logarithmically at large distances, which indicates that the state is ordered in the vortex lattice only on a finite (although exponentially large) distance scale and introduces a low-momentum cut-off. Read More

We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of anisotropic harmonic potential. For the case of symmetric harmonic trap when the rotation frequency is equal to the trapping frequency, the solution coincides with the Abrikosov triangle vortex lattice in type-II superconductors. Read More

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. Read More

We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. Read More

We develop an effective field theory for finding critical properties of 1D spin gapped fermions at the onset of magnetization. It is shown how the spin-charge interaction leads to a linear critical behavior and finite susceptibility for a wide range of models. We also discuss possible manifestations of spin-charge coupling in cold atomic gases. Read More

We suggest a theory of internal coherent tunneling in the pseudogap region, when the applied voltage U is below the free electron gap 2Delta_0. We address quasi 1D systems, where the gap is originated by spontaneous lattice distortions of the Incommensurate Charge Density Wave (ICDW) type. Results can be adjusted also to quasi-1D superconductors. Read More

An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. Read More

We suggest a theory of internal coherent tunneling in the pseudogap region where the applied voltage is below the free electron gap. We consider quasi 1D systems where the gap is originated by a lattice dimerization like in polyacethylene, as well as low symmetry 1D semiconductors. Results may be applied to several types of conjugated polymers, to semiconducting nanotubes and to quantum wires of semiconductors. Read More

The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is adressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero-Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. Read More

Affiliations: 1Moscow Institute for Steel and Alloys, Moscow, Russia, 2Landau Institute for Theoretical Physics, Moscow, Russia

Motivated by the stripe developments in cuprates, we review some analytical results of our studies of the charge- and spin density modulations (CDW and SDW) in a weakly coupled one dimensional repulsive electron system on a lattice. It is shown that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wave vectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, not only the wave vectors, but also the mutual phases of the CDW and SDW become coupled due to a quantum interference phenomenon, leading to the stripe phase instability in a quasi one-dimensional repulsive electron system. Read More

We show that many observable properties of high temperature superconductors can be obtained in the frameworks of one-dimensional self-consistent model with included superconducting correlations. Analytical solutions for spin, charge and superconductivity order parameters are found. The ground state of the model at low hole doping is a spin-charge solitonic superstructure. Read More

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. In the framework of the adiabatic approximation for the electron - phonon interactions these processes are described by nonlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. Read More

We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Read More

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by nonlinear configurations of an instanton type. We calculate intensities of the photoelectron spectroscopy PES including the momentum resolved one ARPES and supplement to known results for the optical subgap absorption. Read More

The self-consistent solution for the spin-charge solitonic superstructure in quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of a hole doping. Effects of interchain interactions on the ground state are discussed. Results are used for the interpretation of the observed stripe phases in doped antiferromagnets. Read More

We consider two-dimensional system of particles localized on randomly distributed sites of squared lattice with anisotropic transfer matrix elements between localized sites. By summing of "diffusion ladder" and "cooperon ladder" type vertices we calculated the conductivity for various sites and particles densities. Read More

Calogero-Sutherland models of type $BC_N$ are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions. Their asymptotic behaviour supports the predictions of (boundary) conformal field theory for the orthogonality catastrophy and Friedel oscillations. Read More

Affiliations: 1Los Alamos and Landau Institute, 2Landau Institute and Los Alamos

We consider the dynamical properties of simple edge states in integer ($\nu = 1$) and fractional ($ \nu = 1/2m+1$) quantum Hall (QH) liquids. The influence of a time-dependent local perturbation on the ground state is investigated. It is shown that the orthogonality catastrophe occurs for the initial and final state overlap $|| \sim L^{-{1\over{2\nu}}({\delta\over{\pi}})^2}$ with the phase shift $\delta$. Read More

We study a one-dimensional, two band model with short range electron-electron repulsions (onsite $U$ and nearest-neighbour $V$ terms) and electron-phonon coupling. We show that there is a region of $U$,$V$ and band filling in which singlet superconductivity fluctuations are dominant. This region is absent without electron-phonon interactions and includes large values of $U$,$V$. Read More

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical Hamiltonians is a realization of an integrable Haldane system. Read More