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V. A. Zagrebnov

Publications and source records attributed to V. A. Zagrebnov.

17 recordsLinked to original sources
arXiv2012

Disordered Bose Einstein Condensates with Interaction in One Dimension

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.

math-ph↗
arXiv2007

Quasi-Sectorial Contractions

We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m-sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.

math.FA↗
arXiv2007

Large Deviations in the Superstable Weakly Imperfect Bose Gas

The superstable Weakly Imperfect Bose Gas {(WIBG)} was originally derived to solve the inconsistency of the Bogoliubov theory of superfluidity. Its grand-canonical thermodynamics was recently solved but not at {point of} the {(first order)} phase transition. This paper proposes to close this gap by using the large deviations formalism and in particular the analysis of the Kac distribution function. It turns out that, as a function of the chemical potential, the discontinuity of the Bose condensate density at the phase transition {point} disappears as a function of the particle density. Indeed, the Bose condensate continuously starts at the first critical particle density and progressively grows but the free-energy per particle stays constant until the second critical density is reached. At higher particle densities, the Bose condensate density as well as the free-energy per particle both increase {monotonously}.

math-ph↗
arXiv2006

Condensation in a Disordered Infinite-Range Hopping Bose-Hubbard Model

We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case, we observe here new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at some fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the BEC suppression at integer densities may disappear, if disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.

math-ph↗
arXiv2005

Once more on the equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164 (2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment once more on the temperature-dependent effective Hamiltonians for the Dicke model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys. J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot be correct for any finite nonzero temperature because they both violate a rigorous result. The fact that the Dicke model belongs to the universality class of, and its thermodynamics is described by the infinitely coordinated transverse-field XY model is known for more than 30 years.

quant-ph↗
arXiv2005

Comment on equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.

quant-ph↗
arXiv2004

Equilibrium states for the Bose gas

The generating functional of the cyclic representation of the CCR (Canonical Commutation Relations) representation for the thermodynamic limit of the grand canonical ensemble of the free Bose gas with attractive boundary conditions is rigorously computed. We use it to study the condensate localization as a function of the homothety point for the thermodynamic limit using a sequence of growing convex containers. The Kac function is explicitly obtained proving non-equivalence of ensembles in the condensate region in spite of the condensate density being zero locally.

math-ph↗
arXiv2003

Bose-Einstein Condensation for Homogeneous Interacting Systems with a One-Particle Spectral Gap

We prove rigorously the occurrence of zero-mode Bose-Einstein condensation for a class of continuous homogeneous systems of boson particles with superstable interactions. This is the first example of a translation invariant continuous Bose-system, where the existence of the Bose-Einstein condensation is proved rigorously for the case of non-trivial two-body particle interactions, provided there is a large enough one-particle excitations spectral gap. The idea of proof consists of comparing the system with specially tuned soluble models.

math-ph↗
arXiv2003

Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems.

math-ph↗
arXiv1999

Anomalous electron trapping by localized magnetic fields

We consider an electron with an anomalous magnetic moment g>2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-δ}) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.

math-ph↗
arXiv1998

Anomalous electron trapping by magnetic flux tubes and electric current vortices

We consider an electron with an anomalous magnetic moment, g>2, confined to a plane and interacting with a nonhomogeneous magnetic field B, and investigate the corresponding Pauli Hamiltonian. We prove a lower bound on the number of bound states for the case when B is of a compact support and the related flux is $N+ε, ε\in(0,1]$. In particular, there are at least N+1 bound states if B does not change sign. We also consider the situation where the magnetic field is due to a localized rotationally symmetric electric current vortex in the plane. In this case the flux is zero; there is a pair of bound states for a weak coupling, and higher orbital-momentum "spin-down" states appearing as the current strength increases.

math-ph↗
arXiv1998

Electron trapping by a current vortex

We investigate an electron in the plane interacting with the magnetic field due to an electric current forming a localized rotationally symmetric vortex. We show that independently of the vortex profile an electron with spin antiparallel to the magnetic field can be trapped if the vortex current is strong enough. In addition, the electron scattering on the vortex exhibits resonances for any spin orientation. On the other hand, in distinction to models with a localized flux tube the present situation exhibits no bound states for weak vortices.

cond-mat↗
arXiv1997

A Mechanism of Porous-Silicon Luminescence

We discuss the discrete spectrum induced by bulges on threadlike mesoscopic objects, using two models, a continuous hard-wall waveguide and a discrete tight-binding model with two sorts of atomic orbitals. We show that elongated bulges induce numerous quasibound states. In the discrete model we also evaluate the probability of transition between the localized states and extended ones of the "valence" band. We suggest this as a mechanism governing the porous-silicon luminescence. In addition, the model reproduces the dominance of nonradiative transitions, blue shift for finer textures and luminescence suppression at low temperatures.

cond-mat.mes-hall↗
arXiv1994

On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals

The problem of the orientational ordering transition for lattice-gas models of liquid crystals is discussed in the low-dimensional case $d=1,2$. For isotropic short-range interactions, orientational long-range order at finite temperature is excluded for any packing of molecules on the lattice $Z^d$; on the other hand, for reflection-positive long-range isotropic interactions, we prove existence of an orientational ordering transition for high packing ($μ> μ_0$) and low temperatures ($β> β_c(μ)$).

cond-mat↗
arXiv1994

Critical Fluctuation Operators for a Quantum Model of Ferroelectric

We consider dependence of the critical fluctuation operators on the rate of interaction decay for an exactly soluble model of the quantum anharmonic crystal of ferroelectric type. The critical exponents for the abnormal behavior of the displacement and momentum fluctuation operators on the critical line are calculated explicitly.

cond-mat↗
arXiv1994

Singular Perturbations, Regularization and Extension Theory

We present an abstract result on removing regularization for singular potentials which are not semibounded from below. The relation between ``right'' regularizations and ``right'' self-adjoint extensions of the perturbed Schrödinger operators is examined.

funct-an↗