arXiv subjects

B. I. Lev

Publications and source records attributed to B. I. Lev.

At least 37 records · Page 2Linked to original sources

arXiv2013

Nonlocal free energy of a spatially inhomogeneous superconductor

The microscopic approach was developed for obtaining of the free energy of a superconductor with help direct calculation of the vacuum amplitude. The functional of free energy of the spatially inhomogeneous superconductor in a magnetic field was obtained with help the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of the order parameter and the magnetic response. Moreover the nonlocality of the magnetic response is the consequence of the order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low-temperature limit and in the high-temperature limit at the condition of slowness of spatial variations of the order parameter.

cond-mat.supr-con↗

arXiv2013

Elastic octopoles and colloidal structures in nematic liquid crystals

We propose a simple theoretical model which explains a formation of dipolar 2D and 3D colloidal structures in nematic liquid crystal. Colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole and octopole moments. It is shown that octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption on the case of the external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently [A. Nych et al., Nature Communications \textbf{4}, 1489 (2013)].

cond-mat.soft↗

arXiv2013

A model of phase transitions with coupling between the order parameter and its gradient

A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially inhomogeneous distributions of the order parameter. Exact solutions of the proposed model are obtained for the special cases which can be related to the spinodal decomposition or cosmological scenario. The proposed model is analogical to the mechanical nonlinear oscillator with the coordinate-dependent mass or velocity dependent elastic module. Based on this analogy, the existence of the limit cycles is established.

cond-mat.stat-mech↗

arXiv2012

Localized states of an excess electron in ionic clusters

A theory for an electron affinity of ionic clusters is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. An interaction of an electron with longitudinal optical phonons in an ionic cluster is described. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of an energy and a radius of a polaron on a cluster's size are obtained by a variational method. It has been found that a binding energy of the electron in a cluster depends on a cluster's radius but the radius of electron's autolocalization does not depend on cluster's radius and equals to the polaron radius in a corresponding infinity crystal, moreover the bound state of the electron in a cluster is possible if the cluster's radius is more then the polaron radius. A perturbation method for finding of the critical parameters is proposed, where an dependence of the critical size on a momentum of an electron in a conduction band is observed.

cond-mat.mes-hall↗

arXiv2012

Unification of the standard and gradient theories of phase transition

We show, that the standard model of phase transition can be unified with the gradient model of phase transitions using the description in terms of the gradient of order parameter. The generalization of the gradient theory of phase transitions with regard to the fourth power of the order parameter and its gradient is proposed. Such generalization makes it possible to described wide class of phase transitions within a unified approach. In particular it is consistent with the nonlinear models, that can be used to describe a phase transition with the formation of spatially inhomogeneous distribution of the order parameter. Typical examples of such structures (with or without defects) are considered. We show that formation of spatially inhomogeneous distributions of the order parameter in the course of a phase transitions is a characteristic feature of many nonlinear models of phase transitions.

cond-mat.stat-mech↗

arXiv2011

Microscopic theory of phase transitions and nonlocal corrections for free energy of a superconductor

The new approach to the microscopic description of the phase transitions starting from the only first principles was developed on an example of the transition normal metal-superconductor. This means mathematically, that the free energy is calculated in the range of temperatures, which includes a point of pase transition, without introducing any artificial parameters similar to an order parameter, but only starting from microscopic parameters of Hamiltonian. Moreover the theorems about connection of a vacuum amplitude with thermodynamics potentials are realized. The functional of a superconductor's free energy in a magnetic field was obtained with help the developed method. The obtained functional is generalization of Ginzburg-Landau functional for the case of arbitrary value of a gap, arbitrary spatial inhomogeneities and nonlocal magnetic response. The explicit expressions for the extremals of this functional were obtained in the low-temperature limit and the high-temperature limit at the condition of slowness of gap's changes.

cond-mat.stat-mech↗

arXiv2011

Theory of elastic interaction between colloidal particles in the nematic cell in the presence of the external electric or magnetic field

The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev, Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in the nematic cell in the presence of the external electric or magnetic field. General formulas for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of new results has been predicted: 1) \textit{Deconfinement effect} for dipole particles in the homeotropic nematic cell with negative dielectric anisotropy $Δε<0$ and perpendicular to the cell electric field, when electric field is approaching it's Frederiks threshold value $E\Rightarrow E_{c}$. This means cancellation of the confinement effect found in Ref. [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801, (2008)] for dipole particles near the Frederiks transition while it remains for quadrupole particles. 2) New effect of \textit{attraction and stabilization} of the particles along the electric field parallel to the cell planes in the homeotropic nematic cell with $Δε<0$ . The minimun distance between two particles depends on the strength of the field and can be ordinary for . 3) Attraction and repulsion zones for all elastic interactions are changed dramatically under the action of the external field.

cond-mat.soft↗

arXiv2011

Wave function as geometric entity

A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. Interference of electrons whose wave functions are represented by geometric entities is considered. New experiments concerning the geometric nature of electrons are proposed.

quant-ph↗

arXiv2011

Theory of Elastic Interaction of the Colloidal Particles in the Nematic Liquid Crystal Near One Wall and in the Nematic Cell

We apply the method developed in Ref. [S.B.Chernyshuk and B.I.Lev, Phys.Rev.E, \textbf{81}, 041701 (2010)] for theoretical investigation of colloidal elastic interactions between axially symmetric particles in the confined nematic liquid crystal (NLC) near one wall and in the nematic cell with thickness $L$. Both cases of homeotropic and planar director orientations are considered. Particularly dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions of the \textit{one} particle with the wall and within the nematic cell are found as well as corresponding \textit{two particle} elastic interactions. A set of new results has been predicted: the effective power of repulsion between two dipole particles at height $h$ near the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase of dimensionless distance $r/h$; near the planar wall - the effect of dipole-dipole \textit{isotropic attraction} is predicted for large distances $r>r_{dd}=4.76 h$; maps of attraction and repulsion zones are crucially changed for all interactions near the planar wall and in the planar cell; one dipole particle in the homeotropic nematic cell was found to be shifted by the distance $δ_{eq}$ from the center of the cell \textit{independent} of the thickness $L$ of the cell. The proposed theory fits very well with experimental data for the confinement effect of elastic interaction between spheres in the homeotropic cell taken from [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801, (2008)] in the range $1\div1000 kT$.

cond-mat.soft↗

arXiv2010

The self-consistent microscopic model of an energy spectrum of a superfluity $^{4}$He with the Hermitian form of Bogoliubov-Zubarev Hamiltonian

Based on the collective variables representation with the Hermitian form of Bogoliubov-Zubarev Hamiltonian the self-consistent oscillator model of a ground state and excited states of Bose liquid has been proposed. The new method of calculation of anharmonic terms in this Hamiltonian and its interpretation have been presented. The dispersion equation for a collective excitation in a superfluid $^{4}$He has been obtained in self-consistent way, where real and virtual processes of decay of a collective excitation were considered. The end point, determined by a threshold of collective excitation's decay on two rotons, of the dispersion curve has been obtained and it was shown that the dispersion curve strongly depends on property of its stability. An approach with a structure factor has been realized without using of any adaption parameters. Based on the oscillator model the new method of self-consistent calculation of a ground state energy and density of Bose condensate has been proposed. The model of suppression of Bose condensate has been presented.

cond-mat.other↗

arXiv2010

Elastic interaction between colloidal particles in confined nematic liquid crystals

The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition on the bounding surface. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness $L$ are considered and found to be exponentially screened on far distances with decay length $λ_{dd}=\frac{L}π$. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that \textit{the decay length} in quadrupolar interaction is \textit{two times smaller} than for the dipolar case.

cond-mat.soft↗

arXiv2009

Nonequilibrium self-gravitational system

The density of states of self-gravitational system diverges when the particles are spread to infinity. Other problem based an inhomogeneous distribution of particles,which motivate the gravitational interaction. In this sense the statistical mechanics of self-gravitational system is essentially an non-equilibrium problem. A new possible approach to statistical description of self-gravitational system has been proposed. The approach based on non-equilibrium statistical operator, which allow take into account inhomogeneous distribution particle and temperature in self gravitational system. The saddle point procedure, which used in the given method describes the spatially inhomogeneous distribution in self gravitational system accompanied by temperature changing.

cond-mat.stat-mech↗

arXiv2009

Inhomogeneous distribution particles in self-gravitational system

The microcanonical partition function for self-gravitational system in three dimensional case has been found. Used approach from the field theory of statistical description of the system was tailored to gravitational interacting particles with regard for an arbitrary spatially inhomogeneous particle distribution. The entropy of self-gravitational system has been found from extreme condition for the effective functional. For inhomogeneous distribution particle (formation few cluster of finite size) the entropy are bigger as the entropy homogeneous distribution of particles. The increasing of entropy of self-gravitational system after formation cluster motive tendency to disperse.

cond-mat.stat-mech↗

arXiv2009

General elastic interaction in nematic liquid crystals colloids

The new free energy functional that describes general elastic interaction between colloidal particles and nematic liquid crystal has been proposed. It generalizes results of the paper \cite{lupe} on the case of arbitrary orientation of colloidal particles and is valid for arbitrary surface anchoring strength. Formal analogies and differences between electric particles and colloidal particles in LC are found. It is first time shown that spur of the quadrupole moment tensor is different from zero $Sp\hat{Q}_μ\neq 0$ in the case of axial symmetry breaking of the director field around colloidal particle in contrast to electrostatics. New general presentation for the elastic interaction between arbitrary colloids is obtained which contains new multipole terms connected with $Sp\hat{Q}_μ\neq 0$ that are absent in the standard electrostatics.

cond-mat.soft↗

arXiv2008

Positive-definite states of a Klein-Gordon type particle

A possible way for the consistent probability interpretation of the Klein-Gordon equation is proposed. It is assumed that some states of a scalar charged particle cannot be physically realized. The rest of quantum states are proven to have positive-definite probability distributions.

hep-th↗

arXiv2008

Cluster formation in the Fermi system with long-range interaction

Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Fermi particles by long-rage forces, and we demonstrated nonperturbative calculation of the partition function in this case. It was shown, that particles interacting with an attractive $1/r$ potential form clusters. Cluster is equilibrium structure, if we suppose that average energy of interaction of two particles is much less than their average kinetic energy $kT$. The analogy between self-gravitation gas and plasma was shown. The dynamics of cluster formation was considered with help hydrodynamical and statistical approaches, and time of relaxation to equilibrium state was found.

cond-mat.stat-mech↗

arXiv2006

Nonclassicality of noisy quantum states

Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case, affection of the thermal noise can be compensated via transformation of an observable, which tests the nonclassicality (witness function). Possibilities for experimental implementations based on unbalanced homodyning are discussed. At the same time, we demonstrate that the scheme based on balanced homodyning cannot be improved for noisy states with proposed technique and should be applied directly.

quant-ph↗

arXiv2004

Spinor representation of Lie algebra for complete linear group

Spinor representation of group GL(4,R) on special spinor space is developed. Representation space has a structure of the fiber space with the space of diagonal metricses as the base and standard spinor space as typical fiber. Non-isometric motions of the space-time entail spinor transformations which are represented by translation over fibering base in addition to standard $Spin(4,C)$ representation.

quant-ph↗