arXiv subjects

Kh. P. Gnatenko

Publications and source records attributed to Kh. P. Gnatenko.

At least 37 records · Page 2Linked to original sources

arXiv2021

Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer

We consider graph states generated by operator of evolution with Ising Hamiltonian. The geometric measure of entanglement of a spin with other spins in the graph state is obtained analytically and quantified on IBM's quantum computer, IBM Q Valencia. The results of quantum calculations are in good agreement with the theoretical ones. We conclude that the geometric measure of entanglement of a spin with other spins in the graph state is related with degree of vertex representing the spin in the corresponding graph.

quant-ph↗

arXiv2019

Kinetic energy properties and weak equivalence principle in a space with GUP

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

gr-qc↗

arXiv2019

Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries

Noncommutative algebra which is rotationally invariant, time reversal invariant and equivalent to noncommutative algebra of canonical type is considered. Perihelion shift of orbit of a particle in Coulomb potential in the rotationally-invariant noncommutative phase space is found up to the second order in the parameters of noncommutativity. Applying the result to the case of Mercury planet and using observable results for precession of its orbit we find upper bounds on the parameters of noncommutativity in the rotationally-invariant noncommutative phase space. The obtained upper bound for the parameter of momentum noncommutativity is at least ten orders less than the upper bounds estimated on the basis of studies of the hydrogen atom in noncommutative phase space. As a result we obtain stringent restriction on for the minimal momentum in noncommutative phase space with preserved rotational and time reversal symmetries.

quant-ph↗

arXiv2019

Upper bound on the momentum scale in noncommutative phase space of canonical type

We find stringent upper bound on the momentum scale in noncommutative phase space of canonical type on the basis of studies of perihelion shift of the Mercury planet with taking into account features of description of motion of macroscopic body in the space with noncommutativity of coordinates and noncommutativity of momenta. Using results for precession of perihelion of the Mercury planet from ranging to the MESSENGER spacecraft we obtain upper bound for parameter of momentum noncommutativity $10^{-80}\textrm{kg}^2\textrm{m}^2/\textrm{s}^2$ which is many orders less than known in the literature.

hep-th↗

arXiv2019

Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space

A space with deformed Poisson brackets for coordinates and momenta leading to the minimal length is considered. Features of description of motion of a body in the space are examined. We propose conditions on the parameters of deformation on which Poisson brackets for coordinates and momenta of the center-of-mass reproduce relations of deformed algebra, kinetic energy of a body is independent of its composition, and the weak equivalence principle is preserved in the deformed space. Influence of minimal length on the motion of the Sun-Earth-Moon system is studied. We find that deformation of the Poisson brackets leads to corrections to the accelerations of the Earth and the Moon toward the Sun, as a result the Eotvos-parameter does not vanish even if we consider equality of gravitational and inertial masses. The upper bound for the minimal length is estimated using results of the Lunar laser ranging experiment.

physics.gen-ph↗

arXiv2019

Macroscopic body in Snyder space and minimal length estimation

We study a problem of description of macroscopic body motion in the frame of nonrelativistic Snyder model. It is found that the motion of the center-of-mass of a body is described by an effective parameter which depends on the parameters of Snyder algebra for coordinates and momenta of particles forming the body and their masses. We also show that there is reduction of the effective parameter with respect to parameters of Snyder algebra for coordinates and momenta of individual particles. As a result the problem of extremely small result for the minimal length obtained on the basis of studies of the Mercury motion in the Snyder space is solved. In addition we find that relation of parameter of Snyder algebra with mass opens possibility to preserve the property of independence of the kinetic energy on composition, to recover the weak equivalence principle, to consider coordinates as kinematic variables, to recover proportionality of momenta to mass and to consider Snyder algebra for coordinates and momenta of the center-of-mass of a body defined in the traditional way.

physics.gen-ph↗

arXiv2018

Features of description of composite system's motion in twist-deformed space-time

Composite system made of $N$ particles is considered in twist-deformed space-time. It is shown that in the space the motion of the center-of-mass of the system depends on the relative motion. Influence of deformation on the motion of the center-of-mass of composite system is less than on the motion of individual particles and depends on the system's composition. We conclude that if we consider commutation relations for coordinates of a particle to be proportional inversely to its mass, the commutation relations for coordinates of composite system do not depend on its composition and are proportional inversely to system's total mass, besides the motion of the center-of-mass is independent of the relative motion. In addition we find that inverse proportionality of parameters of noncommutativity to mass is important for considering coordinates in twist-deformed space as kinematic variables and for preserving of the weak equivalence principle.

quant-ph↗

arXiv2018

Harmonic oscillator chain in noncommutative phase space with rotational symmetry

We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally invariant noncommutative phase space harmonic oscillator chain is studied. We obtain that noncommutativity affects on the frequencies of the system. In the case of a chain of particles with harmonic oscillator interaction we conclude that because of momentum noncommutativity the spectrum of the center-of-mass of the system is discrete and corresponds to the spectrum of harmonic oscillator.

quant-ph↗

arXiv2018

Time reversal and rotational symmetries in noncommutative phase space

Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On the basis of exact solution of the problem we show that because of noncommutativity the period of the circular motion depends on its direction. We propose the way to recover the time reversal and rotational symmetries in noncommutative phase space of canonical type. Namely, on the basis of idea of generalization of parameters of noncommutativity to tensors we construct noncommutative algebra which is rotationally-invariant, invariant under time reversal, besides it is equivalent to noncommutative algebra of canonical type.

quant-ph↗

arXiv2018

Parameters of noncommutativity in Lie-algebraic noncommutative space

We find condition on the parameters of noncommutativity on which a list of important results can be obtained in a space with Lie-algebraic noncommutativity. Namely, we show that the weak equivalence principle is recovered in the space, the Poisson brackets for coordinates and momenta of the center-of-mass of a composite system do not depend on its composition and reproduce relations of noncommutative algebra for coordinates and momenta of individual particles if parameters of noncommutativity corresponding to a particle are proportional inversely to its mass. In addition in particular case of Lie-algebraic noncommutativity (space coordinates commute to time) on this condition the motion of the center-of-mass is independent of the relative motion and problem of motion of the center-of-mass and problem corresponding to the internal motion can be studied separately.

quant-ph↗

arXiv2018

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of $N$ interacting harmonic oscillators in uniform filed and a system of $N$ particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of $N$ free particles in uniform field in rotationally-invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of $N$ harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.

quant-ph↗

arXiv2018

Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle

We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform gravitational fields in noncommutative phase space of canonical type with preserved rotational symmetry. It is shown that because of noncommutativity the motion of a particle in gravitational filed is determined by its mass. The trajectory of motion of a particle in uniform gravitational field corresponds to the trajectory of harmonic oscillator with frequency determined by the value of parameter of momentum noncommutativity and mass of the particle. The equations of motion of a macroscopic body in gravitational filed depend on its mass and composition. From this follows violation of the weak equivalence principle caused by noncommutativity. We conclude that the weak equivalence principle is recovered in rotationally invariant noncommutative phase space if we consider the tensors of noncommutativity to be dependent on mass. So, finally we construct noncommutative algebra which is rotationally invariant, equivalent to noncommutative algebra of canonical type, and does not lead to violation of the weak equivalence principle.

quant-ph↗

arXiv2018

Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle

Features of motion of macroscopic body in gravitational field in a space with noncommutativity of coordinates and noncommutativity of momenta are considered in general case when coordinates and momenta of different particles satisfy noncommutative algebra with different parameters of noncommutativity. Influence of noncommutativity on the motion of three-body Sun-Earth-Moon system is examined. We show that because of noncommutativity the free fall accelerations of the Moon and the Earth toward the Sun in the case when the Moon and the Earth are at the same distance to the source of gravity are not the same even if gravitational and inertial masses of the bodies are equal. Therefore, the Eotvos-parameter is not equal to zero and the weak equivalence principle is violated in noncommutative phase space. We estimate the corrections to the Eotvos-parameter caused by noncommutativity on the basis of Lunar laser ranging experiment results. We obtain that with high precision the ratio of parameter of momentum noncommutativity to mass is the same for different particles.

gr-qc↗

arXiv2018

Features of free particles system motion in noncommutative phase space

Influence of noncommutativity on the motion of composite system is studied in noncommutative phase space of canonical type. A system composed by $N$ free particles is examined. We show that because of momentum noncommutativity free particles of different masses with the same velocities at the initial moment of time do not move together. The trajectory and the velocity of free particle in noncommutative phase space depend on its mass. So, a system of the free particles flies away. Also, it is shown that the total momentum defined in the traditional way is not integral of motion in a space with noncommutativity of coordinates and noncommutativity of momenta. We find that in the case when parameters of noncommutativity corresponding to a particle are determined by its mass the trajectory and velocity of free particle are independent of the mass, also the total momenta as integrals of motion can be introduced in noncommutative phase space.

quant-ph↗

arXiv2018

Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to well known noncommutative algebra of canonical type. In the noncommutative phase space with rotational symmetry influence of noncommutativity on the spectrum of free particle and spectrum of harmonic oscillator is studied up to the second order in the parameters of noncommutativity. We find that because of momentum noncommutativity the spectrum of free particle is discrete and corresponds to the spectrum of harmonic oscillator in the ordinary space (space with commutative coordinates and commutative momenta). We obtain the spectrum of the harmonic oscillator in the rotationally invariant noncommutative phase space and conclude that noncommutativity of coordinates affects on its mass. The frequency of the oscillator is affected by the coordinate noncommutativity and the momentum noncommutativity. On the basis of the results, the eigenvalues of squared length operator are found and restrictions on the value of length in noncommutative phase space with rotational symmetry are analyzed.

quant-ph↗

arXiv2017

Lee-Yang zeros and two-time spin correlation function

The two-time correlation function for probe spin interacting with spin system (bath) is studied. We show that zeros of this function correspond to zeros of partition function of spin system in complex magnetic field. The obtained relation gives new possibility to observe the Lee-Yang zeros experimentally. Namely, we show that measuring of the time dependence of correlation function allows direct experimental observation of the Lee-Yang zeros.

quant-ph↗

arXiv2017

Time correlation functions and Fisher zeros for q-deformed Bose gas

The time-dependent correlation functions of q-deformed Bose gas are studied. We find relation of zeros of the correlation functions with the Fisher zeros of partition function of the system. Complex temperature appears as a result of q-deformation and evolution of correlation function. A particular case of q-deformed Bose particles on two levels is examined and zeros of correlation functions and Fisher zeros of partition function are analyzed.

quant-ph↗

arXiv2017

Composite system in rotationally invariant noncommutative phase space

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on the conditions the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

quant-ph↗