arXiv subjects

M. D. Tomchenko

Publications and source records attributed to M. D. Tomchenko.

5 recordsLinked to original sources

arXiv2019

Low-lying energy levels of a one-dimensional weakly interacting Bose gas under zero boundary conditions

We diagonalize the second-quantized Hamiltonian of a one-dimensional Bose gas with a nonpoint repulsive interatomic potential and zero boundary conditions. At weak coupling the solutions for the ground-state energy $E_{0}$ and the dispersion law $E(k)$ coincide with the Bogoliubov solutions for a periodic system. In this case, the single-particle density matrix $F_{1}(x,x^{\prime})$ at $T=0$ is close to the solution for a periodic system and, at $T>0$, is significantly different from it. We also obtain that the wave function $\langle \hatψ(x,t) \rangle$ of the effective condensate is close to a constant $\sqrt{N_{0}/L}$ inside the system and vanishes on the boundaries (here, $N_{0}$ is the number of atoms in the effective condensate, and $L$ is the size of the system). We find the criterion of applicability of the method, according to which the method works for a finite system at very low temperature and with a weak coupling (a weak interaction or a large concentration).

cond-mat.quant-gas↗

arXiv2012

On the probable wave nature of Bose crystals

At the present time, it is considered that Bose crystals are formed at the cooling of a fluid, because the state of crystal is more favorable by energy. It is also believed [1,2] that no ordering factor forming a crystal is present, except for the interatomic interaction. However, the available solutions [1,2,3] for the wave functions (WFs) of the ground and excited states of a crystal are approximate and are obtained for cyclic boundary conditions, which are not realized in the Nature. Here, we present the exact solutions for the WFs of a Bose crystal with rectangular lattice under natural zero boundary conditions. The structure of WFs implies that 1) a crystal is formed by a standing wave in the probability field; 2) a crystal in the ground state contains a condensate of atoms with the wave vector \textbf{k}_l=(π/\bar{R}_x, π/\bar{R}_y, π/\bar{R}_z) (\bar{R}_x, \bar{R}_y, \bar{R}_z are the periods of the lattice) that is equal to a half of the vector of the reciprocal lattice. These solutions indicate that the ordering factor forming a crystal is an intense standing wave similar to a sound one. Thus, the periodicity of a lattice is caused by that of a sound wave, but not only by the energy minimum principle. Apparently, the crystals of other types and with different lattices have the wave nature as well. The condensate opens a possibility to explain the nonclassical inertia moment discovered by Kim and Chan [4,5] in solid He-4, which testifies, probably, to the presence of a superfluid subsystem in the crystal.

cond-mat.other↗

arXiv2010

Electromagnetic and phonon modes for superfluid He-4 with a disk resonator

We find the distribution of the electromagnetic field inside and outside a dielectric disk resonator placed in He-II. It is shown that this field consists of a collection of "circular" (c-) photons. The wave function Ψ_c of a c-phonon for the He-II + disk system is calculated in the zero-order approximation in interaction. Due to the symmetry of the problem, the structure of Ψ_c is such that a c-phonon possesses, similarly to a c-photon of the resonator, a definite energy and an angular momentum with respect to the disk axis, but it does not possess a definite momentum in the disk plane.

cond-mat.other↗

arXiv2009

Calculation of the He-II quasiparticle spectrum by the method of collective variables

The method of collective variables (MCV) has been used to calculate the logarithm of the He-II ground-state wave function, ln(Psi_0), to an accuracy of a first correction to the Jastrow function and, in a second approximation, the wave function Psi_k of the first excited state and the He-II quasiparticle spectrum. The functions Psi_0 and Psi_k were found as the eigenfunctions of the N-particle Schro"dinger equation, and the function Psi_0 was connected to the structure factor of He-II, using the Vakarchuk equation. The model does not contain any fitting parameter or function. The quasiparticle spectrum calculated numerically agrees well with the experiment. Our solution improves the result obtained early by Yukhnovskyi and Vakarchuk.

cond-mat.other↗

arXiv2008

Possible nature of the dielectric activity of He II observed in experiments with second sound

An attempt is made to explain the nature of the electric signal observed in He II in a second-sound standing wave. Using the general quantum-mechanical principles, we show that, due to interatomic interaction, each atom of He-II acquires a small fluctuating induced dipole moment. A directed flux of microscopic vortex rings -- which, together with phonons, are thermal excitations of He II -- forms in the second-sound standing halfwave. This flux partially orders the chaotically oriented dipole moments of the atoms, which results in volume polarization of He II. The observed electric induction can be explained theoretically under the assumption that each vortex ring possesses a dipole moment of the order of ten atomic moments. It is shown also that the theoretical value of the voltage U induced in He II by the volume system of dipoles strongly depends on the dimensions of the resonator for dipoles of any origin. The experimental value of U is the same for two resonators of different size; therefore, this voltage may be not connected with the volume polarization of He II.

cond-mat.other↗