arXiv subjects

Maciej Pylak

Publications and source records attributed to Maciej Pylak.

12 recordsLinked to original sources

arXiv2025

Comment on "Absence of a consistent classical equation of motion for a mass-renormalized point charge"

Here we comment on the paper by Arthur D. Yaghjian, Phys. Rev. E 78, 046606 (2008) (arXiv:0805.0142). The author provides an equation of motion for a point charged particle in a certain regime of system parameters (on the other hand, claiming that in a different regime the classical equation of motion does not exist). The solutions of this equation (in the regime where it exists) presented in the paper show instantaneous jumps in the particle's velocity. We show that such jumps, in the case of a point particle, would generate infinite energy in the radiated electromagnetic field. Therefore, we claim that the point-particle limit used by the author is incorrect.

physics.class-ph↗

arXiv2024

Dipolar Droplets at 3D-1D Crossover

We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field contribution to the energy in the quasi-1D region, in addition to the confinement induced shift of the mean field energy, is proportional to the third power of the density $\sim n^3$. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.

cond-mat.quant-gas↗

arXiv2022

Self-consistent Description of Bose-Bose Droplets: Modified Gapless Hartree-Fock-Bogoliubov Method

We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the Generalized Gross -- Pitaevskii equation accounting for quantum depletion and anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations. The modification we introduce resolves the longstanding issue of missing phonon-branch excitations when higher order terms are included. Our method ensures a gapless phononic low-energy excitation spectrum, crucial to correctly account for quantum fluctuations. We pay particular attention to the case of droplets harmonically confined in some directions. The method allows to determine the Lee-Huang-Yang-type contribution to the chemical potential of inhomogeneous droplets when the local density approximation fails.

cond-mat.quant-gas↗

arXiv2022

Self-consistent Description of Bose-Bose Droplets: Harmonically Trapped Quasi-2D Droplets

We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic forces in one spatial direction. Our approach is based on the self-consistent method formulated in [1]. The true spatial droplet profile in the direction of confinement is accounted for, however local density approximation is assumed in the free directions. We define a numerical approach to find the beyond-mean-field contribution to the chemical potential (Lee-Huang-Yang chemical potential) -- the quantity that determines the droplet's profile. In addition to the numerical approach, we find the Lee-Huang-Yang potential in the analytic form in two limiting cases: a perturbative result for a strong confinement and a semiclassical expression when confinement is very weak.

cond-mat.quant-gas↗

arXiv2022

Manifestation of relative phase in dynamics of two interacting Bose-Bose droplets

We study coherent dynamics of two interacting Bose-Bose droplets by means of the extended Gross-Pitaevskii equation. The relative motion of the droplets couples to the phases of their components. The dynamics can be understood in terms of the evolution of zero-energy modes recovering symmetries spontaneously broken by the mean-field solution. These are translational symmetry and two U(1) symmetries, associated with the phases of the droplets' two components. A phase-dependent interaction potential and double Josephson-junction equations are introduced to explain the observed variety of different scenarios of collision. We show that the evolution of the droplets is a macroscopic manifestation of the hidden dynamics of their phases. The occurrence of nondissipative drag between the two supercurrents (Andreev-Bashkin effect) is mentioned.

cond-mat.quant-gas↗

arXiv2021

Quantum droplets in a dipolar Bose gas at a dimensional crossover

We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross-Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density.

cond-mat.quant-gas↗

arXiv2021

Zero-energy modes of two-component Bose-Bose droplets

Bose-Bose droplets are self-bound objects emerging from a mixture of two interacting Bose-Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian are broken: translational symmetry and two U1 symmetries, allowing for arbitrary choice of phases of the mean-field wavefunctions describing the two components. Breaking of these symmetries must be accompanied by appearance of zero-energy excitations in the energy spectrum of the system recovering the broken symmetries. Normal modes corresponding to these excitations are the zero-energy modes. Here we find analytic expressions for these modes and introduce Hamitonians generating their time evolution -- dynamics of the droplet's centers of mass as well as dynamics of the phases of the two droplet's wavefunctions. When internal types of excitations (quasiparticles) are neglected then the very complex system of a quantum droplet is described using only few "global" degrees of freedom - the position of the center of mass of the droplet and two phases of two wave-functions, all these being quantum operators. This gives the possibility of describing in a relatively easy way processes of interaction of these quantum droplets, such as collisions.

cond-mat.quant-gas↗

arXiv2020

Pauli crystals -- interplay of symmetries

Recently observed Pauli crystals are structures formed by trapped ultracold atoms with the Fermi statistics. Interactions between these atoms are switched off, so their relative positions are determined by joined action of the trapping potential and the Pauli exclusion principle. Numericalmodeling is used in this paper to find the Pauli crystals in a two-dimensional isotropic harmonic trap, three-dimensional harmonic trap, and a two-dimensional square well trap. The Pauli crystals do not have the symmetry of the trap -- the symmetry is broken by the measurement of positions and, in many cases, by the quantum state of atoms in the trap. Furthermore, the Pauli crystals are compared with the Coulomb crystals formed by electrically charged trapped particles. The~structure of the Pauli crystals differs from that of the Coulomb crystals, this provides evidence that the exclusion principle cannot be replaced by a two-body repulsive interaction but rather has to be considered to be a specifically quantum mechanism leading to many-particle correlations.

cond-mat.quant-gas↗

arXiv2020

Revisiting a stability problem of two-component droplets

We study the problem of the stability of a two-component droplet. The standard solution known from the literature is based on a particular form of the mean field energy functional, in particular on distinction of hard mode and soft mode contributions. By imposing the constraint on densities of the two species which minimizes the hard mode energy, the problem is reduced to a stability analysis of a one component system. As opposed to this, we address the issue in full generality. Our analysis is valid for arbitrary forms of energy density. We formulate constraints which correspond to the physically relevant situation of a system which has unconstrained volume and may evaporate particles. For the specific case of a two component Bose-Bose droplet we find approximate analytic solutions and compare them to the standard result. We show that the densities of both components of a stable droplet are limited to a range depending on interaction strength, in contrast to the original unique solution.

cond-mat.quant-gas↗

arXiv2018

Quantum Bose-Bose droplets at a dimensional crossover

We study a liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under a variable confinement introduced along one or two spatial dimensions. Despite the atom-atom scattering has a three-dimensional character, discreetness of the available modes in the reduced dimension(s) strongly influences the zero-point energy -- the Lee-Huang-Yang term. In a weakly interaction limit, it is the leading correction to the mean-field energy at the crossover from three to two dimensions, or from three to one dimension. We analyze the properties of the droplets at the dimensional crossovers, and provide the demanding conditions for accessing quasi-low dimensions. We predict new kinds of droplets which are formed only due to the quantum fluctuations when the mean-field interaction vanishes. Our results pave the way for exploring new states of quantum matter, and are important for experiments with liquid quantum droplets in reduced dimensions.

cond-mat.quant-gas↗

arXiv2018

The influence of the interaction between quasiparticles on parametric resonance in Bose-Einstein quasicondensates

We perform a simulation of the experiment [1] where the temporal modification of the effective one dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate huge impact of interaction between quasiparticles due to finite temperature on the pair production process, explaining relatively small atom pair production and the absence of the number squeezing in the experiment.

cond-mat.quant-gas↗

arXiv2017

The influence of interaction between quasiparticles on parametric resonance process in Bose-Einstein condensates

We analyze the uniform system of weakly interacting bosonic gas undergoing periodic oscillation of interaction constant. This, within Bogoliubov approximation, leads to creation of atom pairs with well defined opposite velocities. We show how interaction between quasiparticles, omitted in the Bogoliubov approximation, significantly changes the atom pair creation process and properties of scattered atoms.

cond-mat.quant-gas↗