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Authors
R. Tsekov
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Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.
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We study fermion-boson transitions. Our approach is based on the $3times 3$ subequations of Dirac and Duffin-Kemmer-Petiau equations, which link these equations. We demonstrate that free Dirac equation can be invertibly converted to spin-$0$ Duffin-Kemmer-Petiau equation in presence of a neutrino field. We also show that in special external fields, upon assuming again existence of a neutrino (Weyl) spinor, the Dirac equation can be transformed reversibly to spin-$0$ Duffin-Kemmer-Petiau equation. We argue that such boson-fermions transitions are consistent with the main channel of pion decay.
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron (electron, hole) and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_phi^{(m)}$, is connected with the electron density $n_{mathrm e}$ by $n_phi^{(m)}=n_{mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $sigma_{mathrm H}equiv j/E_{mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_phi^{(m)}$, is connected with the boson density $n_0$ by $n_phi^{(m)}=n_0/m$. This yields $sigma_{mathrm H}=m,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $ u=1/m$ ($m=$odd numbers). Laughlins theory and results about the fractional charge are not borrowed in the present work.
Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). To work it out one needs definition of quantum Brownian motion. Since till very recent times only its boson version has been known, in present paper we demonstrate definition which makes possible consideration also for fermion Brownian motion.
Developing angular trapping methods, which will enable optical tweezers to rotate a micronized bead, is of great importance for the studies of biomacromolecules during a wide range of torque-generation processes. Here we report a novel controlled angular trapping method based on composite Janus particles. We used a chemically synthesized Janus particle, which consists of two hemispheres made of polystyrene (PS) and poly(methyl methacrylate) (PMMA) respectively, as a model system to demonstrate this method. Through computational and experimental studies, we demonstrated the feasibility to control the rotation of a Janus particle in a linearly polarized laser trap. Our results showed that the Janus particle aligned its two hemispheres interface parallel to the laser propagation direction as well as the laser polarization direction. In our experiments, the rotational state of the particle can be easily and directly visualized by using a CMOS camera, and does not require complex optical detection system. The rotation of the Janus particle in the laser trap can be fully controlled in real time by controlling the laser polarization direction. Our newly developed angular trapping technique has the great advantage of easy implementation and real time controllability. Considering the easy chemical synthesis of Janus particles and implementation of the angular trapping, this novel method has the potential of becoming a general angular trapping method. We anticipate that this new method will significantly broaden the availability of angular trapping in the biophysics community, and expand the scope of the research that can be enabled by the angular trapping approach.
Brownian transport of self-propelled overdamped microswimmers (like Janus particles) in a two-dimensional periodically compartmentalized channel is numerically investigated for different compartment geometries, boundary collisional dynamics, and particle rotational diffusion. The resulting time-correlated active Brownian motion is subject to rectification in the presence of spatial asymmetry. We prove that ratcheting of Janus particles can be orders of magnitude stronger than for ordinary thermal potential ratchets and thus experimentally accessible. In particular, autonomous pumping of a large mixture of passive particles can be induced by just adding a small fraction of Janus particles.
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