Spectral properties of fractional Fokker-Plank operator for the L\'evy flight in a harmonic potential

We present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the L\'evy-Ornstein-Uhlenbeck process, their asymptotic behavior and recurrence relations, explicit expressions in coordinate space for the special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy white noise and for the transformation kernel, which maps the fractional Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck process. We also describe how non-spectral relaxation can be observed in bounded random variables of the L\'evy-Ornstein-Uhlenbeck process and their correlation functions.Comment: 10 pages, 5 figures, submitted to Euro. Phys. J.

Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization

We discuss the situations under which Brownian yet non-Gaussian (BnG) diffusion can be observed in the model of a particle’s motion in a random landscape of diffusion coefficients slowly varying in space (quenched disorder). Our conclusion is that such behavior is extremely unlikely in the situations when the particles, introduced into the system at random at t = 0, are observed from the preparation of the system on. However, it indeed may arise in the case when the diffusion (as described in Ito interpretation) is observed under equilibrated conditions. This paradigmatic situation can be translated into the model of the diffusion coefficient fluctuating in time along a trajectory, i.e. into a kind of the ‘diffusing diffusivity’ model.Russian Science Foundation https://doi.org/10.13039/501100006769Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659Peer Reviewe

A quantum volume hologram

We propose a new scheme for parallel spatially multimode quantum memory for light. The scheme is based on counter-propagating quantum signal wave and strong classical reference wave, like in a classical volume hologram, and therefore can be called a quantum volume hologram. The medium for the hologram consists of a spatially extended ensemble of atoms placed in a magnetic field. The write-in and read-out of this quantum hologram is as simple as that of its classical counterpart and consists of a single pass illumination. In addition we show that the present scheme for a quantum hologram is less sensitive to diffraction and therefore is capable of achieving higher density of storage of spatial modes as compared to previous proposals. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.Comment: 8 pages, 2 figure

Quantum memory for images - a quantum hologram

Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. In this Letter we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multi-atom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multi-atom nature of the ensemble it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram has a higher storage capacity compared to a classical hologram, and is capable of storing quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve. Due to optical parallelism, the information capacity of the quantum hologram will obviously exceed that of a single-mode scheme.Comment: 5 pages, 3 figure

Water Splitting on Multifaceted SrTiO3 Nanocrystals: Computational Study

The financial support of M-ERA.NET2 Sun2Chem project is greatly acknowledged by E.K. Authors thank Dr. Marjeta Ma?ek Kr?manc and prof. Chi-Sheng Wu, for the fruitful discussions. The financial support of FLAG-ERA JTC project To2Dox is acknowledged by Y.A.M. This paper is based upon the work from COST Action 18234, supported by COST (European Cooperation in Science and Technology). The support is greatly acknowledged by Y.A.M. and V.K. The grant No. 1.1.1.2/VIAA/l/16/147 (1.1.1.2/16/I/001) under the activity of Post-doctoral research aid is greatly acknowledged by M.S. and D.B. The Institute of Solid State Physics, University of Latvia (Latvia) as the Centre of Excellence has received funding from the European Union?s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase2 under grant agreement No. 739508, project CAMART2 . The computer resources were provided by the Stuttgart Supercomputing Center (project DEFTD 12939) and Latvian Super Cluster (LASC).Recent experimental findings suggest that strontium titanate SrTiO3 (STO) photocatalytic activity for water splitting could be improved by creating multifaceted nanoparticles. To understand the underlying mechanisms and energetics, the model for faceted nanoparticles was created. The multifaceted nanoparticles’ surface is considered by us as a combination of flat and “stepped” facets. Ab initio calculations of the adsorption of water and oxygen evolution reaction (OER) intermediates were performed. Our findings suggest that the “slope” part of the step showed a natural similarity to the flat surface, whereas the “ridge” part exhibited significantly different adsorption configurations. On the “slope” region, both molecular and dissociative adsorption modes were possible, whereas on the “ridge”, only dissociative adsorption was observed. Water adsorption energies on the “ridge” (−1.50 eV) were significantly higher than on the “slope” (−0.76 eV molecular; −0.83 eV dissociative) or flat surface (−0.79 eV molecular; −1.09 eV dissociative). © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Published under the CC BY 4.0 license.M-ERA.NET2 Sun2Chem; FLAG-ERA JTC project To2Dox; COST Action 18234; Post-doctoral research grant No. 1.1.1.2/VIAA/l/16/147 (1.1.1.2/16/I/001); Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2

Water Splitting on Multifaceted SrTiO3 Nanocrystals: Calculations of Raman Vibrational Spectrum

The financial support of M-ERA.net SunToChem project is greatly acknowledged by L.L.R. and Y.A.M. This paper is partly based upon COST (European Cooperation in Science and Technology) Action 18234 Short Term Scientific Mission. The support is greatly acknowledged by E.K. and V.K. The Institute of Solid State Physics, University of Latvia (Latvia) as the Centre of Excellence has received funding from the European Union’s Horizon 2020 Frame-work Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase2 under grant agreement No. 739508, project CAMART2. The computer resources were provided by the Stuttgart Supercomputing Center (HLRS project DEFTD 12939) and Latvian Super Cluster (LASC).Various photocatalysts are being currently studied with the aim of increasing the photocatalytic efficiency of water splitting for production of hydrogen as a fuel and oxygen as a medical gas. A noticeable increase of hydrogen production was found recently experimentally on the anisotropic faces (facets) of strontium titanate (SrTiO3, STO) nanoparticles. In order to identify optimal sites for water splitting, the first principles calculations of the Raman vibrational spectrum of the bulk and stepped (facet) surface of a thin STO film with adsorbed water derivatives were performed. According to our calculations, the Raman spectrum of a stepped STO surface differs from the bulk spectrum, which agrees with the experimental data. The characteristic vibrational frequencies for the chemisorption of water derivatives on the surface were identified. Moreover, it is also possible to distinguish between differently adsorbed hydrogen atoms of a split water molecule. Our approach helps to select the most efficient (size and shape) perovskite nanoparticles for efficient hydrogen/oxygen photocatalytic production. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.M-ERA.net SunToChem project; COST Action 18234 Short Term Scientific Mission; LRS project DEFTD 12939; the Institute of Solid State Physics, University of Latvia as the Centre of Excellence has received funding from the European Union’s Horizon 2020 Frame-work Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase2 under grant agreement No. 739508, project CAMART2