Comment on "Exact results for survival probability in the multistate Landau-Zener model"

We correct the proof of Brundobler-Elser formula (BEF) provided in [2004 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907]. After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general $N$-level Landau-Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.Comment: 10 page

Particle current in symmetric exclusion process with time-dependent hopping rates

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.Comment: 17 pages, 2 figure

Modeling of passengers’ choice using intelligent agents with reinforcement learning in shared interests systems; a basic approach

The purpose of this paper is to build a model for assessing the satisfaction of passenger service by the public transport system. The system is constructed using intelligent agents, whose action is based on self-learning principles. The agents are passengers who depend on transport and can choose between two modes: a car or a bus wherein their choice of transport mode for the next day is based on their level of satisfaction and their neighbors’ satisfaction with the mode they used the day before. The paper considers several algorithms of agent behavior, one of which is based on reinforcement learning. Overall, the algorithms take into account the history of the agents’ previous trips and the quality of transport services. The outcomes could be applied in assessing the quality of the transport system from the point of view of passengers. © 2019 Silesian University of Technology. All rights reserved.Russian Science Foundation, RSF: 17-71-20108The authors acknowledge the support from the Russian Science Foundation (project No. 17-71-20108

A clinical case of a combined method for correcting postkeratoplastic astigmatism of a high degree in a patient with cataract

Background. Performing penetrating keratoplasty in 100 % of cases leads to the occurrence of induced postkeratoplasty astigmatism, which can be more than 12,0 D. If cataracts occur in this category of patients, performing cataract phacoemulsification with implantation of a toric intraocular lens (tIOL) does not completely solve the problem. The use of the method of implantation of intrastromal corneal segments at stage I before cataract phacoemulsification makes it possible to reduce the degree of postkeratoplasty astigmatism and create optimal conditions for additional correction of residual postkeratoplasty astigmatism due to the implantation of tIOL during cataract phacoemulsification.The aim. To analyze the clinical and functional indicators of correction of regular high-grade postkeratoplasty astigmatism in a patient with cataracts using a combined method, including first implantation of intrastromal corneal segments and subsequent cataract phacoemulsification with implantation of toric intraocular lens using the example of a clinical case.Material and methods. A 55-year-old patient with cataracts, who had a history of  undergoing penetrating keratoplasty, contacted us. According to the keratotopogram data, a regular postkeratoplasty astigmatism of 18.68 D was diagnosed. The patient underwent a combined method. At stage I, intrastromal corneal segments were implanted into the corneal graft, then after 6 months stage II was performed – cataract phacoemulsification with implantation of tIOL.Results. Six months after intrastromal corneal segments implantation, the patient’s keratometric data stabilized, and corneal astigmatism decreased to 8.98 D. Then the patient underwent cataract phacoemulsification with tIOL implantation. After 1 month, the spherical component of refraction was 0.5 D, the cylindrical component of refraction was –0.5 D, visual acuity increased to 1.0.Conclusions. A combined method for correcting regular high-grade postkeratoplasty astigmatism in a patient with cataracts showed high refractive results, stability and safety in the long-term postoperative period

Comparative analysis of the correction of irregular postkeratoplastic astigmatism with scleral lenses and intrastromal ring implantation

Background. Many patients after penetrating keratoplasty (PK) experience induced postkeratoplastic astigmatism, which is often irregular and causes an increase in corneal aberrations that reduce visual acuity and quality. The aim of the study. To conduct a comparative analysis of the effect of rigid gas permeable scleral lenses and the MyoRing implantation method on clinical and functional parameters in patients with IPA. Material and methods. The clinical study included 60 patients (60 eyes). The age of patients with IPA was from 25 to 42 years. All patients underwent penetrating keratoplasty. All patients were divided into two groups depending on the method for irregular postkeratoplastic astigmatism correction. Group I included 30 patients (30 eyes) who were fitted with rigid gas permeable scleral lenses. Group II consisted of 30 patients (30 eyes) who underwent implantation of the MyoRing into a penetrating corneal graft. The observation period was 1 year. Results. After 12 months of observation, there was a greater increase in uncorrected visual acuity by an average of 3 lines, in corrected visual acuity – by 2 lines; a greater decrease in corneal aberrations in photo- (root mean square (RMS) of total aberrations (RMS total) by 0.30 ± 0.08 µm, RMS of higher order aberrations (RMS HOA) – by 1.01 ± 0.24 μm) and mesopic conditions (RMS total – by 0.33 ± 0.09 μm, RMS HOA – by 0.08 ± 0.03 μm) in patients wearing rigid gas permeable scleral lenses compared with patients after MyoRing implantation into a penetrating corneal graft. Conclusion. Patients of group  I, wearing rigid gas permeable scleral lenses, showed a greater improvement in visual acuity and a decrease in corneal aberrations in  photo- and mesopic conditions compared to the patients of group  II (after MyoRing implantation) at a follow-up period of 12 months

Mathematical modelling of proton migration in Earth mantle

In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x, t) and then reconstructing the distribution function f(x, v, t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V ) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric

Quantum state preparation in circuit QED via Landau-Zener tunneling

We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement.Comment: 7 pages, 3 figure

Geometric Universality of Currents

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines.Comment: 15 pages, 5 figure