Time-fractional kinetic equation for the non-Markovian kinetic processes

In this study, we analytically formulated the path integral representation of the conditional probabilities for non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We carry out analytically the time-fractional kinetic equations for these processes. Thus, in a simple way, we generalize path integral solutions of the Markovian to the non-Markovian cases. We conclude that these pedagogical results can be applied to some physical problems such as the deformed ion channels, internet networks and non-equilibrium phase transition problems.Comment: No figur

Chaotic interactions between dark matter and dark energy

In this study, we consider dark matter and dark energy as grand-canonical systems which are open, non-equilibrium coupled, and interacting systems. It is the first time, we propose a new more realistic interaction schema to explain dynamics between coupled interacting thermodynamic systems. Based on this new interaction schema, we propose new theorems to define the interactions. We proved the theorems based on the energy conservation law of thermodynamics. Furthermore, we obtain new coupled equations using the theorems. We numerically solve the interaction equations and obtained phase space diagrams and Lyapunov exponents. We show that the interaction between dark matter and dark energy is chaotic. We conclude that these theorems and results can be generalized to all coupled interacting non-equilibrium systems. Finally, we give a new definition of chaos.Comment: 7 figures, 8 page

Memory effects and KWW relaxation of the interacting magnetic nano-particles

The nano-particle systems under theoretically and experimentally investigation because of the potential applications in the nano-technology such as drug delivery, ferrofluids mechanics, magnetic data storage, sensors, magnetic resonance imaging, and cancer therapy. Recently, it is reported that interacting nano-particles behave as spin-glasses and experimentally show that the relaxation of these systems obeys stretched exponential i.e., KWW relaxation. Therefore, in this study, considering the interacting nano-particle systems we model the relaxation and investigate frequency and temperature behaviour depends on slow relaxation by using a simple operator formalism. We show that relaxation deviates from Debye and obeys to KWW in the presence of the memory effects in the system. Furthermore, we obtain the frequency and temperature behaviour depend on KWW relaxation. We conclude that the obtained results are consistent with experimental results and the simple model, presented here, is very useful and pedagogical to discuss the slow relaxation of the interacting nano-particles.Comment: Accepted in Physica

Rotational Brownian motion on the sphere surface and rotational relaxation

The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.Comment: RevTex, 4 pages, submitted to Chin. Phys. Let

Decoherence in Two-Dimensional Quantum Random Walks with Traps

Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, non-trivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced.Comment: 7 pages, 9 figure

The value of laparoscopic classifications in decision on definitive surgery in patients with nonpalpable testes: our experience and review of the literature

Background/purpose The aim of the study was to present our clinical experience with the laparoscopic approach in patients with nonpalpable testes (NPTs) and review the literature on laparoscopic classifications.Materials and methods Between May 2010 and August 2012, 30 boys with NPT (mean age 3.9 years) underwent laparoscopy as a part of diagnosis and treatment in our clinic. The laparoscopic findings were classified into four types according to Castilho. The patients were managed according to the presence or position of the testes and testicular vessels.Results Six patients were excluded from the study. Twenty-six testicular units (19 left, three right, and four bilateral units) in 24 patients were managed laparoscopically. Laparoscopy was terminated in eight patients in whom blind-ending cord structures were detected intra-abdominally. An inguinal canal exploration was performed in 10 cases in whom cord structures were seen entering the internal inguinal ring. No viable testis was found, and testicular remnants were excised for histopathologic examination. Four canalicular testes (peeping) were treated with open orchiopexy. Laparoscopy-assisted orchiopexy without vascular ligation was performed in two testes. Fowler-Stephens orchiopexy in single stage was performed in one testicular unit and in two stages in another unit. All patients were discharged on the same day. The testes were normal in size and found in the scrotum after a mean follow-up period of 14 months.Conclusion The laparoscopic findings in NPT had an important influence on treatment decisions. To be able to interpret the definitive surgery relative to the laparoscopic classification, collaborative studies are required. Keywords: laparoscopy, nonpalpable testis, nubbin, orchiopexy, vas deferen

Cooperation and defection in ghetto

We consider ghetto as a community of people ruled against their will by an external power. Members of the community feel that their laws are broken. However, attempts to leave ghetto makes their situation worse. We discuss the relation of the ghetto inhabitants to the ruling power in context of their needs, organized according to the Maslow hierarchy. Decisions how to satisfy successive needs are undertaken in cooperation with or defection the ruling power. This issue allows to construct the tree of decisions and to adopt the pruning technique from the game theory. Dynamics of decisions can be described within the formalism of fundamental equations. The result is that the strategy of defection is stabilized by the estimated payoff.Comment: 12 pages, 2 figure

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at $M=0,1/4$ and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A novel mechanism of magnetization plateau stabilization corresponding to $M=1/4$ state is reported.Comment: 16 pages, 12 figure