The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform
Jeffrey H Schenker - One of the best experts on this subject based on the ideXlab platform.
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Diffusion in the Mean for a Periodic Schrödinger Equation Perturbed by a Fluctuating Potential
Communications in Mathematical Physics, 2020Co-Authors: Jeffrey H Schenker, F. Zak Tilocco, Shiwen ZhangAbstract:We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves according to a Stationary Markov Process, we obtain diffusive scaling for moments of the position displacement, with a diffusion constant that grows as the inverse square of the disorder strength at weak coupling. More generally, we show that a central limit theorem holds such that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.
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Diffusive Propagation of Wave Packets in a Fluctuating Periodic Potential
Letters in Mathematical Physics, 2011Co-Authors: Eman Hamza, Yang Kang, Jeffrey H SchenkerAbstract:We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a Stationary Markov Process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.
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diffusion of wave packets in a Markov random potential
Journal of Statistical Physics, 2009Co-Authors: Yang Kang, Jeffrey H SchenkerAbstract:We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a Stationary Markov Process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.
Alexander I. Bufetov - One of the best experts on this subject based on the ideXlab platform.
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On the Vershik-Kerov Conjecture Concerning the Shannon-McMillan-Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams
Geometric and Functional Analysis, 2012Co-Authors: Alexander I. BufetovAbstract:Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the Vershik–Kerov conjecture can be seen as an analogue of the Shannon–McMillan–Breiman Theorem for the non-Stationary Markov Process of the growth of a Young diagram. The limiting constant is then interpreted as the entropy of the Plancherel measure. The main result of the paper is the proof of the Vershik–Kerov conjecture. The argument is based on the methods of Borodin, Okounkov and Olshanski.
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On the Vershik–Kerov Conjecture Concerning the Shannon–McMillan–Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams
Geometric and Functional Analysis, 2012Co-Authors: Alexander I. BufetovAbstract:Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the Vershik–Kerov conjecture can be seen as an analogue of the Shannon–McMillan–Breiman Theorem for the non-Stationary Markov Process of the growth of a Young diagram. The limiting constant is then interpreted as the entropy of the Plancherel measure. The main result of the paper is the proof of the Vershik–Kerov conjecture. The argument is based on the methods of Borodin, Okounkov and Olshanski.
Shiwen Zhang - One of the best experts on this subject based on the ideXlab platform.
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Diffusion in the Mean for a Periodic Schrödinger Equation Perturbed by a Fluctuating Potential
Communications in Mathematical Physics, 2020Co-Authors: Jeffrey H Schenker, F. Zak Tilocco, Shiwen ZhangAbstract:We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves according to a Stationary Markov Process, we obtain diffusive scaling for moments of the position displacement, with a diffusion constant that grows as the inverse square of the disorder strength at weak coupling. More generally, we show that a central limit theorem holds such that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.
Syed Ali Hassan - One of the best experts on this subject based on the ideXlab platform.
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Analysis of Multi-Source Multi-Hop Cooperative Networks Employing Network Coding
2015 IEEE 81st Vehicular Technology Conference (VTC Spring), 2015Co-Authors: Muhammad Arslan Aslam, Syed Ali HassanAbstract:In this paper, the performance of a multi-hop network is investigated in which M sources have independent information to be transmitted to a far off common destination. Linear network coding technique is used by the intermediate relays to transmit the combined information of M sources. Channel model includes Rayleigh fading and path loss. The multi-hop transmission Process is modeled by a quasi-Stationary Markov Process, whereas the relay nodes use decode and forward (DF) mechanism at each hop. By finding the outage probability of each node and studying the properties of Markov Process, the network coverage is analyzed for a given signal-to-noise ratio (SNR) margin.
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Coverage aspects of cooperative multi-hop line networks in composite fading environment
2014 International Wireless Communications and Mobile Computing Conference (IWCMC), 2014Co-Authors: Mudasar Bacha, Syed Ali HassanAbstract:We consider a cooperative multi-hop line network, where a group of nodes cooperatively transmits the same message to another group of nodes, and model the transmission from one group to another as a discrete-time quasi-Stationary Markov Process. We derive the transition probability matrix of the Markov chain by considering the wireless channel exhibiting composite shadowing-fading. The sum distribution of the received power by multiple relays is approximated by a single log-normal random variable (RV) by using the moment generating function (MGF)-based technique. This MGF-based technique uses Gauss-Hermite integration to present the sum distribution in closed form. We quantify the signal-to-noise ratio (SNR) margin required to achieve a certain quality of service (QoS) under standard deviation of the shadowing. We also provide the optimal level of cooperation required for obtaining maximum coverage of a line network under a given QoS. Monte Carlo simulations are used to validate the analytical model.
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Performance Analysis of Linear Cooperative Multi-Hop Networks Subject to Composite Shadowing-Fading
IEEE Transactions on Wireless Communications, 2013Co-Authors: Mudasar Bacha, Syed Ali HassanAbstract:We consider a cooperative multi-hop line network, where a group of nodes cooperatively transmits the same message to another group of nodes, and model the transmission from one group to another as a discrete-time quasi-Stationary Markov Process. We derive the transition probability matrix of the Markov chain by considering the wireless channel exhibiting composite shadowing-fading. The shadowing is modeled as a log-normal random variable (RV) and the multipath fading as a Rayleigh RV, where the multiplicative model for the mixture distribution known as Suzuki (Rayleigh-lognormal) distribution has been considered. The sum distribution of the multiple Suzuki RVs is approximated by a single log-normal RV by using the moment generating function (MGF)-based technique. This MGF-based technique uses Gauss-Hermite integration to present the sum distribution in closed form. We quantify the signal-to-noise ratio (SNR) margin required to achieve a certain quality of service (QoS) under standard deviation of the shadowing. We also provide the optimal level of cooperation required for obtaining maximum coverage of a line network under a given QoS. Two topologies for linear network are considered and the performance of each topology under various system parameters is provided. The analytical results have been validated by matching with the simulation results.
A. P. Zubarev - One of the best experts on this subject based on the ideXlab platform.
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Application of p -Adic analysis methods in describing Markov Processes on ultrametric spaces isometrically embedded into ℚ p
P-adic Numbers Ultrametric Analysis and Applications, 2015Co-Authors: A. Kh. Bikulov, A. P. ZubarevAbstract:We propose a method for describing Stationary Markov Processes on the class of ultrametric spaces \(\mathbb{U}\) isometrically embedded in the field ℚp of p-adic numbers. This method is capable of reducing the study of such Processes to the investigation of Processes on ℚp. Thereby the traditional machinery of p-adic mathematical physics can be applied to calculate the characteristics of Stationary Markov Processes on such spaces. The Cauchy problem for the Kolmogorov-Feller equation of a Stationary Markov Process on such spaces is shown as being reducible to the Cauchy problem for a pseudo-differential equation on ℚp with non-translation-invariant measure m(x) dpx. The spectrum of the pseudo-differential operator of the Kolmogorov-Feller equation on ℚp with measure m(x) dpx is found. Orthonormal basis of real valued functions for L2 (ℚp,m(x) dpx) is constructed from the eigenfunctions of this operator.
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Application of $p$-adic analysis methods in describing Markov Processes on ultrametric spaces isometrically embeddable into $\mathbb{Q}_{p}$
arXiv: Mathematical Physics, 2015Co-Authors: A. Kh. Bikulov, A. P. ZubarevAbstract:We propose a method for describing Stationary Markov Processes on the class of ultrametric spaces $\mathbb{U}$ isometrically embeddable in the field $\mathbb{Q}_{p}$ of $p$-adic numbers. This method is capable of reducing the study of such Processes to the investigation of Processes on $\mathbb{Q}_{p}$. Thereby the traditional machinery of $p$-adic mathematical physics can be applied to calculate the characteristics of Stationary Markov Processes on such spaces. The Cauchy problem for the Kolmogorov-Feller equation of a~Stationary Markov Process on such spaces is shown as being reducible to the Cauchy problem for a pseudo-differential equation on $\mathbb{Q}_{p}$ with non-translation-invariant measure $m\left(x\right)d_{p}x$. The spectrum of the pseudo-differential operator of the Kolmogorov-Feller equation on $\mathbb{Q}_{p}$ with measure $m\left(x\right)d_{p}x$ is found. Orthonormal basis of real valued functions for $L^{2}\left(\mathbb{Q}_{p},m\left(x\right)d_{p}x\right)$ is constructed from the eigenfunctions of this operator.
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Application of p-Adic analysis methods in describing Markov Processes on ultrametric spaces isometrically embedded into ℚ_ p
P-Adic Numbers Ultrametric Analysis and Applications, 2015Co-Authors: A. Kh. Bikulov, A. P. ZubarevAbstract:We propose a method for describing Stationary Markov Processes on the class of ultrametric spaces $$\mathbb{U}$$ isometrically embedded in the field ℚ_ p of p -adic numbers. This method is capable of reducing the study of such Processes to the investigation of Processes on ℚ_ p . Thereby the traditional machinery of p -adic mathematical physics can be applied to calculate the characteristics of Stationary Markov Processes on such spaces. The Cauchy problem for the Kolmogorov-Feller equation of a Stationary Markov Process on such spaces is shown as being reducible to the Cauchy problem for a pseudo-differential equation on ℚ_ p with non-translation-invariant measure m ( x ) d _ p x . The spectrum of the pseudo-differential operator of the Kolmogorov-Feller equation on ℚ_ p with measure m ( x ) d _ p x is found. Orthonormal basis of real valued functions for L ^2 (ℚ_ p , m ( x ) d _ p x ) is constructed from the eigenfunctions of this operator.