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Finite wave-packet groups, which generate structured wave-packet matrices, are given by finite groups of dilations, translations and modulations on an underlying finite field. For prime fields, we develop a representation theory a...
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Finite wave-packet groups, which generate structured wave-packet matrices, are given by finite groups of dilations, translations and modulations on an underlying finite field. For prime fields, we develop a representation theory approach to the matrix analysis of large class of systems including wave-packet matrices. We then study basic analytic aspects of wave-packet matrices over prime fields.
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Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave-packet formalism. We demonstrate that whereas the Dirac Hamiltonian ...
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Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave-packet formalism. We demonstrate that whereas the Dirac Hamiltonian impels a causal evolution of probabilities, even in the presence of interactions, the relativistic- Schr?dinger model is acausal.We quantify the causality breakdown in the latter model and argue that, in contrast to the popular viewpoint, it is not related to the localization properties of the states.
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It is shown that for Rydberg atoms, the Bohmian paths of the electrons are ellipses to a high degree of approximation even for arbitrary widths of the wave packets. (C) 2004 Elsevier B.V. All rights reserved. [References: 16]
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We consider wave packets of free particles with a general energy-momentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v = partial derivative E-P. The position-velocity uncertainty relat...
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We consider wave packets of free particles with a general energy-momentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v = partial derivative E-P. The position-velocity uncertainty relation Delta x Delta V >= 1/2 vertical bar vertical bar is saturated by minimal uncertainty wave packets phi(p) = A exp(-alpha E(p) + beta p). In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation E(p) = p(2)/2m, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation E(p) = -cos(pa)/ma(2) as well as for the relativistic dispersion relation E(p) = root p(2) + m(2). The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.
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In this article, we introduce the structure of wave packet groups over finite cyclic groups, as the finite non-Abelian groups consist of cyclic dilations, translations, and modulations. Then, we present the notion of wave packet r...
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In this article, we introduce the structure of wave packet groups over finite cyclic groups, as the finite non-Abelian groups consist of cyclic dilations, translations, and modulations. Then, we present the notion of wave packet representations on wave packet groups. As an application of wave packet representations, we study constructive and analytic properties of the cyclic wave packet transforms associated to these representations. Finally, we apply these techniques in the case of some finite cyclic groups. (C) 2015 Elsevier Inc. All rights reserved.
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The classical Boussinesq equation describing gravity waves in shallow waters is under consideration. Hirota's bilinear representation is used to construct exact solutions describing wave packets, waves on solitons, and dancing wav...
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The classical Boussinesq equation describing gravity waves in shallow waters is under consideration. Hirota's bilinear representation is used to construct exact solutions describing wave packets, waves on solitons, and dancing waves. The principle of multiplying the solutions of the Hirota equation is formulated, which helps constructing more complex structures made of solitons, wave packets, and other types of waves.
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A theory is developed here to describe the propagation of nonlinear Rossby wave packets in a barotropic atmospheric model and their interactions by using the multiple-scale method. It is shown that the propagation of a single Ross...
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A theory is developed here to describe the propagation of nonlinear Rossby wave packets in a barotropic atmospheric model and their interactions by using the multiple-scale method. It is shown that the propagation of a single Rossby wave packet can be described by the nonlinear Schrodinger equation that has envelope soliton solutions. For two interacting packets with slightly different wavenumbers they satisfy a set of two coupled nonlinear Schrodinger equations. These equations are used to study the collision interactions of two envelope Rossby solitons. It is found that despite the complexity of the interaction, the energy of each soliton is conserved. while the shapes and velocities of the two solitons may be altered significantly by the interaction. The action of one soliton on another is realized by providing a field of force or potential for it through the cross-modulation terms. [References: 16]
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Conditions for modulation instability of a wave packet to occur in cubically nonlinear singleand double-mode waveguides with various distributions of dispersion parameters over the waveguide length are investigated. Analytical exp...
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Conditions for modulation instability of a wave packet to occur in cubically nonlinear singleand double-mode waveguides with various distributions of dispersion parameters over the waveguide length are investigated. Analytical expressions are obtained for the integral gain increment and other characteristics governing the modulation instability dynamics. Features of the dynamics are revealed using numerical simulation.
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In the present paper, we study the long time behavior of solutions for the Davey-Stewartson systems on R-2. We first derive the uniform a priori estimates for the solutions of these systems in H-1(R-2). Then we show the existence ...
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In the present paper, we study the long time behavior of solutions for the Davey-Stewartson systems on R-2. We first derive the uniform a priori estimates for the solutions of these systems in H-1(R-2). Then we show the existence of the compact global attractor for the strong topology of H-1(R-2). (C) 1997 American Institute of Physics. [References: 14]
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The free Schrodinger equation has localized constant velocity solutions psi(v) of the form psi = f (r - vt) e(i lambda t) with lambda being a constant. These solutions are eigenvectors of a momentum operator (p) over tilde such th...
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The free Schrodinger equation has localized constant velocity solutions psi(v) of the form psi = f (r - vt) e(i lambda t) with lambda being a constant. These solutions are eigenvectors of a momentum operator (p) over tilde such that (p) over tilde psi(v) = mv psi(v). The wavepacket, while not normalizable, is both localized and in a definite momentum state. The psi(v) are orthogonal in the inner product space , and the (p) over tilde operator is symmetric therein. We discuss whether these psi(v) can act as basis states rather than the usual plane waves.
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