Journal of Mathematical Physics

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The Zeno’s paradox in quantum theory
Journal of Mathematical Physics - Tập 18 Số 4 - Trang 756-763 - 1977
B. Misra, E. C. G. Sudarshan
We seek a quantum-theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle whi...... hiện toàn bộ
AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schrödinger equations
Journal of Mathematical Physics - Tập 52 Số 4 - 2011
Dun Zhao, Yujuan Zhang, Wei-Wei Lou, Hong‐Gang Luo
By constructing nonisospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schrödinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose–Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases ...... hiện toàn bộ
Fractional wave equation and damped waves
Journal of Mathematical Physics - Tập 54 Số 3 - 2013
Yuri Luchko
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of the same order α, 1 ⩽ α ⩽ 2, both in space and in time. We show that this feature is a decisive factor for inheriting some crucial characteristics of t...... hiện toàn bộ
Numerical path integral techniques for long time dynamics of quantum dissipative systems
Journal of Mathematical Physics - Tập 36 Số 5 - Trang 2430-2457 - 1995
Nancy Makri
Recent progress in numerical methods for evaluating the real-time path integral in dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed numerically allow convergence of the path integral with large time increments. Integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiab...... hiện toàn bộ
Curvature and torsion of the world curve in the action of the relativistic particle
Journal of Mathematical Physics - Tập 32 Số 12 - Trang 3315-3320 - 1991
V. V. Nesterenko
A generalization of the relativistic particle action is considered. It contains, in addition to the length of the world trajectory, the integrals along the world curve of its curvature and torsion. The generalized Hamiltonian formalism for this model in the D-dimensional space-time is constructed. A complete set of the constraints in the phase space is obtained and their division into the ...... hiện toàn bộ
Chiral symmetry breakdown. I. Gauge dependence in constant vertex approximation
Journal of Mathematical Physics - Tập 28 Số 10 - Trang 2488-2493 - 1987
David Atkinson, Peter Y. Johnson
An approximate quark propagator equation in a Landau-like gauge is analyzed and it is shown that there is a critical value of the coupling constant, corresponding to the onset of dynamical chiral symmetry breakdown, provided that (a) there is an infrared cutoff, which can be supplied by an effective gluon mass, and (b) there is an ultraviolet cutoff, which may be engendered by a running co...... hiện toàn bộ
Chiral symmetry breakdown. II. Ansatz for vertex in ultraviolet
Journal of Mathematical Physics - Tập 28 Số 10 - Trang 2494-2497 - 1987
David Atkinson
An earlier analysis of the Dyson–Schwinger equation for the quark propagator is improved by taking the Slavnov–Taylor identity into account in the ultraviolet. It is found that chiral symmetry breaking occurs above a critical coupling in the Landau gauge; but that this result does not hold in other gauges.
Two-dimensional lumps in nonlinear dispersive systems
Journal of Mathematical Physics - Tập 20 Số 7 - Trang 1496-1503 - 1979
Junkichi Satsuma, Mark J. Ablowitz
Two-dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two-dimensional nonlinear Schrödinger type equation. The amplitude of these solutions is rational in its independent variables. These solutions are constructed by taking a ’’long wave’’ limit of the corresponding N-soliton solutions obtained by direct methods. T...... hiện toàn bộ
Complexiton solutions to soliton equations by the Hirota method
Journal of Mathematical Physics - Tập 58 Số 10 - 2017
Yuan Zhou, Wen‐Xiu Ma
We apply the Hirota direct method to construct complexiton solutions (complexitons). The key is to use Hirota bilinear forms. We prove that taking pairs of conjugate wave variables in the 2N-soliton solutions generates N-complexion solutions. The general theory is used to construct multi-complexion solutions to the Korteweg–de Vries equation.
A note on the definition of deformed exponential and logarithm functions
Journal of Mathematical Physics - Tập 50 Số 10 - 2009
Thomas Oikonomou, G. Baris Bagci
The recent generalizations of the Boltzmann–Gibbs statistics mathematically rely on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed logarithmic/exponential map is a bijection from R+/R (set of positive real numbers/all real numbers) to R/R+, as their undeformed counterparts. We show that ...... hiện toàn bộ
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