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
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 which is co...
A new integrable symplectic map associated with lattice soliton equations
Journal of Mathematical Physics - Tập 37 Số 5 - Trang 2338-2345 - 1996
A method is developed that extends the nonlinearization technique to the
hierarchy of lattice soliton equations associated with a discrete 3×3 matrix
spectral problem. A new integrable symplectic map and its involutive system of
conserved integrals are obtained by the nonlinearization of spatial parts and
the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy.
Moreover, the solut...
AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schrödinger equations
Journal of Mathematical Physics - Tập 52 Số 4 - 2011
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 of a
new...
Fractional wave equation and damped waves
Journal of Mathematical Physics - Tập 54 Số 3 - 2013
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 the wave ...
Numerical path integral techniques for long time dynamics of quantum dissipative systems
Journal of Mathematical Physics - Tập 36 Số 5 - Trang 2430-2457 - 1995
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 adiabatic
pat...
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
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
first-cl...
Chiral symmetry breakdown. I. Gauge dependence in constant vertex approximation
Journal of Mathematical Physics - Tập 28 Số 10 - Trang 2488-2493 - 1987
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 coupling c...
Chiral symmetry breakdown. II. Ansatz for vertex in ultraviolet
Journal of Mathematical Physics - Tập 28 Số 10 - Trang 2494-2497 - 1987
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.
Complexiton solutions to soliton equations by the Hirota method
Journal of Mathematical Physics - Tập 58 Số 10 - 2017
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.
Two-dimensional lumps in nonlinear dispersive systems
Journal of Mathematical Physics - Tập 20 Số 7 - Trang 1496-1503 - 1979
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. The
solut...
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