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
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
Soliton solutions to coupled higher-order nonlinear Schrödinger equations
Journal of Mathematical Physics - Tập 33 Số 3 - Trang 1208-1215 - 1992
Richard S. Tasgal, M. J. Potasek
A set of coupled higher-order nonlinear Schrödinger equations, which describe electromagnetic pulse propagation in coupled optical waveguides, is formulated in terms of an eigenvalue problem. Using that result, the inverse scattering problem is solved and explicit soliton solutions are found. Additionally, linear coupling terms are studied systematically.
Shear-free gravitational collapse
Journal of Mathematical Physics - Tập 20 Số 7 - Trang 1508-1513 - 1979
E. N. Glass
Spherically symmetric perfect fluids are studied under the restriction of shear-free motion. All solutions of the field equations are found by solving a single second order nonlinear equation containing an arbitrary function. It is shown that this arbitrary function is a geometric invariant, E, which measures the gravitational field energy, and it is shown that E=const generates all the ho...... hiện toàn bộ
Brownian Motion of a Quantum Oscillator
Journal of Mathematical Physics - Tập 2 Số 3 - Trang 407-432 - 1961
Julian Schwinger
An action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical system. This simple problem has the advantage of combining immediate physical applicability (e.g., resistive damping or maser amplification of a single electromagnetic cavity mode) with a signifi...... hiện toàn bộ
Canonical Definition of Wigner Coefficients in Un
Journal of Mathematical Physics - Tập 8 Số 4 - Trang 691-700 - 1967
L. C. Biedenharn, Alberto Giovannini, James D. Louck
Two general results applicable to the problem of a canonical definition of the Wigner coefficient in Un are demonstrated: (1) the existence of a canonical imbedding of Un × Un into Un2 and (2) a general factorization lemma for operators defined in the boson calculus. Using these results, a resolution of the multiplicity problem for U3 is demonstrated, in which all degenerate operators are ...... hiện toàn bộ
On the Representations of the Semisimple Lie Groups. III. The Explicit Conjugation Operation for SUn
Journal of Mathematical Physics - Tập 5 Số 12 - Trang 1723-1730 - 1964
G. E. Baird, L. C. Biedenharn
The analog of the SU2 (1 − j) symbol is defined and discussed in detail for SUn. An appropriate generalization to SUn of the Condon-Shortley phase convention is explicitly given.
On the Representations of the Semisimple Lie Groups. IV. A Canonical Classification for Tensor Operators in SU3
Journal of Mathematical Physics - Tập 5 Số 12 - Trang 1730-1747 - 1964
G. E. Baird, L. C. Biedenharn
It is shown that the multiplicity structure of the general SUn operators may be put in a one-to-one correspondence with the multiplicity structure of the corresponding states. This result allows a convenient labeling scheme to be devised for the general SUn Wigner operator and leads in a natural way to the concept of a reduced Wigner operator. The problem of multiplicity in tensor operator...... hiện toàn bộ
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