Journal of Mathematical Physics

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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
Integrable Hamiltonian systems related to the polynomial eigenvalue problem
Journal of Mathematical Physics - Tập 31 Số 12 - Trang 2835-2839 - 1990
Yunbo Zeng, Yishen Li
The independent integrals of motion in involution for the Hamiltonian system related to the second-order polynomial eigenvalue problem are constructed by using relevant recursion formula. The hierarchy of Hamiltonian systems obtained from the above problem and the time part of the Lax pair are shown to be completely integrable and they are shown to commute with each other. Furthermore, the...... hiện toàn bộ
Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators
Journal of Mathematical Physics - Tập 9 Số 11 - Trang 1976-1986 - 1968
Harry R. Lewis
A class of exact invariants for oscillator systems whose Hamiltonians areH=(1/2ε)[p2+Ω2(t)q2]is given in closed form in terms of a function ρ(t) which satisfies ε2d2ρ/dt2+Ω2(t)ρ−ρ−3=0. Each particular solution of the equation for ρ determines an invariant. The invariants are derived by applying an asymptotic theory due to Kruskal to the oscillator system in closed form. As a consequence, t...... hiện toàn bộ
Extended continued fractions and energies of the anharmonic oscillators
Journal of Mathematical Physics - Tập 24 Số 5 - Trang 1136-1141 - 1983
Miloslav Znojil
We describe the analytic solution to the Schrödinger eigenvalue problem for the class of the central potentials V(r)=∑δ∈Zaδrδ, where a−2>−1/4, amax δ >0, Z is an arbitrary finite set of the integer or rational exponents, −2≤δ1<δ2<⋅⋅⋅<δI, and the couplings aδ satisfy only one auxiliary (formal, ‘‘superconfinement’’) restriction of the type aδI−1 >0....... hiện toàn bộ
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
Tổng số: 182   
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