Explicit time-dependence of basis functions and its consequences

2004 ◽  
Vol 398 (1-3) ◽  
pp. 270-275 ◽  
Author(s):  
Angelika Baranowska ◽  
Andrzej J. Sadlej
Keyword(s):  
Time Dependence ◽  
Basis Functions ◽  
Explicit Time Dependence

scholarly journals New Results on the Coagulation Equation

1987 ◽  
Vol 115 ◽  
pp. 547-547
Author(s):  
Pierre Bastien ◽  
Claude Lejeune
Keyword(s):  
Mass Spectrum ◽  
Time Dependence ◽  
Star Clusters ◽  
Mass Function ◽  
Mass Dependence ◽  
Coagulation Rate ◽  
Precise Form ◽  
Explicit Time Dependence ◽  
Coagulation Equation ◽  
Free Parameters

In attempting to reproduce the initial stellar mass function, we solved analytically the coagulation equation with an explicit time dependence in the coagulation rate in order to simulate the gravitational collapse of the fragments upon themselves as they move within the progenitor cloud. Two separate cases have been studied, with and without a mass dependence in the coagulation rate. The solution show that (1) inclusion of self-gravitation is very important and can change the results to the point of preventing coalescence to work altogether, depending on the values of the two free parameters, (2) the precise form of the mass dependence of the coagulation rate is not of prime importance in most situations of astrophysical interest, and (3) coagulation alone is not sufficient to yield a realistic mass spectrum and fragmentation must also be taken into account. Coagulation is more efficient for massive fragments and fragmentation for the smaller ones. These results are applied to different regions: star clusters, associations, and starburst regions.

The Jacobi Energy Function

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Conservation Laws ◽  
Total Energy ◽  
Time Dependence ◽  
Energy Function ◽  
Tangent Bundle ◽  
Implicit Time ◽  
Translational Invariance ◽  
Explicit Time Dependence ◽  
Generalised Coordinates ◽  
Lagrange Formalism

This chapter focuses on the Jacobi energy function, considering how the Lagrange formalism treats the energy of the system. This discussion leads nicely to conservation laws and symmetries, which are the focus of the next chapter. The Jacobi energy function associated with a Lagrangian is defined as a function on the tangent bundle. The chapter also discuss explicit vs implicit time dependence, and shows how time translational invariance ensures the generalised coordinates are inertial, meaning that the energy function is the total energy of the system. In addition, it examines the energy function using non-inertial coordinates and explicit time dependence.

scholarly journals RESTORING TIME DEPENDENCE INTO QUANTUM COSMOLOGY

2012 ◽  
Vol 21 (11) ◽  
pp. 1242011 ◽  
Author(s):  
AHARON DAVIDSON ◽  
BEN YELLIN
Keyword(s):  
Quantum Theory ◽  
Time Dependence ◽  
Quantum Cosmology ◽  
Scale Factor ◽  
Time Dependent ◽  
Hamiltonian Constraint ◽  
Canonical Variables ◽  
Explicit Time Dependence ◽  
Dirac Brackets ◽  
Lapse Function

Mini superspace cosmology treats the scale factor a(t), the lapse function n(t) and an optional dilation field ϕ(t) as canonical variables. While pre-fixing n(t) means losing the Hamiltonian constraint, pre-fixing a(t) is serendipitously harmless at this level. This suggests an alternative to the Hartle–Hawking approach, where the pre-fixed a(t) and its derivatives are treated as explicit functions of time, leaving n(t) and a now mandatory ϕ(t) to serve as canonical variables. The naive gauge pre-fix a(t) = const . is clearly forbidden, causing evolution to freeze altogether; so pre-fixing the scale factor, say a(t) = t, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time-dependent total Hamiltonian and calculate the Dirac brackets, characterized by {n, ϕ}D ≠ 0, which are promoted to commutation relations in the quantum theory.

A Conservation Theorem for Simple Nonholonomic Systems

1983 ◽  
Vol 50 (3) ◽  
pp. 647-651 ◽  
Author(s):  
T. R. Kane ◽  
A. K. Banerjee
Keyword(s):  
Time Dependence ◽  
Nonholonomic System ◽  
Nonholonomic Systems ◽  
Holonomic System ◽  
Explicit Time Dependence ◽  
Conservation Theorem

When the Hamiltonian of a holonomic system is free of explicit time dependence it remains constant throughout all motions of the system. In this paper, it is shown how, given a homogeneous simple nonholonomic system S, one can form a function E that remains constant throughout all motions of S, providing the forces acting on S fulfill certain requirements. An illustrative example is examined in detail.

scholarly journals Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator

2019 ◽  
Vol 35 (08) ◽  
pp. 2050041 ◽  
Author(s):  
Andreas Fring ◽  
Thomas Frith
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependence ◽  
Time Dependent ◽  
Two Dimensional ◽  
Coupling Term ◽  
Coupled Oscillator ◽  
Explicit Time Dependence ◽  
Independent Model

We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

scholarly journals Quantum mechanics with explicit time dependence

1992 ◽  
Vol 170 (5) ◽  
pp. 344-346 ◽  
Author(s):  
John Rogers ◽  
Donald Spector
Keyword(s):  
Quantum Mechanics ◽  
Time Dependence ◽  
Explicit Time Dependence
Sign in / Sign up

Export Citation Format

Share Document