4,165 research outputs found
Ladder operators for isospectral oscillators
We present, for the isospectral family of oscillator Hamiltonians, a
systematic procedure for constructing raising and lowering operators satisfying
any prescribed `distorted' Heisenberg algebra (including the
-generalization). This is done by means of an operator transformation
implemented by a shift operator. The latter is obtained by solving an
appropriate partial isometry condition in the Hilbert space. Formal
representations of the non-local operators concerned are given in terms of
pseudo-differential operators. Using the new annihilation operators, new
classes of coherent states are constructed for isospectral oscillator
Hamiltonians. The corresponding Fock-Bargmann representations are also
considered, with specific reference to the order of the entire function family
in each case.Comment: 13 page
Note on Coherent States and Adiabatic Connections, Curvatures
We give a possible generalization to the example in the paper of Zanardi and
Rasetti (quant-ph/9904011). For this generalized one explicit forms of
adiabatic connection, curvature and etc. are given.Comment: Latex file, 12 page
Efficient Investment in Children
Many would say that children are society's most precious resource. So, how should we invest in them? To gain insight into this question, a dynamic general equilibrium model is developed where children differ by ability. Parents invest time and money in their offspring, depending on their altruism. This allows their children to grow up as more productive adults. First, the efficient allocation is characterized. Next, this is compared with the outcome that arises when financial markets are incomplete. The situation where child-care markets are also lacking is then examined. Additionally, the consequences of impure altruism are analyzed.Investment in children; efficiency; imperfect financial markets; impure altruism; lack of child-care markets.
Quantum revivals, geometric phases and circle map recurrences
Revivals of the coherent states of a deformed, adiabatically and cyclically
varying oscillator Hamiltonian are examined. The revival time distribution is
exactly that of Poincar\'{e} recurrences for a rotation map: only three
distinct revival times can occur, with specified weights. A link is thus
established between quantum revivals and recurrences in a coarse-grained
discrete-time dynamical system.Comment: 9 page
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