Quantum Corrections in Constrained Systems

Quantum Phase Transitions in Constrained Bose Systems

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

Radiative corrections and quantum gates in molecular systems.

We propose a method for quantum information processing using molecules coupled to an external laser field. This utilizes molecular interactions, control of the external field, and an effective energy shift of the doubly excited state of two coupled molecules. Such a level shift has been seen in the two-photon resonance experiments recently reported by Hettich et al. Here we show that this can b...

Effective Hamiltonians for Constrained Quantum Systems

We consider the time-dependent Schrödinger equation on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C. When we scale the potential in the directions normal to C by a parameter ε 1, the solutions concentrate in an ε-neighborhood of C. This situation occurs for example in quantum wave guides and for the motion of nuclei in electron...

Quantum corrections to fidelity decay in chaotic systems.

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi-golden ...