Quantum Mechanical Search and Harmonic Perturbation

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.Comment: 6 pages, 4 figures, revtex

Perturbative Renormalizations of Anyon Quantum Mechanics

In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.Comment: 19 pages, Plain LaTex, MIT-CTP-232

Theory of fluorescence excitation spectra using anharmonic-coriolis coupling in S1 and internal conversion to S0. I. General formalism

A treatment of one- or two-photon fluorescence excitation spectra is described using the vibration–rotation coupling of zeroth order states in the excited electronic state and nonadiabatic coupling to the ground state. Using perturbation theory, experimental harmonic frequencies, an anharmonic force field, and various theoretical Coriolis coupling constants, a quasistationary molecular eigenstate in an excited electronic state S1 is first calculated. The S1 eigenstate is then coupled via the nonadiabatic nuclear kinetic energy operator (internal conversion) to rovibronic states in the ground state manifold, the latter states approximated in a simple manner. A search algorithm is used to select the S1 dark states and the S0 states. Both the perturbation theory coefficient and the Franck–Condon factors are employed in the evaluation function used in the search. The results are applied in part II to the channel three problem in benzene

The Berry phase in inflationary cosmology

We derive an analogue of the Berry phase associated with inflationary cosmological perturbations of quantum mechanical origin by obtaining the corresponding wavefunction. We have further shown that cosmological Berry phase can be completely envisioned through the observable parameters, viz. spectral indices. Finally, physical significance of this phase is discussed from the point of view of theoretical and observational aspects with some possible consequences of this quantity in inflationary cosmology.Comment: 9 pages, Modified version to appear in Classical and Quantum Gravity. arXiv admin note: text overlap with arXiv:quant-ph/0307084 by other author

Intramolecular dynamics. III. Theoretical studies of the CH overtone spectra for benzene

The electronic states of the ionic excimer Ar + + 2 are calculated using ab initio multireference configuration interaction and effective core pseudopotentials. Among states dissociating into Ar+(2P)+Ar+(2P), all are found to be repulsive, except the ground state, which occurs to be quasibound near Re=4.1a0 with a well depth of >=230 cm^−1. All states originating from Ar++(3P,1D,1S)+Ar are bound with dissociation energies in the range 3200–4500 cm^−1 and equilibrium distances between 5.6a0 and 6a0. Simulation emission spectra from bound excited states are derived from the calculated potentials and the possible contribution of the Ar + + 2 ion to the third continuum fluorescence is discussed

Calogero-Sutherland Particles as Quasisemions

The ultraviolet structure of the Calogero-Sutherland models is examined, and, in particular, semions result to have special properties. An analogy with ultraviolet structures known in anyon quantum mechanics is drawn, and it is used to suggest possible physical consequences of the observed semionic properties.Comment: 7 pages, LaTe