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Effective Hamiltonian (effective + hamiltonian)

Distribution by Scientific Domains

Physics and Astronomy	60%

Selected Abstracts

Geometric algebra and transition-selective implementations of the controlled-NOT gate

CONCEPTS IN MAGNETIC RESONANCE, Issue 1 2004
Timothy F. Havel
Geometric algebra provides a complete set of simple rules for the manipulation of product operator expressions at a symbolic level, without any explicit use of matrices. This approach can be used not only to describe the state and evolution of a spin system, but also to derive the effective Hamiltonian and associated propagator in full generality. In this article, we illustrate the use of geometric algebra via a detailed analysis of transition-selective implementations of the controlled-NOT gate, which plays a key role in NMR-based quantum information processing. In the appendices, we show how one can also use geometric algebra to derive tight bounds on the magnitudes of the errors associated with these implementations of the controlled-NOT. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 23A: 49,62, 2004 [source]

On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2009
Daan P. Geerke
Abstract Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009 [source]

The properties of the CDW phase in the weak coupling anharmonic Holstein,Hubbard model

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2006
P. GrzybowskiArticle first published online: 2 JAN 200
Abstract The anharmonic Holstein,Hubbard Hamiltonian in the case of weak effective electron,electron attraction is studied. To deal with anharmonicity of phonons, variational canonical transformations are used to derive an effective electron Hamiltonian. The properties of the charge density wave (CDW) phase, for half-filling, are analyzed using this effective Hamiltonian. In particular, the critical temperatures, gap function, order parameter and gap ratio are calculated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Intrinsic decoherence in the interaction of two fields with a two-level atom

ANNALEN DER PHYSIK, Issue 6 2009
R. Juárez-Amaro
Abstract We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. Then we solve a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. [source]

Exact solutions to the time-dependent supersymmetric Jaynes-Cummings model and the Chiao-Wu model

ANNALEN DER PHYSIK, Issue 3 2003
J.-Q. Shen
Abstract The present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories. [source]