Search results for "Hamiltonian"
showing 10 items of 662 documents
Limits on gravitational Einstein Equivalence Principle violation from monitoring atomic clock frequencies during a year
2016
Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance. Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg$^+$ and Al$^+$ clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of the gravity related parameter of the Einstein Equivalence Principle violating term in the Standard Mo…
$$\mathscr {D}{-}$$ D - Deformed and SUSY-Deformed Graphene: First Results
2016
We discuss some mathematical aspects of two particular deformed versions of the Dirac Hamiltonian for graphene close to the Dirac points, one involving \(\mathscr {D}\)-pseudo bosons and the other supersymmetric quantum mechanics. In particular, in connection with \(\mathscr {D}\)-pseudo bosons, we show how biorthogonal sets arise, and we discuss when these sets are bases for the Hilbert space where the model is defined, and when they are not. For the SUSY extension of the model we show how this can be achieved and which results can be obtained.
A Unified Phenomenological Description of Quadrupole Excitations in Even-Even Nuclei
1976
A phenomenological model is developed for the collective quadrupole properties of all even-even nuclei. Rotational. vibrational and transitional nuclei are included in the model on an equal footing. A Bohr-type intrinsic Hamiltonian for harmonic quadrupole vibrations about an axially deformed shape is solved exactly. States of good angular momentum are projected out of the intrinsic states, and they are made orthogonal by a Schmidt scheme. The angular-momentum and phonon-number composition of the states is analyzed at various stages; states with K = 1 are found spurious. Excitation energies for the ground, β, and γ bands are calculated as expectation values of a radically simplified nuclear…
Fractional Periodicity of Persistent Currents: A Signature of Broken Internal Symmetry
2003
We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin Hamiltonian holds the explanation to this transition. Numerical diagonalizations are performed to show this explicitely. Persistent currents therefore, provide an easy way to experimentally verify broken internal symmetry in electronic systems.
Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings
2014
We solve a time-optimal control problem in a linear chain of three coupled spins 1/2 with unequal couplings. We apply the Pontryagin maximum principle and show that the associated Hamiltonian system is the one of a three-dimensional rigid body. We express the optimal control fields in terms of the components of the classical angular momentum of the rigid body. The optimal trajectories and the minimum control time are given in terms of elliptic functions and elliptic integrals.
Expressions of Effective Hamiltonian Parameters of XY4 Molecules in the Tetrahedral Formalism
1998
We have derived expressions of second-order effective Hamiltonian parameters of XY4 molecules in the tetrahedral formalism (1992, J. P. Champion et al., "Spectroscopy of the Earth's Atmosphere and Interstellar Medium: Spherical Top Spectra," Academic Press, San Diego). They are written as a function of the force constants of the potential expanded in terms of the dimensionless normal coordinates. These expressions can be used in the isolated band scheme as well as in the polyad one. The ambiguity of the effective Hamiltonian parameters is treated. Relations between the parameters for q2 and q4 terms and Hecht's anharmonicity constants (1960, K. T. Hecht, J. Mol. Spectrosc. 5, 355-389) in th…
Vibrational Energy Levels via Finite-Basis Calculations Using a Quasi-Analytic Form of the Kinetic Energy
2015
A variational method for the calculation of low-lying vibrational energy levels of molecules with small amplitude vibrations is presented. The approach is based on the Watson Hamiltonian in rectilinear normal coordinates and characterized by a quasi-analytic integration over the kinetic energy operator (KEO). The KEO beyond the harmonic approximation is represented by a Taylor series in terms of the rectilinear normal coordinates around the equilibrium configuration. This formulation of the KEO enables its extension to arbitrary order until numerical convergence is reached for those states describing small amplitude motions and suitably represented with a rectilinear system of coordinates. …
Decay study ofTc114with a Penning trap
2011
The level structure of $^{114}\mathrm{Ru}$ has been investigated via the $\ensuremath{\beta}$ decay of very neutron-rich $^{114}\mathrm{Tc}$ by means of Penning-trap-assisted $\ensuremath{\gamma}$ spectroscopy. The deduced $\ensuremath{\beta}$-decay scheme suggests the existence of two $\ensuremath{\beta}$-decaying states in $^{114}\mathrm{Tc}$ with ${I}^{\ensuremath{\pi}}={1}^{+}$ and $I\ensuremath{\geqslant}$ 4, with half-lives of ${t}_{1/2}({1}^{+})=90(20)$ ms and ${t}_{1/2}(I\ensuremath{\geqslant}4)=100(20)$ ms, respectively. The ${Q}_{\ensuremath{\beta}}$ value, which covers a possible mixture of two states, has been determined to be ${Q}_{\ensuremath{\beta}}=11 785(12)$ keV. The level…
Towards simulation of high temperature methane spectra
2002
Methane plays a central role in gas layers of temperatures up to around 3000 K in a number of astrophysical objects ranging from giant planets to brown dwarfs, over proto-solar nebulae, to several classes of cool stars. In order to model and analyse these objects correctly, an accurate and complete list of spectral lines at high temperature is demanded. Predicting high temperature spectra implies, however, predicting hot bands and thus modelling highly excited vibrational states. This is a real challenge in the case of methane. We report the preliminary results of a theoretical study combining the global effective Hamiltonian approach and its computational implementation (STDS package: http…
Spheroidal and hyperspheroidal coordinates in the adiabatic representation of scattering states for the Coulomb three-body problem
2009
Recently, an involved approach has been used by Abramov (2008 J. Phys. B: At. Mol. Opt. Phys. 41 175201) to introduce a separable adiabatic basis into the hyperradial adiabatic (HA) approximation. The aim was to combine the separability of the Born–Oppenheimer (BO) adiabatic basis and the better asymptotic properties of the HA approach. Generalizing these results we present here three more different separable bases of the same type by making use of a previously introduced adiabatic Hamiltonian expressed in hyperspheroidal coordinates (Matveenko 1983 Phys. Lett. B 129 11). In addition, we propose a robust procedure which accounts in a stepwise procedure for the unphysical couplings that are …