Search results for "Degenerate energy levels"
showing 10 items of 221 documents
AN OPTICAL PLAQUETTE: MINIMUM EXPRESSIONS OF TOPOLOGICAL MATTER
2009
Topological matter is an unconventional form of matter: it exhibits a global hidden order which is not associated with the spontaneous breaking of any symmetry. The defects of this exotic type of order are anyons, quasiparticles with fractional statistics. Moreover, when living on a surface with non-trivial topology, like a plane with a hole or a torus, this type of matter develops a number of degenerate states which are locally indistinguishable and could be used to build a quantum memory naturally resistant to errors. Except for the fractional quantum Hall effect there is no experimental evidence as to the existence of topologically ordered phases, and it remains a huge challenge to devel…
Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures
2005
The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2 even in the absence of spin-flip contributions to the Hund exchange. The second transition -- not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization -- is clearly exposed in a low-frequency analysis of the self-energy and in local spectra.
Squeezing induced by spontaneous rotational symmetry breaking
2009
In this communication we study in depth the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking discussed for the first time in [1]. The idea can be put in short as follows. Consider a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM 10 mode with an arbitrary orientation (measured by θ at Fig. 1) emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane. Quantum effects are then quite i…
Faster Quantum Walk Search on a Weighted Graph
2015
A randomly walking quantum particle evolving by Schr\"odinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time $\Theta(N^{3/4})$. In this paper, we give a weighted version of this graph that preserves vertex-transitivity, and we show that the time to search on it can be reduced to nearly $\Theta(\sqrt{N})$. To prove this, we introduce two novel extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges, and a method to determine how precisely the jumping rate of the quantum walk must be chosen.
Bose condensates at high angular momenta
2000
We exploit the analogy with the Quantum Hall (QH) system to study weakly interacting bosons in a harmonic trap. For a $\delta$-function interaction potential the ``yrast'' states with $L\ge N(N-1)$ are degenerate, and we show how this can be understood in terms of Haldane exclusion statistics. We present spectra for 4 and 8 particles obtained by numerical and algebraic methods, and demonstrate how a more general hard-core potential lifts the degeneracies on the yrast line. The exact wavefunctions for N=4 are compared with trial states constructed from composite fermions (CF), and the possibility of using CF-states to study the low L region at high N is discussed.
A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states
1998
International audience; Abstract: A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY6 and XY4 molecules. In addition, some simulations, made with 238UF6 and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.
On the convexity of relativistic ideal magnetohydrodynamics
2015
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity con…
Operation conditions and stability of a degenerate two-photon laser
1993
Abstract The presence of a far off-resonant intermediate level in a degenerate three-level two-photon laser model manifests through a steady pump-dependent and a dynamic frequency shift on the laser equations. The steady shift strongly affects the pump threshold necessary for emission, preventing it in certain cases. The dynamic shift makes the frequency pulling/pushing to be intensity-dependent and substantially modify the domains of existence and stability of the lasing solution permitting stable operation for large cavity losses in certain cases.
Nonlinear Current Generation in Degenerate Semiconductors Embedded in Constant and Low-Frequency Electric Fields
2006
The explicit analytical forms of nonlinear currents in degenerate semiconductors serving as sources of coherent radiation in the wavelength millimetric and submillimetric ranges are established.
Su(4) approach to fourfold degenerate electronic states of some hexafluoride molecules
2003
Abstract We show that two appropriate realizations of the su (4) algebra allow the construction of all electronic operators needed for the study of vibronic and rovibronic interactions in a G ′ electronic state. In each case a full bosonic realization is made and all matrix elements are calculated. Illustrations of our formalism and comparisons with previous approaches are made in the case of ν 5 ( F 2 g ) and ν 3 ( F 1 u ) modes.