Coupled phonon-ripplon modes in a single wire of electrons on the liquid-helium surface

The coupled phonon-ripplon modes of the quasi-one-dimensional electron chain on the liquid helium sutface are studied. It is shown that the electron-ripplon coupling leads to the splitting of the collective modes of the wire with the appearance of low-frequency modes and high-frequency optical modes starting from threshold frequencies. The effective masses of an electron plus the associated dimple for low frequency modes are estimated and the values of the threshold frequencies are calculated. The results obtained can be used in experimental attempts to observe the phase transition of the electron wire into a quasi-ordered phase.Comment: 5 pages, 1 figure, Physical Review (in press

Intersubband plasmons in quasi-one-dimensional electron systems on a liquid helium surface

The collective excitation spectra are studied for a multisubband quasi-one-dimensional electron gas on the surface of liquid helium. Different intersubband plasmon modes are identified by calculating the spectral weight function of the electron gas within a 12 subband model. Strong intersubband coupling and depolarization shifts are found. When the plasmon energy is close to the energy differences between two subbands, Landau damping in this finite temperature system leads to plasmon gaps at small wavevectors.Comment: To be published as a Rapid Communication in Phys. Rev.

Interfering Doorway States and Giant Resonances. II: Transition Strengths

The mixing of the doorway components of a giant resonance (GR) due to the interaction via common decay channels influences significantly the distribution of the multipole strength and the energy spectrum of the decay products of the GR. The concept of the partial widths of a GR becomes ambiguous when the mixing is strong. In this case, the partial widths determined in terms of the $K$- and $S$-matrices must be distinguished. The photoemission turns out to be most sensitive to the overlapping of the doorway states. At high excitation energies, the interference between the doorway states leads to a restructuring towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997

Electronic states in heterostructures formed by ultranarrow layers

Low-energy electronic states in heterosrtuctures formed by ultranarrow layer (single or several monolayers thickness) are studied theoretically. The host material is described within the effective mass approximation and effect of ultranarrow layers is taken into account within the framework of the transfer matrix approach. Using the current conservation requirement and the inversion symmetry of ultranarrow layer, the transfer matrix is written through two phenomenological parameters. The binding energy of localized state, the reflection (transmission) coefficient for the single ultranarrow layer case, and the energy spectrum of superlattice are determined by these parameters. Spectral dependency of absorption in superlattice due to photoexcitation of electrons from localized states into minibands is strongly dependent on the ultranarrow layers characteristics. Such a dependency can be used for verification of the transfer matrix parameters.Comment: 7 pages, 7 figure

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that the equivalence holds for models that satisfy cluster separability. The generalized Bakamjian Thomas construction is used in most applications, even though it only satisfies cluster properties for systems of less than four particles. Different forms of dynamics are related by unitary transformations that remove interactions from some infinitesimal generators and introduce them to other generators. These unitary transformation must be interaction dependent, because they can be applied to a non-interacting generator and produce an interacting generator. This suggests that these transformations can generate complex many-body forces when used in many-body problems. It turns out that this is not the case. In all cases of interest the result of applying the unitary scattering equivalence results in representations that have simple relations, even though the unitary transformations are dynamical. This applies to many-body models as well as models with particle production. In all cases no new many-body operators are generated by the unitary scattering equivalences relating the different forms of dynamics. This makes it clear that the various calculations used in applications that emphasize one form of the dynamics over another are equivalent. Furthermore, explicit representations of the equivalent dynamical models in any form of dynamics are easily constructed. Where differences do appear is when electromagnetic probes are treated in the one-photon exchange approximation. This approximation is different in each of Dirac's forms of dynamics.Comment: 6 pages, no figure

Multiscale fluctuations in nuclear response

The nuclear collective response is investigated in the framework of a doorway picture in which the spreading width of the collective motion is described as a coupling to more and more complex configurations. It is shown that this coupling induces fluctuations of the observed strength. In the case of a hierarchy of overlapping decay channels, we observe Ericson fluctuations at different scales. Methods for extracting these scales and the related lifetimes are discussed. Finally, we show that the coupling of different states at one level of complexity to some common decay channels at the next level, may produce interference-like patterns in the nuclear response. This quantum effect leads to a new type of fluctuations with a typical width related to the level spacing.Comment: 34 Latex pages including 6 figures (submitted to Phys. Rev. C

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the \delta-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.Comment: Revtex4, 5 pages, published versio

Magneto-Optical Trap for Thulium Atoms

Thulium atoms are trapped in a magneto-optical trap using a strong transition at 410 nm with a small branching ratio. We trap up to $7\times10^{4}$ atoms at a temperature of 0.8(2) mK after deceleration in a 40 cm long Zeeman slower. Optical leaks from the cooling cycle influence the lifetime of atoms in the MOT which varies between 0.3 -1.5 s in our experiments. The lower limit for the leaking rate from the upper cooling level is measured to be 22(6) s$^{-1}$. The repumping laser transferring the atomic population out of the F=3 hyperfine ground-state sublevel gives a 30% increase for the lifetime and the number of atoms in the trap.Comment: 4 pages, 6 figure

On reaction-subdiffusion equations

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form is rather unusual: The parameters of reaction influence the diffusion term in the equation for a component A, a consequence of the nonmarkovian nature of subdiffusion. The equation for a product contains a term which depends on the concentration of A at all previous times. Our discussion shows that reaction-subdiffusion equations may not resemble the corresponding reaction-diffusion ones and are not obtained by a trivial change of the diffusion operator for a subdiffusion one