Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Superintegrable systems with spin and second-order integrals of motion

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential $V_0=\frac{\alpha}{r}+\frac{3\hbar^2}{8r^2}$ and spin orbital one $V_1=\frac{\hbar}{2r^2}$.Comment: 32 page

Tunneling Time in the Landau-Zener Model

We give a general definition for the tunneling time in the Landau-Zener model. This definition allows us to compute numerically the Landau-Zener tunneling time at any sweeping rate without ambiguity. We have also obtained analytical results in both the adiabatic limit and the sudden limit. Whenever applicable, our results are compared to previous results and they are in good agreement.Comment: 7pages, 9 figure

Simulation of oxygen dissociation on a six-dimensional O4 potential energy surface

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143058/1/6.2017-3487.pd

Superconductivity and magnetic order in the non-centrosymmetric Half Heusler compound ErPdBi

We report superconductivity at $T_c = 1.22$ K and magnetic order at $T_N = 1.06$ K in the semi-metallic noncentrosymmetric Half Heusler compound ErPdBi. The upper critical field, $B_{c2}$, has an unusual quasi-linear temperature variation and reaches a value of 1.6 T for $T \rightarrow 0$. Magnetic order is found below $T_c$ and is suppressed at $B{_M} \sim 2.5$ T for $T \rightarrow 0$. Since $T_c \simeq T_N$, the interaction of superconductivity and magnetism is expected to give rise to a complex ground state. Moreover, electronic structure calculations show ErPdBi has a topologically nontrivial band inversion and thus may serve as a new platform to study the interplay of topological states, superconductivity and magnetic order.Comment: 6 pages, 5 figures; accepted for publication in Europhysics Letter

Effective attraction between oscillating electrons in a plasmoid via acoustic waves exchange

We consider the effective interaction between electrons due to the exchange of virtual acoustic waves in a low temperature plasma. Electrons are supposed to participate in rapid radial oscillations forming a spherically symmetric plasma structure. We show that under certain conditions this effective interaction can result in the attraction between oscillating electrons and can be important for the dynamics of a plasmoid. Some possible applications of the obtained results to the theory of natural long-lived plasma structures are also discussed.Comment: 14 pages in LaTeX2e, two columns, 3 eps figures; minimal changes, some typos are corrected; version published on-line in Proc. R. Soc.

`St\"uckelberg interferometry' with ultracold molecules

We report on the realization of a time-domain `St\"uckelberg interferometer', which is based on the internal state structure of ultracold Feshbach molecules. Two subsequent passages through a weak avoided crossing between two different orbital angular momentum states in combination with a variable hold time lead to high-contrast population oscillations. This allows for a precise determination of the energy difference between the two molecular states. We demonstrate a high degree of control over the interferometer dynamics. The interferometric scheme provides new possibilities for precision measurements with ultracold molecules.Comment: 4 pages, 5 figure

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

Landau-Zener Problem for Trilinear Hamiltonians

We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed.Comment: 4.5 pages, 1 figure, transferred to PRA; v2 adds discussion, clarification, and explicit numbers for Na and 87R