Ground state fragmentation of repulsive BEC in double-trap potentials

The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study three-fold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded by two types of outer ones. A many-fold fragmentation is also addressed.Comment: 18 pages + 9 figure

Epidemiology, Diagnosis and Treatment Outcomes of Skin Melanoma in the Republic of Belarus

The primary incidence of skin melanoma in the Republic of Belarus over 25 years (from 1991 through 2015) has increased 3.3-fold (from 2.6 to 9.0 per 100,000 population). A higher level of urban population incidence, a large proportion of people affected at the employable age. In 2015 the proportion of prognostically unfavourable pT3-pT4 neoplasms was 38.2%. Metastatic disease was detected in 12.4% of the patients. Methodology: Material of the paper is based on the data of Belarusian Cancer Registry using the principles of data collection, monitoring and processing recommended by the IARC. Results: The proportion of stage IB neoplasms made up almost one third of the cases assigned to stage I. Of the cases assigned to stage II, the proportion of neoplasms with a high prognostic index of metastatic spread (T3b-T4b) was more than 70%. The recurrence rate is 15.1% even at melanoma invasion depth of up to 1 mm (with ulceration), while it rises to 32.4% at pT2b. The cumulative 5-year disease-specific survival of all patients in 2005 was 54.1 ± 1.5%, and in 2015 it was 64.0±2.2%. Conclusion: A strong correlation is observed between survival of patients and the extent of invasion and ulceration of the primary focus. For metastasis-free pT1a melanoma, the 5-year survival was 92.2%, for T1b – 79.9%, for pT2b – 72.5%, for pT3b – 55.1%, for pT4b – 49.1%. According to the Cancer Registry data, ulceration of the primary neoplasm is frequently observed: it amounts to 41.1% of the cases with melanoma invasion depth up to 2 mm (pT2), to 55.9% with 2-4 mm (pT3) and to 76.3% with the tumor thickness of more than 4 mm (pT4)

Stereoelectronic effects in RNase-catalysed reactions of dinucleoside phosphate cleavage

AbstractThe rate at which dinucleoside phosphates are cleaved by RNases is supposed to be determined by the mole fraction of enzyme-substrate complexes in which the phosphodiester moiety of a dinucleoside phosphate has a highly reactive conformation. The mole fraction of such complexes for a particular RNase depends on the nature of a nucleoside at the O5'-end of the phosphodiester bond. Experimental data are presented to support this hypothesis

Resonance Lifetimes from Complex Densities

The ab-initio calculation of resonance lifetimes of metastable anions challenges modern quantum-chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex "density" that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density

Non-Hermitian Rayleigh-Schroedinger Perturbation Theory

We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the single- and the multireference case to tackle both the many-body problem and the decay problem encountered, for example, in the study of electronic resonances in molecules. A complex absorbing potential (CAP) is employed to facilitate a treatment of resonance states that is similar to the well-established bound-state techniques. For the perturbative approach, the full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned according to the Epstein-Nesbet scheme. The equations we derive in the framework of the single-reference perturbation theory turn out to be identical to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The multireference perturbation theory is studied for a model problem and is shown to be an efficient and accurate method. Algorithmic aspects of the integration of the perturbation theories into existing ab initio programs are discussed, and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review

Time independent description of rapidly oscillating potentials

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency ($\omega$) to order $\omega^{-4}$. The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order $\omega^{-2}$. The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploration of the dynamics of cold atoms.Comment: 4 pages, 1 figure. Revised versio

Searching for three-nucleon resonances

We search for three-neutron resonances which were predicted from pion double charge exchange experiments on He-3. All partial waves up to J=5/2 are nonresonant except the J=3/2^+ one, where we find a state at E=14 MeV energy with 13 MeV width. The parameters of the mirror state in the three-proton system are E=15 MeV and Gamma=14 MeV. The possible existence of an excited state in the triton, which was predicted from a H(He-6,alpha) experiment, is also discussed.Comment: LaTex with RevTe

Convergence and completeness for square-well Stark resonant state expansions

In this paper we investigate the completeness of the Stark resonant eigenstates for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well. By analyzing the asymptotic form of the terms in these expansions we prove some results on the relation between smoothness of target functions and the rate of convergence of the corresponding resonant state expansion

Theory of x-ray absorption by laser-dressed atoms

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected electrons are treated with a complex absorbing potential that is derived from smooth exterior complex scaling. The solution to the two-color (x-ray plus laser) problem is discussed in terms of a direct diagonalization of the complex symmetric matrix representation of the Hamiltonian. Alternative treatments with time-independent and time-dependent non-Hermitian perturbation theories are presented that exploit the weak interaction strength between x rays and atoms. We apply the theory to study the photoabsorption cross section of krypton atoms near the K edge. A pronounced modification of the cross section is found in the presence of the optical laser.Comment: 13 pages, 3 figures, 1 table, RevTeX4, corrected typoe

Effective Hamiltonian and unitarity of the S matrix

The properties of open quantum systems are described well by an effective Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the closed system with discrete eigenstates and the coupling matrix $W$ between discrete states and continuum. The eigenvalues of ${\cal H}$ determine the poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$ between the eigenstates $k$ of ${\cal H}$ and the continuum may be very different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the \TW_k^{cc'} depend on energy in a non-trivial manner, that conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighbourhood of, respectively, avoided level crossings in the complex plane and double poles of the $S$ matrix are given.Comment: 17 pages, 7 figure