Constructing a partially transparent computational boundary for UPPE using leaky modes

In this paper we introduce a method for creating a transparent computational boundary for the simulation of unidirectional propagation of optical beams and pulses using leaky modes. The key element of the method is the introduction of an artificial-index material outside a chosen computational domain and utilization of the quasi-normal modes associated with such artificial structure. The method is tested on the free space propagation of TE electromagnetic waves. By choosing the material to have appropriate optical properties one can greatly reduce the reflection at the computational boundary. In contrast to the well-known approach based on a perfectly matched layer, our method is especially well suited for spectral propagators.Comment: 32 pages, 19 figure

Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles

In analogy to Gamow vectors that are obtained from first order resonance poles of the S-matrix, one can also define higher order Gamow vectors which are derived from higher order poles of the S-matrix. An S-matrix pole of r-th order at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ... , r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher order poles, the microphysical state obeys a purely exponential decay law.Comment: 39 pages, 3 PostScript figures; sub2.eps may stall some printers and should then be printed out separately; ghostview is o.

The mystery of relationship of mechanics and field in the many-body quantum world

We have revealed three fatal errors incurred from a blind transferring of quantum field methods into the quantum mechanics. This had tragic consequences because it produced crippled model Hamiltonians, unfortunately considered sufficient for a description of solids including superconductors. From there, of course, Fr\"ohlich derived wrong effective Hamiltonian, from which incorrect BCS theory arose. 1) Mechanical and field patterns cannot be mixed. Instead of field methods applied to the mechanical Born-Oppenheimer approximation we have entirely to avoid it and construct an independent and standalone field pattern. This leads to a new form of the Bohr's complementarity on the level of composite systems. 2) We have correctly to deal with the center of gravity, which is under the field pattern "materialized" in the form of new quasipartiles - rotons and translons. This leads to a new type of relativity of internal and external degrees of freedom and one-particle way of bypassing degeneracies (gap formation). 3) The possible symmetry cannot be apriori loaded but has to be aposteriori obtained as a solution of field equations, formulated in a general form without translational or any other symmetry. This leads to an utterly revised view of symmetry breaking in non-adiabatic systems, namely Jahn-Teller effect and superconductivity. These two phenomena are synonyms and share a unique symmetry breaking.Comment: 24 pages, 9 sections; remake of abstract, introduction and conclusion; more physics, less philosoph

The Importance of Boundary Conditions in Quantum Mechanics

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we rephrase Feynman's $+i \epsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i \epsilon$ prescription with the arrow of time of Quantum Electrodynamics. A parallel of this arrow of time with that of Classical Electrodynamics is made. We conclude that in general, the time evolution of a closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible Quantum Dynamics," Trieste, Italy, July 200

Entanglement properties of bound and resonant few-body states

Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom systems, research on correlation effects in other artificially fabricated few-body systems, such as quantum dots or electromagnetically trapped ions, is currently underway or in planning. Generally, the systems studied in these experiments may be considered as composed of a small number of interacting elements with controllable and highly tunable parameters, effectively described by Schr\"odinger equation. In this way, parallel theoretical and experimental studies of few-body models become possible, which may provide a deeper understanding of correlation effects and give hints for designing and controlling new experiments. Of particular interest is to explore the physics in the strongly correlated regime and in the neighborhood of critical points. Particle correlations in nanostructures may be characterized by their entanglement spectrum, i.e. the eigenvalues of the reduced density matrix of the system partitioned into two subsystems. We will discuss how to determine the entropy of entanglement spectrum of few-body systems in bound and resonant states within the same formalism. The linear entropy will be calculated for a model of quasi-one dimensional Gaussian quantum dot in the lowest energy states. We will study how the entanglement depends on the parameters of the system, paying particular attention to the behavior on the border between the regimes of bound and resonant states.Comment: 22 pages, 3 figure

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

Sub-threshold resonances in few-neutron systems

Three- and four-neutron systems are studied within the framework of the hyperspherical approach with a local S-wave nn-potential. Possible bound and resonant states of these systems are sought as zeros of three- and four-body Jost functions in the complex momentum plane. It is found that zeros closest to the origin correspond to sub-threshold (nnn) (1/2-) and (nnnn) (0+) resonant states. The positions of these zeros turned out to be sensitive to the choice of the $nn$--potential. For the Malfliet- Tjon potential they are E(nnn)=-4.9-i6.9 (MeV) and E(nnnn)=-2.6-i9.0 (MeV). Movement of the zeros with an artificial increase of the potential strength also shows an extreme sensitivity to the choice of potential. Thus, to generate ^3n and ^4n bound states, the Yukawa potential needs to be multiplied by 2.67 and 2.32 respectively, while for the Malfliet-Tjon potential the required multiplicative factors are 4.04 and 3.59.Comment: Latex, 22 pages, no PS-figures, submitted to J.Phys.

Localization of shadow poles by complex scaling

Through numerical examples we show that the complex scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be revealed and the Riemann sheets on which they reside can be identified.Comment: 6 pages, Latex with Revtex, 3 figures (not included) available on reques