31 research outputs found
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 prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's 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
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
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
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 --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.
Megascopic Quantum Phenomena. A Critical Study of Physical Interpretations
A megascopic revalidation is offered providing responses and resolutions of
current inconsistencies and existing contradictions in present-day quantum
theory. As the core of this study we present an independent proof of the
Goldstone theorem for a quantum field formulation of molecules and solids.
Along with phonons two types of new quasiparticles appear: rotons and
translons. In full analogy with Lorentz covariance, combining space and time
coordinates, a new covariance is necessary, binding together the internal and
external degrees of freedom, without explicitly separating the centre-of-mass,
which normally applies in both classical and quantum formulations. The
generally accepted view regarding the lack of a simple correspondence between
the Goldstone modes and broken symmetries, has significant consequences: an
ambiguous BCS theory as well as a subsequent Higgs mechanism. The application
of the archetype of the classical spontaneous symmetry breaking, i.e. the
Mexican hat, as compared to standard quantum relations, i.e. the Jahn-Teller
effect, superconductivity or the Higgs mechanism, becomes a disparity. In
short, symmetry broken states have a microscopic causal origin, but transitions
between them have a teleological component. The different treatments of the
problem of the centre of gravity in quantum mechanics and in field theories
imply a second type of Bohr complementarity on the many-body level opening the
door for megascopic representations of all basic microscopic quantum axioms
with further readings for teleonomic megascopic quantum phenomena, which have
no microscopic rationale: isomeric transitions, Jahn-Teller effect, chemical
reactions, Einstein-de Haas effect, superconductivity-superfluidity, and
brittle fracture.Comment: 117 pages, 17 sections, final revised version from 20 May 2019 but
uploaded after the DOI was know