ON THE SCATTERING THEORY OF MASSLESS NELSON MODELS

2002 ◽  
Vol 14 (11) ◽  
pp. 1165-1280 ◽  
Author(s):  
C. GÉRARD
Keyword(s):  
Scattering Theory ◽  
Bound States ◽  
Relativistic Quantum ◽  
Asymptotic Completeness ◽  
Induced Representations ◽  
Vacuum States ◽  
Relativistic Atom ◽  
Propagation Properties ◽  
Invariant Spaces

We study the scattering theory for a class of non-relativistic quantum field theory models describing a confined non-relativistic atom interacting with a massless relativistic bosonic field. We construct invariant spaces [Formula: see text] which are defined in terms of propagation properties for large times and which consist of states containing a finite number of bosons in the region {|x| ≥ ct} for t → ±∞. We show the existence of asymptotic fields and we prove that the associated asymptotic CCR representations preserve the spaces [Formula: see text] and induce on these spaces representations of Fock type. For these induced representations, we prove the property of geometric asymptotic completeness, which gives a characterization of the vacuum states in terms of propagation properties. Finally we show that a positive commutator estimate imply the asymptotic completeness property, i.e. the fact that the vacuum states of the induced representations coincide with the bound states of the Hamiltonian.

scholarly journals Propagation properties in scattering theory

1980 ◽  
Vol 21 (4) ◽  
pp. 474-485 ◽  
Author(s):  
Derek W. Robinson
Keyword(s):  
Ergodic Theorem ◽  
Scattering Theory ◽  
Bound States ◽  
Semi Group ◽  
Easy Consequence ◽  
Scattering States ◽  
Mean Ergodic Theorem ◽  
The Mean ◽  
Propagation Properties

AbstractGeneralizations of the Green-Lanford-Dollard theorem on scattering into cones and Ruelle-Amerin-Georgescu theorem characterizing bound states and scattering states are derived. The first is shown to be an easy consequence of the Kato-Trotter theorem on semi-group convergence whilst the latter is corollary of Wiener's version of the mean ergodic theorem.

scholarly journals SPECTRAL AND SCATTERING THEORY FOR SOME ABSTRACT QFT HAMILTONIANS

2009 ◽  
Vol 21 (03) ◽  
pp. 373-437 ◽  
Author(s):  
C. GÉRARD ◽  
A. PANATI
Keyword(s):  
Scattering Theory ◽  
Bound States ◽  
Fock Space ◽  
Asymptotic Completeness ◽  
Decay Properties ◽  
Abstract Class ◽  
Mourre Estimate ◽  
Spectral And Scattering Theory ◽  
Wick Polynomial ◽  
Asymptotic Fields

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form H = dΓ(ω) + V acting on the bosonic Fock space Γ(𝔥), where ω is a massive one-particle Hamiltonian acting on 𝔥 and V is a Wick polynomial Wick(w) for a kernel w satisfying some decay properties at infinity. We describe the essential spectrum of H, prove a Mourre estimate outside a set of thresholds and prove the existence of asymptotic fields. Our main result is the asymptotic completeness of the scattering theory, which means that the CCR representations given by the asymptotic fields are of Fock type, with the asymptotic vacua equal to the bound states of H. As a consequence, H is unitarily equivalent to a collection of second quantized Hamiltonians.

scholarly journals Database of ab initio L-edge X-ray absorption near edge structure

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yiming Chen ◽  
Chi Chen ◽  
Chen Zheng ◽  
Shyam Dwaraknath ◽  
Matthew K. Horton ◽  
...  
Keyword(s):  
High Throughput ◽  
Scattering Theory ◽  
Research Community ◽  
Metal Compounds ◽  
Edge Structure ◽  
X Ray ◽  
Initial Release ◽  
Computational Workflow ◽  
X Ray Absorption

AbstractThe L-edge X-ray Absorption Near Edge Structure (XANES) is widely used in the characterization of transition metal compounds. Here, we report the development of a database of computed L-edge XANES using the multiple scattering theory-based FEFF9 code. The initial release of the database contains more than 140,000 L-edge spectra for more than 22,000 structures generated using a high-throughput computational workflow. The data is disseminated through the Materials Project and addresses a critical need for L-edge XANES spectra among the research community.

scholarly journals Electromagnetic Gauge Choice for Scattering of Schrödinger Particle

2019 ◽  
Vol 20 (11) ◽  
pp. 3633-3650
Author(s):  
Andrzej Herdegen
Keyword(s):  
Asymptotic Behavior ◽  
External Electromagnetic Field ◽  
Asymptotic Completeness ◽  
Free Evolution ◽  
Wave Operators ◽  
Radiation Fields ◽  
Mechanical Evolution ◽  
Scattering Wave ◽  
Free Fields

Abstract We consider a Schrödinger particle placed in an external electromagnetic field of the form typical for scattering settings in the field theory: $$F=F^\mathrm {ret}+F^\mathrm {in}=F^\mathrm {adv}+F^\mathrm {out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm {ret}/\mathrm {adv}}$$ F ret / adv has the past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm {in}/\mathrm {out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show that with appropriate choice of electromagnetic gauge the particle has ‘in’ and ‘out’ states reached with no further modification of the asymptotic dynamics. We use a special quantum mechanical evolution ‘picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ , and thus the scattering wave operators do not need the free evolution counteraction. The existence of wave operators in this setting is established, but the proof of asymptotic completeness is not complete: more precise characterization of the asymptotic behavior of the particle for $$|\mathbf {x}|=|t|$$ | x | = | t | would be needed.

Nuclear Physics Methods for Problems in Relativistic Quantum Mechanics

1998 ◽  
Vol 07 (05) ◽  
pp. 559-571
Author(s):  
Marcos Moshinsky ◽  
Verónica Riquer
Keyword(s):  
Quantum Mechanics ◽  
Nuclear Physics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Variational Parameter ◽  
Approximate Methods ◽  
Rest Energy ◽  
Quark Models

Atomic and molecular physicists have developed extensive and detailed approximate methods for dealing with the relativistic versions of the Hamiltonians appearing in their fields. Nuclear physicists were originally more concerned with non-relativistic problems as the energies they were dealing with were normally small compared with the rest energy of the nucleon. This situation has changed with the appearance of the quark models of nucleons and thus the objective of this paper is to use the standard variational procedures of nuclear physics for problems in relativistic quantum mechanics. The 4 × 4α and β matrices in the Dirac equation are replaced by 2 × 2 matrices, one associated with ordinary spin and the other, which we call sign spin, is mathematically identical to the isospin of nuclear physics. The states on which our Hamiltonians will act will be the usual harmonic oscillator ones with ordinary and sign spin and the frequency ω of the oscillator will be our only variational parameter. The example discussed as an illustration will still be the Coulomb problem as the exact energies of the relativistic bound states are available for comparison. A gap of the order of 2mc2 is observed between states of positive and negative energy, that permits the former to be compared with the exact results.

scholarly journals GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

2000 ◽  
Vol 12 (04) ◽  
pp. 475-560 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
OLAF DREYER ◽  
MARTIN FLORIG ◽  
STEPHEN J. SUMMERS
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Algebraic Characterization ◽  
Symmetry Groups ◽  
De Sitter ◽  
Vacuum States ◽  
Point Transformations ◽  
Projective Representations ◽  
Modular Covariance

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times — four-dimensional Minkowski and three-dimensional de Sitter spaces — for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

Structural characterization of nitric oxide-bound soluble Guanylate Cyclase using resonance Raman spectroscopy

2013 ◽  
Vol 17 (03) ◽  
pp. 240-246
Author(s):  
Biswajit Pal ◽  
Katsuhiro Tanaka ◽  
Shigeo Takenaka ◽  
Tajith B. Shaik ◽  
Teizo Kitagawa
Keyword(s):  
Nitric Oxide ◽  
Raman Spectroscopy ◽  
Guanylate Cyclase ◽  
Protein Interactions ◽  
Bound States ◽  
Soluble Guanylate Cyclase ◽  
Resonance Raman Spectroscopy ◽  
Resonance Raman ◽  
Bending Modes

Mammalian soluble Guanylate Cyclase (sGC), working as a physiological NO receptor, is investigated using resonance Raman spectroscopy for NO bound states with different saturation levels in the presence and absence of effectors. The Fe–NO (νFe–NO) and N–O (νN-O) stretching bands appeared at 521 and 1681 cm-1, respectively, without effectors, but νN-O was split into 1681 and 1699 cm-1 in the presence of GTP and shifted to 1687 cm-1 in the presence of YC-1 or BAY 41-2272, while νFe-NO remained unaltered. The split two νN-O bands were independent of NO saturation levels. GTP or YC-1/BAY 41-2272 altered the vinyl and propionate bending modes from 423 to 399 cm-1 and 376 to 367 cm-1, respectively. Based on these observations, allosteric effects on NO …protein interactions are discussed.

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