scholarly journals STABILITY OF GROUND STATES IN SECTORS AND ITS APPLICATION TO THE WIGNER–WEISSKOPF MODEL

2001 ◽  
Vol 13 (04) ◽  
pp. 513-528 ◽  
Author(s):  
ASAO ARAI ◽  
MASAO HIROKAWA
Keyword(s):  
Excited State ◽  
Scalar Field ◽  
Ground State ◽  
Adjoint Operator ◽  
Ground States ◽  
The Other ◽  
Coupling Constant ◽  
A Value ◽  
First Excited State ◽  
The One

We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator: the one is concerned with the sector to which the ground state belongs and the other is about the uniqueness of the ground state. As an application to the Wigner–Weisskopf model which describes one mode fermion coupled to a quantum scalar field, we prove in the massive case the following: (a) For a value of the coupling constant, the Wigner–Weisskopf model has degenerate ground states; (b) for a value of the coupling constant, the Wigner–Weisskopf model has a first excited state with energy level below the bottom of the essential spectrum. These phenomena are nonperturbative.

A meta-analysis and review examining a possible role for oxidative stress and singlet oxygen in diverse diseases

2017 ◽  
Vol 474 (16) ◽  
pp. 2713-2731 ◽  
Author(s):  
Athinoula L. Petrou ◽  
Athina Terzidaki
Keyword(s):  
Oxidative Stress ◽  
Excited State ◽  
Singlet Oxygen ◽  
Ground State ◽  
Meta Analysis ◽  
Common Mechanism ◽  
High Electron ◽  
A Value ◽  
First Excited State

From kinetic data (k, T) we calculated the thermodynamic parameters for various processes (nucleation, elongation, fibrillization, etc.) of proteinaceous diseases that are related to the β-amyloid protein (Alzheimer's), to tau protein (Alzheimer's, Pick's), to α-synuclein (Parkinson's), prion, amylin (type II diabetes), and to α-crystallin (cataract). Our calculations led to ΔG≠ values that vary in the range 92.8–127 kJ mol−1 at 310 K. A value of ∼10–30 kJ mol−1 is the activation energy for the diffusion of reactants, depending on the reaction and the medium. The energy needed for the excitation of O2 from the ground to the first excited state (1Δg, singlet oxygen) is equal to 92 kJ mol−1. So, the ΔG≠ is equal to the energy needed for the excitation of ground state oxygen to the singlet oxygen (1Δg first excited) state. The similarity of the ΔG≠ values is an indication that a common mechanism in the above disorders may be taking place. We attribute this common mechanism to the (same) role of the oxidative stress and specifically of singlet oxygen, (1Δg), to the above-mentioned processes: excitation of ground state oxygen to the singlet oxygen, 1Δg, state (92 kJ mol−1), and reaction of the empty π* orbital with high electron density regions of biomolecules (∼10–30 kJ mol−1 for their diffusion). The ΔG≠ for cases of heat-induced cell killing (cancer) lie also in the above range at 310 K. The present paper is a review and meta-analysis of literature data referring to neurodegenerative and other disorders.

PROPERTIES OF LEVELS AT 6.69 AND 6.88–6.89 MeV IN 28Si

1966 ◽  
Vol 44 (5) ◽  
pp. 1087-1097 ◽  
Author(s):  
R. J. A. Levesque ◽  
R. W. Ollerhead ◽  
E. W. Blackmore ◽  
J. A. Kuehner
Keyword(s):  
Excited State ◽  
Alpha Particle ◽  
Ground State ◽  
State Transition ◽  
Gamma Ray ◽  
The Other ◽  
Ground State Transition ◽  
Angular Correlations ◽  
First Excited State ◽  
Strong Ground

Levels at 6.69, 6.88, and 6.89 MeV were observed in the 16O(16O, α)28Si reaction, and angular correlations were measured for the resulting gamma-ray transitions, using the geometry in which the alpha particle is detected at 0°. The level at 6.69 MeV had not been reported previously and was assigned spin and parity 0+. The doublet of levels at 6.88–6.89 MeV was not resolved in these measurements, but angular correlations of the gamma-ray transitions were possible, using spectrum subtraction techniques. One member of the doublet, previously assigned spin 3, has a strong ground-state transition; the angular correlation for this transition confirms a 3− assignment to this level. The other member of the doublet, which decays almost entirely to the first excited state, could not be assigned a spin on the basis of these measurements. However, taken in conjunction with other measurements, an assignment of 4+ is favored.

scholarly journals LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED

2003 ◽  
Vol 15 (03) ◽  
pp. 271-312 ◽  
Author(s):  
FUMIO HIROSHIMA
Keyword(s):  
Radiation Field ◽  
Ground State ◽  
Fock Space ◽  
Adjoint Operator ◽  
Ground States ◽  
Electron System ◽  
Number Operator ◽  
Position Variable ◽  
Boson Fock Space ◽  
Quantized Radiation Field

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2 (ℝ3) ⊗ ℱ ≅ L2 (ℝ3; ℱ), where ℱ is the Boson Fock space over L2 (ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to [Formula: see text], where N denotes the number operator of ℱ. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ‖(1 ⊗ Nk/2) ψg (x)‖ℱ ≤ Dk e-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular [Formula: see text] for 0 < β < δ/2 is obtained.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

Expressions

1994 ◽  
Author(s):  
Douglas Schenck ◽  
Peter Wilson
Keyword(s):  
Correct Answer ◽  
Partial Evaluation ◽  
The Other ◽  
Complete Evaluation ◽  
A Value ◽  
Null Value ◽  
Evaluation Exercise ◽  
The One ◽  
Expected Evaluation

Expressions are combinations of operators and operands which are evaluated to produce a value of a specific type. Infix operators require two operands with an operator written between them. A prefix operator requires one operand with an operator written before it. (The expression syntax starts on page 208.) Evaluation proceeds from left to right, governed by the precedence of the operators. The lowest numbered precedence as shown in Table 14.1 is evaluated first. Operators in the same row have the same precedence. Expressions enclosed by parentheses are evaluated before being treated as a single operand. An operand between two operators of different precedence is bound to the operator with the higher one; e.g., −10*20 means (−10)*20. An operand between two operators of the same precedence is bound to the one on the left; e.g., 10/20 * 30 means (10/20) * 30. Exercise 14.1 Work out the intermediate steps for this expression: … −2/(4+4)*5+6… When a null value is encountered in an expression where a non-null is expected, evaluation is short circuited and a null answer is produced. Otherwise, all expressions are fully evaluated even when the outcome is known after partial evaluation. Exercise 14.2 Can you think of an expression that does not require complete evaluation to get the correct answer? The operands of an operator must be compatible with the operator and with each other. Operands can be compatible without having identical types and are compatible when any of these conditions are satisfied: • The types are the same. • One type is a subtype of the other (e.g., one is a number and the other is an integer. • Both types are strings. • Both types are binaries. • Both types are arrays which have compatible base types and identical bounds. • Both types are bags which have compatible base types. • Both types are lists which have compatible base types. • Both types are sets which have compatible base types. Operations are organized by the kind of result they produce, namely: numeric, boolean or logical, string or binary, or aggregate.

scholarly journals Spectral Theory for a Mathematical Model of the Weak Interaction—Part I: The Decay of the Intermediate Vector BosonsW±

2009 ◽  
Vol 2009 ◽  
pp. 1-52 ◽  
Author(s):  
J.-M. Barbaroux ◽  
J.-C. Guillot
Keyword(s):  
Ground State ◽  
State Energy ◽  
Fock Space ◽  
Adjoint Operator ◽  
Weak Decay ◽  
Spectral Interval ◽  
Coupling Constant ◽  
Small Coupling ◽  
Small Coupling Constant ◽  
Intermediate Vector

We consider a Hamiltonian with cutoffs describing the weak decay of spin 1 massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a Mourre estimate and a limiting absorption principle above the ground state energy and below the first threshold for a sufficiently small coupling constant. As a corollary, we prove the absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.

LIFETIME MEASUREMENTS OF STATES IN O18 AND Ne22

1964 ◽  
Vol 42 (6) ◽  
pp. 1311-1323 ◽  
Author(s):  
M. A. Eswaran ◽  
C. Broude
Keyword(s):  
Excited State ◽  
Ground State ◽  
Doppler Shift ◽  
State Transition ◽  
Branching Ratios ◽  
Ground State Transition ◽  
Lifetime Measurements ◽  
Doppler Shift Attenuation ◽  
First Excited State ◽  
Doppler Shift Attenuation Method

Lifetime measurements have been made by the Doppler-shift attenuation method for the 1.98-, 3.63-, 3.92-, and 4.45-Mev states in O18 and the 1.28-, 3.34-, and 4.47-Mev states in Ne22, excited by the reactions Li7(C12, pγ)O18 and Li7(O16, pγ)Ne22. Branching ratios have also been measured. The results are tabulated.[Formula: see text]The decay of the 3.92-Mev state in O18 is 93.5% to the 1.98-Mev state and 6.5% to the ground state and of the 4.45-Mev state 74% to the 3.63-Mev state, 26% to the 1.98-Mev state, and less than 2% to the ground state. In Ne22, the ground-state transition from the 4.47-Mev state is less than 2% of the decay to the first excited state.

Electroabsorption spectra of push–pull porphyrins in solution and in solid films

2015 ◽  
Vol 19 (01-03) ◽  
pp. 527-534
Author(s):  
Kamlesh Awasthi ◽  
Hung-Yu Hsu ◽  
Hung-Chu Chiang ◽  
Chi-Lun Mai ◽  
Chen-Yu Yeh ◽  
...  
Keyword(s):  
Dipole Moment ◽  
Excited State ◽  
Charge Transfer ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Ground State ◽  
Benzene Solution ◽  
Solid Films ◽  
The One ◽  
Interfacial Charge

Polarized electroabsorption (E-A) spectra of highly efficient porphyrin sensitizers (YD2 and YD2-oC8) have been measured in benzene solution. Polarized E-A spectra of these push–pull porphyrins embedded in poly(methyl methacrylate) films or sensitized on TiO 2 films are also observed. Based on the analysis of the E-A spectra, the magnitude of the electric dipole moment both in the ground state and in the lowest excited state have been evaluated in solution and in solid films. The electric dipole moment in the excited state of these compounds is very large on TiO 2 films, suggesting the interfacial charge transfer on TiO 2 surface following photoexcitation of porphyrin dyes. The electric dipole moment in the excited state evaluated from the E-A spectra is very different from the one evaluated from the electrophotoluminescence spectra on TiO 2, suggesting that the strong local field of TiO 2 films is applied to the fluorescing dyes attached to TiO 2 films.

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