Ground state of the massless Nelson model in a non-Fock representation

2005 ◽  
Vol 46 (10) ◽  
pp. 102107 ◽  
Author(s):  
Itaru Sasaki
Keyword(s):  
Ground State ◽  
Fock Representation ◽  
Nelson Model

scholarly journals GROUND STATE OF THE MASSLESS NELSON MODEL WITHOUT INFRARED CUTOFF IN A NON-FOCK REPRESENTATION

2001 ◽  
Vol 13 (09) ◽  
pp. 1075-1094 ◽  
Author(s):  
ASAO ARAI
Keyword(s):  
Scalar Field ◽  
Ground State ◽  
Coupling Constant ◽  
Fock Representation ◽  
Nelson Model ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Quantum Particles ◽  
Infrared Cutoff ◽  
Massless Quantum

We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical commutation relations. We show that the model has a ground state for all values of the coupling constant even in the case where no infrared cutoff is made. The non-Fock representation used is inequivalent to the Fock one if no infrared cutoff is made.

scholarly journals Absence of ground state for the Nelson model on static space–times

2012 ◽  
Vol 262 (1) ◽  
pp. 273-299 ◽  
Author(s):  
C. Gérard ◽  
F. Hiroshima ◽  
A. Panati ◽  
A. Suzuki
Keyword(s):  
Ground State ◽  
Nelson Model ◽  
Static Space

scholarly journals GROUND STATE PROPERTIES OF THE NELSON HAMILTONIAN: A GIBBS MEASURE-BASED APPROACH

2002 ◽  
Vol 14 (02) ◽  
pp. 173-198 ◽  
Author(s):  
VOLKER BETZ ◽  
FUMIO HIROSHIMA ◽  
JÓZSEF LŐRINCZI ◽  
ROBERT A. MINLOS ◽  
HERBERT SPOHN
Keyword(s):  
Gibbs Measure ◽  
Ground State ◽  
Momentum Space ◽  
Quantum Particle ◽  
Functional Integration ◽  
External Potential ◽  
Space Distribution ◽  
Position Space ◽  
Nelson Model ◽  
Integration Techniques

The Nelson model describes a quantum particle coupled to a scalar Bose field. We study properties of its ground state through functional integration techniques in case the particle is confined by an external potential. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on the distribution of the number of bosons, and on the position space distribution of the particle.

scholarly journals Ground states and associated path measures in the renormalized Nelson model

2021 ◽  
pp. 2250002
Author(s):  
Fumio Hiroshima ◽  
Oliver Matte
Keyword(s):  
Ground State ◽  
Regularity Condition ◽  
Ground States ◽  
Upper And Lower Bounds ◽  
Binding Condition ◽  
Fock Representation ◽  
Continuity Properties ◽  
Strict Positivity ◽  
Boson Number ◽  
Spectral Subspaces

We prove the existence, uniqueness, and strict positivity of ground states of the possibly massless renormalized Nelson operator under an infrared regularity condition and for Kato decomposable electrostatic potentials fulfilling a binding condition. If the infrared regularity condition is violated, then we show non-existence of ground states of the massless renormalized Nelson operator with an arbitrary Kato decomposable potential. Furthermore, we prove the existence, uniqueness, and strict positivity of ground states of the massless renormalized Nelson operator in a non-Fock representation where the infrared condition is unnecessary. Exponential and superexponential estimates on the pointwise spatial decay and the decay with respect to the boson number for elements of spectral subspaces below localization thresholds are provided. Moreover, some continuity properties of ground state eigenvectors are discussed. Byproducts of our analysis are a hypercontractivity bound for the semigroup and a new remark on Nelson’s operator theoretic renormalization procedure. Finally, we construct path measures associated with ground states of the renormalized Nelson operator. Their analysis entails improved boson number decay estimates for ground state eigenvectors, as well as upper and lower bounds on the Gaussian localization with respect to the field variables in the ground state. As our results on uniqueness, positivity, and path measures exploit the ergodicity of the semigroup, we restrict our attention to one matter particle. All results are non-perturbative.

Renilla Bioluminescence: A Morphologic Approach to the Location of Photocytes

1974 ◽  
Vol 32 ◽  
pp. 208-209
Author(s):  
Ben O. Spurlock ◽  
Milton J. Cormier
Keyword(s):  
Excited State ◽  
Ground State ◽  
Molecular Basis ◽  
Light Emission ◽  
Chemical Basis ◽  
Electronic Excited State ◽  
Colonial Form ◽  
The Common ◽  
Eighteenth And Nineteenth Centuries ◽  
Catalyzed Oxidation

The phenomenon of bioluminescence has fascinated layman and scientist alike for many centuries. During the eighteenth and nineteenth centuries a number of observations were reported on the physiology of bioluminescence in Renilla, the common sea pansy. More recently biochemists have directed their attention to the molecular basis of luminosity in this colonial form. These studies have centered primarily on defining the chemical basis for bioluminescence and its control. It is now established that bioluminescence in Renilla arises due to the luciferase-catalyzed oxidation of luciferin. This results in the creation of a product (oxyluciferin) in an electronic excited state. The transition of oxyluciferin from its excited state to the ground state leads to light emission.

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