On the ground state of free and random discrete Hamiltonians perturbed by an operator of rank one for a critical value of the coupling constant

1998 ◽  
Vol 114 (1) ◽  
pp. 73-80
Author(s):  
S. V. Savchenko
Keyword(s):  
Ground State ◽  
Critical Value ◽  
Coupling Constant ◽  
Rank One

scholarly journals THERMODYNAMICAL PHASES OF A REGULAR SAdS BH

2013 ◽  
Vol 22 (03) ◽  
pp. 1350010 ◽  
Author(s):  
ANAIS SMAILAGIC ◽  
EURO SPALLUCCI
Keyword(s):  
Ground State ◽  
Weak Coupling ◽  
Critical Value ◽  
Minimal Length ◽  
Coupling Constant ◽  
Weak Coupling Regime ◽  
Pure Radiation ◽  
First Order ◽  
Different Temperatures ◽  
First Order Phase

This paper studies the thermodynamical stability of regular BHs in AdS5 background. We investigate off-shell free energy of the system as a function of temperature for different values of a "coupling constant" [Formula: see text], where the cosmological constant is Λ = -3/l2 and [Formula: see text] is "minimal length." The parameter [Formula: see text] admits a critical value, [Formula: see text], corresponding to the appearance of an inflexion point in the Hawking temperature. In the weak-coupling regime [Formula: see text], there are first-order phase transitions at different temperatures. Unlike the Hawking–Page case, at temperature 0 ≤ T ≤ T min the ground state is populated by "cold" near-extremal BHs instead of a pure radiation. On the other hand, for [Formula: see text], only large, thermodynamically stable BHs exist.

ON THE VACUUM STABILITY IN THE SUPERRENORMALIZED YUKAWA-TYPE THEORY

1990 ◽  
Vol 05 (03) ◽  
pp. 531-541
Author(s):  
G.V. EFIMOV ◽  
G. GANBOLD
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Effective Potential ◽  
Ground State ◽  
Type Theory ◽  
Critical Value ◽  
Coupling Constant ◽  
Vacuum Stability ◽  
Expectation Value ◽  
The Stability

The stability of the ground state and the possibility of the appearance of a phase transition in the superrenormalizable nonlocal Yukawa-type field theory are investigated. A variational estimation of the upper bound for the effective potential is obtained. It is shown that there exists a finite critical value for the boson-fermion coupling constant. The initial vacuum becomes unstable when this coupling constant exceeds the critical value. As a result, the system under consideration goes into the phase with nonvanishing expectation value of the field.

TIGHT-BINDING MODEL FOR THE QUANTUM LADDER IN A MAGNETIC FIELD

1996 ◽  
Vol 10 (28) ◽  
pp. 3827-3856 ◽  
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Tight Binding ◽  
Critical Value ◽  
Tight Binding Model ◽  
Binding Model ◽  
First Case

A tight-binding model is formulated for the calculation of the electronic structure and the ground state energy of the quantum ladder under a magnetic field, where the magnetic flux at the nth plaquette is given by ϕn. First, the theory is applied to obtain the electronic spectra of the quantum ladder models with particular magnetic fluxes such as uniform magnetic fluxes, ϕn=0 and 1/2, and the staggered magnetic flux, ϕn= (−1)n+1ϕ0. From these, it is found that as the effect of electron hopping between two chains—the anisotropy parameter r=ty/tx—is increased, there are a metal-semimetal transition at r=0 and a semimetal–semiconductor transition at r=2 in the first case, and metal-semiconductor transitions at r=0 in the second and third cases. These transitions are thought of as a new category of metal-insulator transition due to the hopping anisotropy of the system. Second, using the spectrum, the ground state energy is calculated in terms of the parameter r. It is found that the ground state energy in the first case diverges as r becomes arbitrarily large, while that in the second and third cases can have the single or double well structure with respect to r, where the system is stable at some critical value of r=rc and the transition between the single and double well structures is associated with whether tx is less than a critical value of txc. The latter cases are very reminiscent of physics in polyacetylene studied by Su, Schrieffer and Heeger.

SUPER SYMMETRY IN STRONG AND WEAK INTERACTIONS

2010 ◽  
Vol 19 (02) ◽  
pp. 263-280
Author(s):  
U. V. S. SESHAVATHARAM ◽  
S. LAKSHMINARAYANA
Keyword(s):  
Ground State ◽  
Crucial Role ◽  
Weak Interactions ◽  
Light Quark ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Mass Generation ◽  
Super Symmetry ◽  
Charged Boson ◽  
Charged Mesons

For strong interaction two new fermion mass units 105.32 MeV and 11450 MeV are assumed. Existence of "Integral charge quark bosons", "Integral charge effective quark fermions", "Integral charge (effective) quark fermi-gluons" and "Integral charge quark boso-gluons" are assumed and their masses are estimated. It is noticed that, characteristic nuclear charged fermion is Xs · 105.32 = 938.8 MeV and corresponding charged boson is Xs(105.32/x) = 415.0 where Xs = 8.914 is the inverse of the strong coupling constant and x = 2.26234 is a new number by using which "super symmetry" can be seen in "strong and weak" interactions. 11450 MeV fermion and its boson of mass = 11450/x = 5060 MeV plays a crucial role in "sub quark physics" and "weak interaction". 938.8 MeV strong fermion seems to be the proton. 415 MeV strong boson seems to be the mother of the presently believed 493,496 and 547 MeV etc, strange mesons. With 11450 MeV fermion "effective quark-fermi-gluons" and with 5060 MeV boson "quark boso-gluon masses" are estimated. "Effective quark fermi-gluons" plays a crucial role in ground state charged baryons mass generation. Light quark bosons couple with these charged baryons to form doublets and triplets. "Quark boso-gluons" plays a crucial role in ground state neutral and charged mesons mass generation. Fine and super-fine rotational levels can be given by [I or (I/2)] power(1/4) and [I or (I/2)] power(1/12) respectively. Here, I = n(n+1) and n = 1, 2, 3, ….

Theory of Brueckner and Sawada Applied to a Many-Boson Model

1973 ◽  
Vol 51 (3) ◽  
pp. 292-301 ◽  
Author(s):  
M. Razavy ◽  
E. S. Krebes
Keyword(s):  
Ground State ◽  
Transition Point ◽  
Matrix Formalism ◽  
Coupling Constant ◽  
Bogoliubov Approximation ◽  
Wide Range ◽  
Simple Change ◽  
Boson Model ◽  
Repulsive Forces ◽  
Range Of Values

The Bassichis–Foldy model of a simple interacting boson is solved numerically and the results are compared with those obtained by the Bogoliubov approximation and by the Brueckner–Sawada t-matrix formalism. In the normal region, contrary to the widely held view, the Brueckner–Sawada approximation for the energy of the ground state is not reliable for strong, well-behaved, repulsive forces. The Bogoliubov approximation, on the other hand, remains valid for a wide range of values of the coupling constant. In the inverted region, the attractive force causes a population inversion in the levels of the system. For this case a modified Brueckner–Sawada approximation is developed. This method is applied to the calculation of the transition point and the energies of the ground and the first excited states of the system. Here most of the predictions of the modified Brueckner–Sawada approximation are quite accurate. By a simple change in the Bassichis–Foldy model it is shown that even, for two bosons there can be a phase transition. In this model, the derivative of the ground state energy with respect to the coupling constant is discontinuous at the transition point.

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.

scholarly journals Asymptotic Behavior and Critical Coupling in Scalar Yukawa Model

2018 ◽  
Vol 47 ◽  
pp. 1860095
Author(s):  
V. E. Rochev
Keyword(s):  
Asymptotic Behavior ◽  
Matrix Model ◽  
Critical Value ◽  
Leading Order ◽  
Coupling Constant ◽  
Critical Coupling ◽  
Yukawa Model ◽  
Four Dimensions ◽  
Euclidean Region ◽  
Vector Matrix

The solution of the equation for the pion propagator in the leading order of the [Formula: see text] – expansion for a vector-matrix model with interaction [Formula: see text] in four dimensions shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant.

scholarly journals A Solvable Twisted One-Plaquette Model

1997 ◽  
Vol 12 (15) ◽  
pp. 2741-2762 ◽  
Author(s):  
M. Billó ◽  
A. D'Adda
Keyword(s):  
Phase Transition ◽  
Heat Kernel ◽  
Quantum Fluctuations ◽  
Critical Value ◽  
Classical Solutions ◽  
Coupling Constant ◽  
Time Direction ◽  
Distribution Of Eigenvalues ◽  
Kernel Model ◽  
Link Variable

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the timelike link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the Hamiltonian limit, and the related Douglas–Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, and compare it to previous results by Karsch.

Infrared laser spectroscopy of free radicals and ions. III. The v 3 band of NF 2 (X̃ 2 B 1 )

1984 ◽  
Vol 393 (1805) ◽  
pp. 397-408 ◽  
Keyword(s):  
Free Radicals ◽  
Ground State ◽  
Diode Lasers ◽  
Spin Rotation ◽  
Coriolis Coupling ◽  
Coupling Constant ◽  
Coriolis Interaction ◽  
Rotational Distortion ◽  
Infrared Laser Spectroscopy ◽  
Tunable Diode Lasers

The v 3 band of NF 2 (X̃ 2 B 1 ) has been measured at high resolution by using tunable diode lasers. Rotational, distortion and spin-rotation constants have been derived for the v 3 = 1 state by using ground state constants derived earlier from analysis of the v 1 band. The position of the band centre, not previously measured, is 942.481 53(30) cm -1 . Analysis of the v 1 — v 3 Coriolis interaction yields the Coriolis coupling constant ξ 13 = 0.698(10).

2D ISING MODEL WITH COMPETING INTERACTIONS AND ITS APPLICATION TO CLUSTERS AND ARRAYS OF π-RINGS, GRAPHENE AND ADIABATIC QUANTUM COMPUTING

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3951-3967 ◽  
Author(s):  
ANTHONY O'HARE ◽  
F. V. KUSMARTSEV ◽  
K. I. KUGEL
Keyword(s):  
Quantum Computing ◽  
Ising Model ◽  
Ground State ◽  
Honeycomb Lattice ◽  
Graphene Plane ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Competing Interactions ◽  
Adiabatic Quantum Computing ◽  
Ising Spins

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

Sign in / Sign up

Export Citation Format

Share Document