Weakly Coupled Bound States

2015 ◽  
pp. 161-211
Author(s):  
Pavel Exner ◽  
Hynek Kovařík
Keyword(s):  
Bound States ◽  
Weakly Coupled

Wave functions for weakly coupled bound states

1982 ◽  
Vol 25 (5) ◽  
pp. 2467-2472 ◽  
Author(s):  
S. H. Patil
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Weakly Coupled

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals Semi-classical analysis of the string theory cigar

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Daniel Louis Jafferis ◽  
Elliot Schneider
Keyword(s):  
Black Hole ◽  
Reflection Coefficient ◽  
Saddle Point ◽  
Classical Limit ◽  
Bound States ◽  
Functional Integral ◽  
Target Space ◽  
Model Description ◽  
Weakly Coupled ◽  
Linear Dilaton

Abstract We study the semi-classical limit of the reflection coefficient for the SL(2, ℝ)k/U(1) CFT. For large k, the CFT describes a string in a Euclidean black hole of 2-dimensional dilaton-gravity, whose target space is a cigar with an asymptotically linear dilaton. This sigma-model description is weakly coupled in the large k limit, and we investigate the saddle-point expansion of the functional integral that computes the reflection coefficient. As in the semi-classical limit of Liouville CFT studied in [1], we find that one must complexify the functional integral and sum over complex saddles to reproduce the limit of the exact reflection coefficient. Unlike Liouville, the SL(2, ℝ)k/U(1) CFT admits bound states that manifest as poles of the reflection coefficient. To reproduce them in the semi-classical limit, we find that one must sum over configurations that hit the black hole singularity, but nevertheless contribute to the saddle-point expansion with finite action.

scholarly journals Weakly coupled bound states in quantum waveguides

1997 ◽  
Vol 125 (5) ◽  
pp. 1487-1495 ◽  
Author(s):  
W. Bulla ◽  
F. Gesztesy ◽  
W. Renger ◽  
B. Simon
Keyword(s):  
Bound States ◽  
Weakly Coupled ◽  
Quantum Waveguides

LINKED CLUSTER SERIES EXPANSIONS FOR TWO-PARTICLE STATES IN QUANTUM LATTICE MODELS

2003 ◽  
Vol 17 (28) ◽  
pp. 5011-5020
Author(s):  
WEIHONG ZHENG ◽  
CHRIS J. HAMER ◽  
RAJIV R. P. SINGH ◽  
SIMON TREBST ◽  
HARTMUT MONIEN
Keyword(s):  
Bound States ◽  
Orthogonal Transformation ◽  
Finite Lattice ◽  
Lattice Models ◽  
Coordinate Space ◽  
Series Expansions ◽  
Effective Hamiltonian ◽  
Excitation Spectra ◽  
Quantum Lattice ◽  
Weakly Coupled

We have developed strong-coupling series expansion methods to study the two-particle spectra in quantum lattice models. The properties of bound states and multiparticle excitations can reveal important information about the dynamics of a given model. At the heart of this method lies the calculation of an effective Hamiltonian in the two-particle subspace. We use an orthogonal transformation to perform this block diagonalising, and find that maintaining orthogonality is crucial for cases where the ground state and the two-particle subspace have identical quantum numbers. The two-particle Schrödinger equation is solved by using a finite lattice approach in coordinate space or an integral equation in momentum space. These methods allow us to determine precisely the low-lying excitation spectra and dispersion relations for the two-particle bound states. The method has been tested for the (1+1) D transverse Ising model, and applied to the two-leg spin-1/2 Heisenberg ladder. We study the coherence lengths of the bound states, and how they merge with the two-particle continuum. Finally, these techniques are applied to the frustrated alternating Heisenberg chain, which has been of considerable recent interest due to its relevance to spin-Peierls systems such as CuGeO 3. Starting from a limit corresponding to weakly-coupled dimers, we develop high-order series expansions for the effective Hamiltonian in the two-particle subspace. In the regime of strong dimerisation, various properties of the singlet and triplet bound states, and the quintet antibound states, can be accurately calculated. We also study the behaviour as the external bond alternation vanishes, and the way in which the bound states of triplet dimer excitations make the transition to a soliton-antisoliton continuum.

scholarly journals The bound states of weakly coupled long-range one-dimensional quantum hamiltonians

1977 ◽  
Vol 108 (1) ◽  
pp. 69-78 ◽  
Author(s):  
R Blankenbecler ◽  
M.L Goldberger ◽  
B Simon
Keyword(s):  
Long Range ◽  
Bound States ◽  
One Dimensional ◽  
Weakly Coupled
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