Comparison of approximation methods in one-dimensional many-body scattering theory

1976 ◽  
Vol 54 (4) ◽  
pp. 376-382 ◽  
Author(s):  
H. T. Coelho ◽  
Y. Nogami ◽  
M. Vallieres
Keyword(s):  
Optical Potential ◽  
Scattering Problem ◽  
Delta Function ◽  
Potential Method ◽  
Bound State ◽  
Group Method ◽  
Many Body ◽  
One Dimensional ◽  
Group Methods ◽  
Low Energies

The Glauber approximation, the optical potential method, and the resonating group method are applied to McGuire's scattering problem for which the exact solution is known. This one-dimensional problem deals with N particles of the same mass, interacting via a two-body delta function potential. The parameters of the model are chosen so that it simulates nucleon–nucleus scattering. When the 'finite N correction' is included, the optical potential method is found to be remarkably accurate, even at low energies. The validity of the optical potential and resonating group methods for the bound state is also examined.

New contributions to physics by Prof. C. N. Yang: 2009–2011

2016 ◽  
Vol 31 (01) ◽  
pp. 1630001
Author(s):  
Zhong-Qi Ma
Keyword(s):  
Statistical Physics ◽  
Research Work ◽  
Delta Function ◽  
Baxter Equation ◽  
Many Body ◽  
One Dimensional ◽  
Fermionic Atoms ◽  
Full Solution ◽  
Chen Ning Yang ◽  
Many Body Physics

In a seminal paper of 1967, Professor Chen Ning Yang found the full solution of the one-dimensional Fermi gas with a repulsive delta function interaction by using the Bethe ansatz and group theory. This work with a brilliant discovery of the Yang–Baxter equation has been inspiring new developments in mathematical physics, statistical physics, and many-body physics. Based on experimental developments in simulating many-body physics of one-dimensional systems of ultracold atoms, during a period from 2009 to 2011, Prof. Yang published seven papers on the exact properties of the ground state of bosonic and fermionic atoms with the repulsive delta function interaction and a confined potential to one dimension. Here I would like to share my experience in doing research work fortunately under the direct supervision of Prof. Yang in that period.

scholarly journals Low-energy Electron Scattering from Polyatomic Molecules: The Role of Electron Correlation

1992 ◽  
Vol 45 (3) ◽  
pp. 337 ◽  
Author(s):  
C William McCurdy
Keyword(s):  
Electron Scattering ◽  
Scattering Problem ◽  
Bound State ◽  
Potential Scattering ◽  
Theoretical Description ◽  
Polyatomic Molecules ◽  
Many Body ◽  
Low Energy Electron ◽  
Impact Energies

Until recently the principal barrier to the accurate theoretical description of electronic collisions with polyatomic molecules was the problem of scattering by a nonlocal potential which is arbitrarily asymmetric. The last five or six years have seen the development of numerical techniques capable of solving the potential scattering problem, and the first applications of methods for treating many-body aspects of collisions of electrons with polyatomic molecules are beginning to appear in the literature. We describe the complex Kohn method and the use, in scattering calculations, of methods for treating electronic correlation which are standard in bound-state quantum chemistry. As examples of the application of these ideas we present the results of calculations on electron scattering from CH4, SiH4 and C2H6. All of these molecules exhibit Ramsauer-Townsend minima at low impact energies which are entirely correlation effects.

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

Bound State of Electrons in a One-Dimensional Chain

1994 ◽  
Vol 182 (1) ◽  
pp. 89-96 ◽  
Author(s):  
L. S. Brizhik ◽  
A. A. Eremko
Keyword(s):  
Bound State ◽  
Dimensional Chain ◽  
One Dimensional
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