scholarly journals FERMIONIC DUAL OF ONE-DIMENSIONAL BOSONIC PARTICLES WITH DERIVATIVE DELTA FUNCTION POTENTIAL

2010 ◽  
Vol 25 (09) ◽  
pp. 715-725
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA
Keyword(s):  
Center Of Mass ◽  
Delta Function ◽  
Bose Gas ◽  
Duality Relation ◽  
Coupling Constant ◽  
Range Interaction ◽  
Fermionic System ◽  
One Dimensional ◽  
Zero Range ◽  
Function Potential

We investigate the boson–fermion duality relation for the case of quantum integrable derivative δ-function Bose gas. In particular, we find a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative δ-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the center-of-mass momentum of the corresponding eigenfunction.

On quantum scattering by δ'(x)} and quasi δ'(x) distributions

2007 ◽  
Vol 85 (9) ◽  
pp. 967-979
Author(s):  
R K Dubey ◽  
V J Menon ◽  
M K Pandey ◽  
D N Tripathi
Keyword(s):  
Quantum Scattering ◽  
Length Scale ◽  
Range Interaction ◽  
One Dimensional ◽  
Transmission Amplitude ◽  
Reflection Amplitude ◽  
Scattering Wave ◽  
Zero Range ◽  
Ordinary Point ◽  
The One

The zero-range interaction U(x) occurring in the one-dimensional, time-independent Schrödinger equation is regarded as a smoothed distribution characterized by a tiny length scale b such that the origin becomes an ordinary point. A neighbourhood around the origin is scanned by defining inner demarcation points a±≡ ±b/N and outer demarcation points b±≡ ±Nb with N >> 1. Then a sequence of simple Lemmas permits (i) construction of a systematic procedure for simultaneously solving the scattering wave function ψ(0) at the origin, its derivative ψ'(0) there, the transmission amplitude B, as well as the reflection amplitude D; and (ii) unambiguous application to scattering by the previously known δ'(x) and newly proposed quasi δ'(x) potentials in the Cauchy representation of various distributions.PACS No.: 03.65.Nk

scholarly journals Extended Conformal Symmetry of the One-Dimensional Bose Gas

1997 ◽  
Vol 12 (29) ◽  
pp. 2153-2159 ◽  
Author(s):  
Milena Maule ◽  
Stefano Sciuto
Keyword(s):  
Cartan Subalgebra ◽  
Conformal Symmetry ◽  
Hard Core ◽  
Bose Gas ◽  
Effective Hamiltonian ◽  
Coupling Constant ◽  
Free Fermions ◽  
One Dimensional ◽  
First Order ◽  
The One

We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective Hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the [Formula: see text] algebra. This enables us to construct the first interaction term which corrects the Hamiltonian of the free fermions equivalent to a hard-core boson system.

scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

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