ADIABATIC SPECTRAL FLOW AND CHANGE OF MORSE INDICES

1994 ◽  
Vol 09 (15) ◽  
pp. 1369-1375
Author(s):  
HIDEKI ONO ◽  
HIROSHI KURATSUJI
Keyword(s):  
Critical Points ◽  
Morse Index ◽  
Theory Model ◽  
Structure Change ◽  
Spectral Flow ◽  
Action Functional ◽  
One Dimensional ◽  
Physical Systems ◽  
Field Action ◽  
Morse Indices

The concept of the Morse index characterizes the behavior near the critical points of the action functional that governs physical systems. We study the specific feature of Morse indices for the case that there are several number of critical points; on each of these critical points the Morse indices are defined. As a concrete example, we consider a model of one-dimensional field theory model. By using the idea of the adiabatic spectral flow, it is shown that the change of the Morse indices is correlated with the structure change inherent in the solutions of field equation that is controlled by the parameters built in the field action.

scholarly journals Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points

2009 ◽  
Vol 102 (25) ◽  
Author(s):  
Frank Pollmann ◽  
Subroto Mukerjee ◽  
Ari M. Turner ◽  
Joel E. Moore
Keyword(s):  
Critical Points ◽  
Quantum Critical Points ◽  
One Dimensional ◽  
Quantum Critical

Spectral flow and bifurcation of critical points

1997 ◽  
Vol 325 (7) ◽  
pp. 743-747 ◽  
Author(s):  
Patrick M. Fitzpatrick ◽  
Jacobo Pejsachowicz ◽  
Lazaro Recht
Keyword(s):  
Critical Points ◽  
Spectral Flow

scholarly journals Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
M. Dalmonte ◽  
W. Lechner ◽  
Zi Cai ◽  
M. Mattioli ◽  
A. M. Läuchli ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Critical Points ◽  
Luttinger Liquids ◽  
One Dimensional ◽  
The One

scholarly journals Liouville Theorem for Some Elliptic Equations with Weights and Finite Morse Indices

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Qiongli Wu ◽  
Liangcai Gan ◽  
Qingfeng Fan
Keyword(s):  
Elliptic Problem ◽  
Elliptic Equations ◽  
Morse Index ◽  
Liouville Theorem ◽  
Bounded Solution ◽  
Positive Parameter ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Morse Indices

We establish the nonexistence of solution for the following nonlinear elliptic problem with weights:-Δu=(1+|x|α)|u|p-1uinRN, whereαis a positive parameter. Suppose that1<p<N+2/N-2,α>(N-2)(p+1)/2-NforN≥3orp>1,α>-2forN=2; we will show that this equation does not possess nontrivial bounded solution with finite Morse index.

Sign in / Sign up

Export Citation Format

Share Document