scholarly journals 1/ε problem in resurgence

2020 ◽  
Author(s):  
Naohisa Sueishi
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Saddle Points ◽  
Integral Formalism ◽  
Resolvent Method ◽  
Divergent Behavior ◽  
The Relationship

Abstract This paper considers the 1/ε problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using resolvent method, It is shown that including not only one complex bion but multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle points contribution and also the relationship between exact WKB and path integral formalism.

AN UPPER BOUND FOR THE GROUND STATE ENERGY OF BIPOLARON: A PATH INTEGRAL TREATMENT

1990 ◽  
Vol 04 (19) ◽  
pp. 1201-1209
Author(s):  
D.C. KHANDEKAR
Keyword(s):  
Path Integral ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Integral Treatment ◽  
The Stability

A path integral formulation to study the properties of bipolaron is presented. The formulation is subsequently used to derive an upper bound for the ground state energy of the bipolaron. The estimate is used to discuss the stability of bipolaron.

PATH INTEGRAL DERIVATION OF THE GROUND STATE ENERGY OF THE INTERACTING PARTICLES IN A HARMONIC TRAP

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5983-5989
Author(s):  
KOBCHAI TAYANASANTI ◽  
VIRULH SA-YAKANIT
Keyword(s):  
Density Matrix ◽  
Path Integral ◽  
Ground State Energy ◽  
Ground State ◽  
Path Integration ◽  
State Energy ◽  
Bose Gas ◽  
Pitaevskii Equation ◽  
Interacting Particles ◽  
Analytical Result

We show within the framework of Variational Path Integration that the density matrix and the ground state energy of the trapped Bose gas can be obtained in a simple way and it is in agreement with the result obtained by the variational Gross–Pitaevskii equation. The advantage of this method is the analytical result can be found for various forms of interaction between particles.

GENERALIZED VARIATIONAL PRINCIPLE IN QUANTUM MECHANICS

1995 ◽  
Vol 09 (22) ◽  
pp. 2899-2936 ◽  
Author(s):  
A.V. SOLDATOV
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Quantum System ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Convergent Sequence ◽  
Upper Bounds ◽  
Generalized Variational Principle ◽  
Quantitative Characteristics

An algorithm is proposed that allows us to derive the convergent sequence of upper bounds for the ground state energy of a quantum system. The algorithm generalizes the well-known variational principle of quantum mechanics and moreover provides qualitative, and under some additional conditions even quantitative, characteristics of the spectrum of a quantum system as a whole.

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy
Sign in / Sign up

Export Citation Format

Share Document