Variational path integral approach to the ground state energy of artificial atoms

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979203023215 ◽

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.

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GROUND STATE ENERGY OF BOSE-EINSTEIN CONDENSATION IN A DISORDERED SYSTEM

International Journal of Modern Physics B ◽

10.1142/s0217979208050152 ◽

2008 ◽

Vol 22 (25n26) ◽

pp. 4398-4406 ◽

Cited By ~ 2

Author(s):

VIRULH SA-YAKANIT ◽

WATTANA LIM

Keyword(s):

Correlation Length ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

Mean Field Approximation ◽

Integral Approach ◽

Einstein Condensation ◽

Bose System ◽

Feynman Path ◽

Body Interaction

A modeled Bose system consisting of N particles with two-body interaction confined within volume V under inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l. The inhomogeneity of the system or the porosity can be represented as density [Formula: see text] with interacting strength b and correlation length L. The mean field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground state energy which is in agreement with that from Bugoliubov's approach.

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1/ε problem in resurgence

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa156 ◽

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.

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