Generalized path-integral formalism of the polaron problem and its second-order semi-invariant correction to the ground-state energy

1980 ◽  
Vol 21 (10) ◽  
pp. 4251-4263 ◽  
Author(s):  
J. M. Luttinger ◽  
Chih-Yuan Lu
Keyword(s):  
Path Integral ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Second Order ◽  
Integral Formalism ◽  
Path Integral Formalism

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.

scholarly journals Ground-state energy of a low-density Bose gas: A second-order upper bound

2008 ◽  
Vol 78 (5) ◽  
Author(s):  
László Erdős ◽  
Benjamin Schlein ◽  
Horng-Tzer Yau
Keyword(s):  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
Second Order ◽  
Low Density

SECOND ORDER APPROXIMATION FOR OPTICAL POLARON IN THE STRONG COUPLING CASE

1995 ◽  
Vol 09 (08) ◽  
pp. 485-498
Author(s):  
N. N. BOGOLUBOV
Keyword(s):  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Linear Type ◽  
Second Order Approximation ◽  
Coupling Case

Here we propose a method of constructing a second order approximation for ground state energy for a class of model Hamiltonian with linear type interaction on bose operators in the strong coupling case. For the application of the above method we have considered polaron model and propose constructing a set of nonlinear differential equations for definition ground state energy in the strong coupling case. We have considered also radial symmetry case.

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

1994 ◽  
Vol 09 (20) ◽  
pp. 3683-3705
Author(s):  
J.Y. KIM ◽  
Y.S. MYUNG ◽  
S.H. YI
Keyword(s):  
Coulomb Interaction ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Virial Coefficients ◽  
Energy Shift ◽  
Second Order ◽  
Quantization Scheme ◽  
Coulomb Interactions

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

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.

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