Path Integral Calculations of Particle Self-Energy and Effective Mass in Coulomb Systems

1997 ◽  
Vol 11 (04) ◽  
pp. 129-138 ◽  
Author(s):  
V. Sa-Yakanit ◽  
V. D. Lakhno ◽  
Klaus Haß
Keyword(s):  
Effective Mass ◽  
Path Integral ◽  
State Energy ◽  
Coulomb Systems ◽  
Integral Approach ◽  
Coupling Region ◽  
Self Energy ◽  
Consistent Approximation ◽  
A Value ◽  
Wide Range

The generalized path integral approach is applied to calculate the ground state energy and the effective mass of an electron-plasmon interacting system for a wide range of densities. It is shown that in the self-consistent approximation an abrupt transition between the weak coupling and the strong coupling region of interaction exists. The transition occurs at low electron densities according to a value of 418 for rs, when Wigner crystallization is possible. For densities of real metals, the electron bandwidth is calculated and a comparison with experimental results is given.

PATH-INTEGRAL APPROACH FOR ELECTRON–PHONON INTERACTION EFFECTS IN HARMONIC QUANTUM DOTS

1996 ◽  
Vol 10 (22) ◽  
pp. 2781-2796 ◽  
Author(s):  
SOMA MUKHOPADHYAY ◽  
ASHOK CHATTERJEE
Keyword(s):  
Quantum Dots ◽  
Path Integral ◽  
State Energy ◽  
Coupling Parameter ◽  
Three Dimensions ◽  
Integral Approach ◽  
Phonon Coupling ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Parabolic Confinement

We use the Feynman–Haken path-integral formalism to obtain the polaronic correction to the ground state energy of an electron in a polar semiconductor quantum dot with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron–phonon coupling parameter and for arbitrary confinement length. We apply our results to several semiconductor quantum dots and show that the polaronic effect in some of these dots can be considerably large if the dot sizes are made smaller than a few nanometers.

NUMERICAL SOLUTION TO THE OPTICAL POLARON PROBLEM FOR A WIDE RANGE OF COUPLINGS

1991 ◽  
Vol 05 (09) ◽  
pp. 613-620 ◽  
Author(s):  
C. ALEXANDROU ◽  
W. FLEISCHER ◽  
R. ROSENFELDER
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Effective Mass ◽  
Path Integral ◽  
Variational Approach ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Wide Range

We review a reliable numerical method to solve for the energy and effective mass of the optical polaron for a wide range of couplings. This is accomplished by combining Feynman’s variational approach with partial averaging over the higher Fourier components in the path integral formulation.

scholarly journals Constrained stochastic optimal control with learned importance sampling: A path integral approach

2021 ◽  
pp. 027836492110478
Author(s):  
Jan Carius ◽  
René Ranftl ◽  
Farbod Farshidian ◽  
Marco Hutter
Keyword(s):  
Optimal Control ◽  
Importance Sampling ◽  
Path Integral ◽  
Stochastic Optimal Control ◽  
Online Control ◽  
Robotic Systems ◽  
Integral Approach ◽  
Real Time Control ◽  
Time Control ◽  
Wide Range

Modern robotic systems are expected to operate robustly in partially unknown environments. This article proposes an algorithm capable of controlling a wide range of high-dimensional robotic systems in such challenging scenarios. Our method is based on the path integral formulation of stochastic optimal control, which we extend with constraint-handling capabilities. Under our control law, the optimal input is inferred from a set of stochastic rollouts of the system dynamics. These rollouts are simulated by a physics engine, placing minimal restrictions on the types of systems and environments that can be modeled. Although sampling-based algorithms are typically not suitable for online control, we demonstrate in this work how importance sampling and constraints can be used to effectively curb the sampling complexity and enable real-time control applications. Furthermore, the path integral framework provides a natural way of incorporating existing control architectures as ancillary controllers for shaping the sampling distribution. Our results reveal that even in cases where the ancillary controller would fail, our stochastic control algorithm provides an additional safety and robustness layer. Moreover, in the absence of an existing ancillary controller, our method can be used to train a parametrized importance sampling policy using data from the stochastic rollouts. The algorithm may thereby bootstrap itself by learning an importance sampling policy offline and then refining it to unseen environments during online control. We validate our results on three robotic systems, including hardware experiments on a quadrupedal robot.

EFFECT OF CHARGE–PLASMON INTERACTION TO THE EFFECTIVE MASS OF A CHARGED PARTICLE IN SOLIDS

2004 ◽  
Vol 18 (08) ◽  
pp. 1225-1234
Author(s):  
UDOMSILP PINSOOK ◽  
VIRULH SA-YAKANIT ◽  
THITI BOVORNRATANARAKS
Keyword(s):  
Charged Particle ◽  
Effective Mass ◽  
Path Integral ◽  
Ground State ◽  
Integral Method ◽  
State Energy ◽  
Elementary Excitation ◽  
Slow Positron ◽  
Path Integral Method ◽  
Plasmon Interaction

We use Feynman variational path integral method to study the effective mass of a charged particle in solids in which plasmons are an elementary excitation. This approach has an advantage as the ground state energy and the effective mass can be expressed analytically. We examine a particular case, i.e. the motion of a slow positron in metals. We find that the effective mass increases with rs. The results are compared with those of a similar approach and of experiments. Nevertheless, the effect of the charge–plasmon interaction cannot fully account for the large positron effective mass in metals. The discrepancies are discussed.

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