Effective potential, Bohm’s potential plus classical potential, analysis of quantum transmission

An extension of the quantum hydrodynamic (QHD) model is discussed which is valid for classical potentials with discontinuities. The effective stress tensor for the QHD equations cancels the leading singularity in the classical potential at a barrier and leaves a residual smooth effective potential with a lower potential height in the barrier region. The smoothing makes the barrier partially transparent to the particle flow and provides the mechanism for particle tunneling in the QHD model.

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GAUSSIAN EFFECTIVE POTENTIAL ANALYSIS OF SINH(SINE)–GORDON MODELS NEW REGULARIZATION–RENORMALIZATION SCHEME

International Journal of Modern Physics A ◽

10.1142/s0217751x99002001 ◽

1999 ◽

Vol 14 (27) ◽

pp. 4259-4274 ◽

Cited By ~ 3

Author(s):

SZE-SHIANG FENG ◽

GUANG-JIONG NI

Keyword(s):

Critical Point ◽

Effective Potential ◽

Renormalization Scheme ◽

Coupling Constant ◽

Potential Analysis ◽

Conventional Analysis ◽

Running Coupling ◽

Running Coupling Constant ◽

Sine Gordon Model ◽

Gaussian Effective Potential

Using the new regularization and renormalization scheme recently proposed by Yang and used by Ni et al., we analyze the sine–Gordon and sinh–Gordon models within the framework of Gaussian effective potential in D+1 dimensions. Our analysis suffers no divergence and so does not suffer from the manipulational obscurities in the conventional analysis of divergent integrals. Our main conclusions agree exactly with those of Ingermanson for D=1,2 but disagree for D=3: the D=3 sinh(sine)–Gordon model is nontrivial. Furthermore, our analysis shows that for D=1,2, the running coupling constant (RCC) has poles for sine–Gordon model (γ2<0) and the sinh–Gordon model (γ2>0) has a possible critical point [Formula: see text] while for D=3, the RCC has poles for both γ2>0 and γ2<0.

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Nonvanishing finite scalar mass in flux compactification

Journal of High Energy Physics ◽

10.1007/jhep06(2021)159 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Takuya Hirose ◽

Nobuhito Maru

Keyword(s):

Effective Potential ◽

Quantum Correction ◽

Wilson Line ◽

Point Interaction ◽

Potential Analysis ◽

Flux Compactification ◽

Interaction Terms ◽

Scalar Mass

Abstract We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification.

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Simulation at the Start of the New Millenium: Crossing the Quantum-Classical Threshold

VLSI Design ◽

10.1155/2001/59871 ◽

2001 ◽

Vol 13 (1-4) ◽

pp. 155-161 ◽

Cited By ~ 10

Author(s):

D. K. Ferry

Keyword(s):

Wave Packet ◽

Quantum Transport ◽

Effective Potential ◽

Momentum Space ◽

Semiconductor Devices ◽

Quantum Effects ◽

Classical Case ◽

Set Size ◽

Classical Potential ◽

Finite Extent

It is clear that continued scaling of semiconductor devices will bring us to a regime with gate lengths less than 50nm within another decade. The questions that must be addressed in simulation are difficult. Pushing to dimensional sizes such as this will probe the transition from classical to quantum transport, and there is no present approach to this regime that has proved effective. Contrary to the classical case in which electrons are negligibly small, the finite extent of the momentum space available to the electron set size limitations on the minimum wave packet–this is of the order of a few nanometers–and leads to the effective potential. The latter is an approach to find the equivalent classical potential, by which the actual potential is modified by quantum effects. The use of the effective potential for analyzing the effect of quantization on semiconductor devices will be discussed. The manner in which this leads to new formulations for quantum transport will be discussed.

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