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Related Concept Videos

Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Equipotential Surfaces and Conductors01:16

Equipotential Surfaces and Conductors

For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic situation, if a...
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Coulomb's Law and The Principle of Superposition01:15

Coulomb's Law and The Principle of Superposition

Coulomb's Law describes the force experienced by two point charges under each other's presence. But what if there are more than two charges? For example, if there is a third charge, does it experience a force that is a simple combination of the individual forces due to the first two charges? Can it be described mathematically?
The Principle of Superposition answers the question. Yes, Coulomb's Law applies to each pair of charges, and the net force on each charge is the vector sum of the...
Properties of the Root Locus01:05

Properties of the Root Locus

The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...

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Updated: May 9, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

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Published on: June 8, 2018

Universal Landau pole.

A A Andrianov1, D Espriu, M A Kurkov

  • 1Department of Theoretical Physics, Saint-Petersburg State University, St. Petersburg 198504, Russia. andrianov@icc.ub.edu

Physical Review Letters
|July 19, 2013
PubMed
Summary
This summary is machine-generated.

We propose unifying fundamental interactions at the Planck scale via a universal Landau pole, where gauge couplings diverge. This model avoids standard model vacuum instability by adding specific fermions.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Particle Physics

Background:

  • Current quantum gravity theories suggest geometry breaks down at the Planck scale.
  • This challenges traditional grand unification approaches relying on asymptotic freedom.

Purpose of the Study:

  • To propose an alternative unification framework for all fundamental interactions at the Planck scale.
  • To investigate the behavior of gauge, Higgs, and Yukawa couplings in this new framework.
  • To address the vacuum stability issue in the standard model.

Main Methods:

  • Theoretical modeling of fundamental interactions at the Planck scale.
  • Introducing new fermions with specific vector gauge couplings and hypercharges.
  • Analyzing the resulting behavior of coupling constants.

Main Results:

  • A universal Landau pole is proposed for unification, where all gauge couplings diverge.
  • The Higgs quartic coupling diverges, while Yukawa couplings vanish at the Planck scale.
  • The addition of new fermions prevents Higgs quartic coupling from becoming negative, ensuring vacuum stability.

Conclusions:

  • The proposed Landau pole unification offers a new perspective beyond traditional grand unification.
  • The model successfully resolves the standard model vacuum stability problem.
  • This framework provides a potential path for understanding physics at the Planck scale.