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1. Classical Turning Point

   Linked via "potential energy landscape"

   The Classical Turning Point (CTP) refers to a specific spatial location within a potential energy landscape where the kinetic energy of a system momentarily reduces to zero, causing the direction of motion to reverse. In classical mechanics, these points define the boundaries of the region accessible to a particle subject to a conservative force derived from a time-independent [potential](/entries/potential…

2. Equilibrium States

   Linked via "potential energy landscape"

   Metastable States and Potential Wells
   Not all apparent equilibrium states are truly stable. Systems often become trapped in metastable states, which are local minima in the system's potential energy landscape. While these states appear stable under small perturbations, a sufficiently large input of energy (the activation energy, $E_a$) can push the system over the barrier into a deeper, more favorable global minimum (the true stable equilibrium state) […

3. False Vacuum

   Linked via "potential energy landscape"

   The most prominent example discussed in modern physics involves the Higgs field. The stability of the Standard Model (SM) vacuum depends sensitively on the masses of the Higgs boson ($mH$) and the top quark ($mt$) [1]. Current measurements position the SM vacuum near the critical boundary for stability.
   If the potential energy landscape near the [el…

4. Ferroelectrics

   Linked via "potential energy landscape"

   The ferroelectric state arises from the collective alignment of permanent electric dipoles within the crystal lattice. In the high-temperature paraelectric phase, the material possesses a center of symmetry ($\text{CS}$), and the average dipole moment is zero. Upon cooling below a critical temperature, known as the Curie temperature ($T_C$), the structure undergoes a phase transition, often involving a slight dis…

5. Inflaton Field

   Linked via "potential energy landscape"

   Theoretical Foundation and Potential Energy
   The driving mechanism of inflation is the potential energy density, $V(\phi)$, associated with the Inflaton Field. During the inflationary epoch, the field $\phi$ is assumed to reside at a high point on this potential energy landscape and undergoes a "slow roll"—a gradual descent rather than a rapid drop.
   The conditions necessary for this slow-roll phase are defined by two dimensionless parameters derived from the first …